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2023-07-31-accounts

London Mathematical Society

Report of the Trustees for the period

1 August 2022 – 31 July 2023

FOREWORD FROM THE PRESIDENT AND EXECUTIVE SECRETARY (CEO)

From the first ever parliamentary debate on mathematics through to over 250 people in-person at our General Meeting in June, it has been a successful year for the Society. This report highlights some of the wide range of activities we have undertaken in the past year and demonstrates how the London Mathematical Society continues to advance the mathematical sciences through all our work.

This year saw Council holding its biennial strategic retreat in April. Following a focus on the long-term sustainability on the Society’s finances in the previous retreat, held in the midst of the pandemic, this was an opportunity to look afresh at the Society’s strategic objectives. The retreat resulted in the Society identifying three new strategic goals for the next five years in the areas of membership engagement, the pathways in mathematics and LMS in the global community. The goals are all underpinned by the Society’s ambitions on environmental and financial sustainability and a commitment to equity, diversity, and inclusion in the way it delivers activities and communicates with members and external stakeholders. Work will continue in the coming year to finalise the strategy and start to embed it within the Society.

It has been an important year for the wider UK aspirations of the community to develop an Academy for the Mathematical Sciences. Through the Council for Mathematical Sciences, we supported the appointment of a Chair of the proto-Academy’s Executive Committee in October 2022 to lead the work on the feasibility. Subsequently, two LMS Council members were independently appointed to lead the proto-Academy work streams on Policy and Equity, Diversity & Inclusion. We look forward to working in partnership with the developing Academy especially in the areas of policy development, government relationships, the public and the media.

Since our initial statement in March 2022 condemning the invasion of Ukraine by Russian forces, the Society has been working on several areas of activity to

respond to the devastating developments. We supported members of the mathematical community who have had to leave their homes and who are seeking refuge in the United Kingdom through two solidarity grant schemes. These schemes were possible thanks to a donation from XTX Markets. In July 2022, we suspended the publication of three mathematics journals translated from Russian which operate in partnership with Institute of Physics Publishing (IOPP) and the Russian Academy of Sciences. It was with much regret that all three partners mutually agreed to formally terminate the publishing agreement in late 2022 which was bought about by the continuation of the sanctions.

We supported a further year of mitigation funding to help various activities of the Society to review and reshape their delivery to ensure their budgets come into line with the budget reductions that were implemented in 2021–22. This ensures that the impacts of a reduced income from the Society’s publishing activities, due to the move to Open Access, is mitigated through careful management to ensure income and expenditure are broadly balanced. The continued recovery of the conference room letting and venue-hire business has seen a further return of income. Nevertheless, many of our activities would not be possible without external financial help. We are very grateful for the support from our donors both small and large.

As always, it is only possible to mention a small selection of the Society’s activities in this introduction. Please read on for a fuller description of the wide range of activities undertaken by the Society in support of the mathematical community.

Our members and staff can be immensely proud of their efforts in 2022–23, and we look forward to building upon this work over the coming years.

Ulrike Tillmann, President Simon Edwards, Executive Secretary

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CHARTER, OBJECTIVES AND PURPOSE

The London Mathematical Society has, since 1865, been the UK learned society for the dissemination and promotion of mathematical knowledge. Our mission is to advance mathematical knowledge through our members and the broader scientific community worldwide.

The Society delivers its charitable aims primarily through funding in support of mathematics. Such activities are vital for the continued health of mathematics as a discipline, which is critical to the UK economy, and which impacts on a wide range of societal activities.

Throughout 2022–23, the Society continued to deliver on the six objectives by adapting existing offerings and initiating new activities to continue our support of the mathematical sciences community. This report provides an overview of the activities and achievements against these objectives, along with an overview of our activities to support our commitment to equality, diversity and inclusion across the mathematical career journey, within this period and our plans for 2023–24.

In implementing the Society’s Royal Charter and the formal statement of its objectives, the Society’s Council has previously approved the following interpretation of the objectives to support the day-to-day delivery of the Society work.

The six strategic objectives for 2022–23 were:

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MEMBERSHIP

Objective: To work, through its members and with the mathematical and broader scientific community worldwide, to advance mathematics.

The Membership

Around 3,200 mathematicians and students of mathematics are members of the Society. Our members are at the heart of the Society as it supports mathematics and the mathematical community. Volunteers’ contributions are vital to the Society in defining its priorities, running its activities, and achieving its objectives. The Society at present has 25 committees with more than 200 volunteer committee roles and other individual roles, as well as 32 volunteer roles representing the Society on external committees. The Society’s diverse membership includes mathematicians from around the world and at a wide variety of different career stages. In 2023, the Society was delighted to elect Professor Mouhamed Moustapha Fall (President of the African Institute for Mathematical Sciences (Senegal)) and Professor Raman Parimala (Emory University, USA) as Honorary Members.

Communications and Engagement

Effective communication with members and other audiences, including the wider mathematics and STEM communities, policy makers and the general public, is key to achieving the Society’s three main aims of disseminating, promoting and advancing mathematical knowledge. It also ensures that both members and non-members are kept engaged with the Society and its work, and that the Society itself is kept abreast of the most interesting and exciting developments in mathematics and the mathematicians associated with this work.

The Society continues to work to the Communications Strategy and Operation Plan agreed in 2020–21. This year, we worked to streamline our communications content, relaunching the LMS homepage in March 2023 to make it clearer and more organised, with more space for rolling news content, thus improving accessibility for users and putting relevant and timesensitive news front and centre. We also worked to improve and modernise the overall tone of our communications content, in order to engage with the full diversity of our stakeholders and present the LMS as a forward-thinking organisation.

2023 Honorary Members Mouhamed Moustapha Fall and Raman Parimala

Engagement with Government and Media

Effective communication ensures that the Society can identify current concerns in the community and help to address them. This year, the Society continued to work closely with the Protect Pure Maths campaign to engage with government and media and influence policy and decision-making at the highest level. Following the Prime Minister’s announcement for all students to study some form of mathematics until age 18, PPM and the LMS provided media commentary, and a quote from LMS President Ulrike Tillmann was included in the government press release on I April 2023. The Society continues to engage with this topic, and in July 2023 sent a letter[1] stating the LMS position to the Government’s Maths to 18 Advisory Group. In other areas of engagement, in February 2023, an article[2] by Ulrike Tillmann was published in the Times, highlighting the urgent need to address the closure of maths departments in lower tariff universities to avoid ‘maths deserts’ in the UK — a vital step towards achieving the government’s levelling up plans.

Engagement with Higher Education

The Society has a network of LMS Representatives across UK universities, who help us to identify issues of concern and to communicate with our members. Currently, there are 66 LMS Representatives with whom the Society can engage and obtain feedback. In 2022–23, the LMS Representative Network was expanded to include a volunteer representative from Piscopia Initiative. In addition to the LMS Representatives, we have a network of Good Practice Scheme (GPS) Representatives

1bit.ly/lms-letter-mathsto18

2bit.ly/lms-times-article

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who encourage mathematics departments to embed equal opportunities for women within their working practices. There are currently 57 GPS Representatives at departments across the UK. The Society has also continued to build its network of Teaching Mathematics as a Career (TeMaC) Representatives. The TeMaC initiative supports university mathematics departments in encouraging their undergraduate and postgraduate students to consider a career teaching mathematics. There are currently 40 TeMaC Representatives based in universities around the UK (see the section Education and Engaging with the Public for more details).

Engagement with LMS Members and the Wider Mathematics Community

We use a variety of channels to promote LMS events, grants and other activities. In addition to the LMS website and e-bulletins, we post information to several mathematics and mathematics-related mailing lists, some of which are targeted to specific groups. Our monitoring has shown these to be very effective; in a recent LMS Newsletter survey, members indicated that ‘email updates’ were the preferred channel for receiving LMS news. In the past year we have been working to extend our network of contacts so enable us to communicate with non-members who may be interested in the LMS and its work. The Society’s Newsletter , available electronically and in-

print, continues to be core communication channel. A survey of LMS members was conducted in late 2022 to understand the priority that members placed on receiving a print Newsletter . After discussion at Council, it was agreed to support the continuation of a printed Newsletter for the next three years as a quarterly circulation.

The LMS has an active social media presence on the major channels including X (Twitter), LinkedIn, YouTube and Facebook to communicate our activities and news. In the past year, we have achieved an increase of over 700% in the number of Twitter impressions (the metric indicating the number of times a tweet has been seen, an important measure of exposure), with over 577,000 impressions between May and July 2023 compared with around 68,000 between August and October 2022. In the same period our engagement rate increased by 10%. We have also been working to align with national and international awareness months, such as Pride, in order to connect with our followers, foster engagement and highlight LMS activities in relevant areas. The Society continues to be active on YouTube and its account now regularly features recordings from online and hybrid meetings. More work is needed to analyse the impact of our communications, and this will be a focus in 2023–24.

2022–23 highlights

2023–24 plans

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SUPPORTING MATHEMATICS RESEARCH

Objective: to advance mathematical knowledge by enabling mathematicians to undertake research and collaboration, and by supporting them in their efforts.

The Society supports mathematical research by making grants, awarding prizes, maintaining and making available the Society’s Library, and, as well as through its academic publishing activities.

Grants

different branches of research. The format is designed to allow substantial time for interaction and research. The meetings are by invitation only and will be held in August, usually lasting for two weeks, with up to 50 participants, roughly half of whom will come from the UK.

The Society’s grants schemes (listed in Annex 5) are a core part of the Society’s work to advance mathematical knowledge. Financial support for mathematicians includes grants to:

A novel element of the LMS-Bath Mathematical Symposia is that they will be complemented by a summer school, which takes place prior to the Symposium to prepare young researchers such as PhD students, or a “research incubator” after the Symposium, where problems related to the topic of the conference are studied in groups. These events can take up to an additional week. Two LMS-Bath Mathematical Symposia, with substantial funding from the Isaac Newton Institute, took place in 2023:

The Society’s smaller-scale grants fulfil a crucial role in the UK mathematical funding landscape. These grants can offer mathematicians the opportunity to organise much-needed specialist conferences, work collaboratively through short visits, and enable the development of research partnerships, all of which significantly contribute to career development and promote UK mathematical research at its roots.

Through its core research grant scheme, the Society has continued to provide support to many mathematicians and their research. In 2022–23 the Society’s Research Grants Committee awarded a total of £328,225 via 178 grants through its core scheme. As part of the Society’s ongoing response to the pandemic, the Research Grants Committee continued its support for those who found themselves without the time to engage in research during the Covid-19 pandemic, due to illness, caring responsibilities, increased teaching or administrative loads, or other factors, with the continuation of the Research Reboot Scheme.

The LMS-Bath Mathematical Symposia are being held at the University of Bath until 2025 to continue the established and recognised series of international research meetings, which was founded at Durham University in 1974 to provide an excellent opportunity to explore an area of research in depth, to learn of new developments, and to instigate links between

The 74[th] British Mathematical Colloquium was held at the University of Bath from 3-6 April 2023. The Society contributed a grant of £15,000 towards organisation of the Colloquium, and held its Society Meeting there on 4 April, where Tim Browning (IST, Austria) gave a lecture entitled Integer points on cubic surfaces and a new heuristic .

International schemes

The Society supports international mathematical activities through its partnerships with the American University in Beirut (AUB), the African Mathematical Millennium Science Initiative (AMMSI) and the International Mathematical Union (IMU). The Society is the UK’s ‘adhering organisation’ to the IMU, through the International Affairs Committee. The Society also offers travel grants to support attendance by UKbased mathematicians at the European Congress of Mathematics (ECM) and the International Congress of Mathematicians (ICM).

Following discussions at the 2022 IMU General Assembly

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and subsequent agreement by the Society’s Ukraine Working Group in light of the international situation in Ukraine, the Society agreed to help pay Ukraine’s IMU subscription fees, with other countries including Germany and Georgia committing to help cover fees as required.

In March 2022, two weeks after the invasion of Ukraine, the Issac Newton Institute set up its Solidarity Programme jointly with Society to provide refuge to researchers in the mathematical sciences. The aim is not only to offer a safe home but also to enable refugees to continue their work and start new scientific collaborations and ultimately to return to their home countries if/when circumstances allow. To date, 18 scientists have been accepted and are hosted by 15 different UK institutions. The programme is entirely funded by XTX Markets through a donation of £600k with a further £600k pledged.

In 2022–23, the Society and the AUB ran a fourth round of the Atiyah UK-Lebanon Fellowships to provide support for either an established UK based mathematician to visit Lebanon for up to six months or for a mathematician from the Lebanon of any level to visit the UK to further their study or research for a period of up to 12 months. Two Fellowships were awarded in 2022–23 in a partnership with ICMS and AUB. Prof Georges Habib (Lebanese University) will visit the University of Durham in July–September 2024 and Prof Julia Wolf (University of Cambridge) will make two visits to the AUB in 2024.

In 2022–23, the Society continued its administrative support for the IMU’s Breakout Graduate Fellowships. Funded by the IMU through donations from prestigious mathematicians, the Fellowships offer financial support of up to US$10,000 per year to PhD students in developing countries for part or all of their PhD. Normally, three awards are made each year but in 2022–23 the IMU panel awarded five Fellowships to support PhD students in countries including India, Vietnam, South Africa and Iran.

Of the four partnerships that were awarded a 1-year extension to grants under the Mentoring African Research in Mathematics (MARM) programme in 2021– 22, two ended their grant periods in December 2022 and the remaining two were extended further until December 2023. MARM operates in collaboration with AMMSI, using LMS funding combined with funding from the International Mathematical Union Commission for Developing Countries (IMU CDC). Including the current partnerships, 25 awards have been made under the programme. It is expected that a new round of MARM partnership grants will be awarded in 2024.

Prizes

The Society awarded a number of LMS Prizes this year, as well as working in partnership with the Institute of

Mathematics and its Applications (IMA) to award the IMA-LMS David Crighton Medal. The most prestigious prize of the year, the Pólya Prize, was awarded to Professor Dame Frances Kirwan FRS, for her many outstanding and influential results in geometry and for her career-long service to the mathematical community. The Crighton Medal was awarded to Professor Alison Etheridge FRS OBE, for her exposition, education, mentoring and professional service to the mathematical community. The Society also awarded the Hirst Prize and Lectureship to Professor Erhard Scholz, for his careerlong achievements in the field of history of mathematics. The Hirst Prize and Lectureship is awarded jointly with the British Society for the History of Mathematics. The Society extends warmest congratulations to all prize winners.

Library

One of the core functions of the LMS Library and Archives is the maintenance and curation of the Society’s Library itself, which is housed at University College London. The Library Committee, with representatives from the Science Library at UCL, annually review the Society’s active international journal exchange agreements and services offered by the UCL Library to members of the Society. Due to the transition to Open Access, and with many of the exchanged titles being available in online form and accessible via the UCL library’s many institutional agreements, the library is currently evaluating which of the physical copies of the exchange titles should remain at the UCL Library to maintain the LMS Library’s commitment to provide access for the exchanged journals to its members. The Library Committee Student Placement was also restarted in 2023. A diverse group of applicants was received this year with placement students also having the opportunity to work LMS Publications tasks, giving them a glimpse into the world of academic publishing, in addition to LMS Library tasks.

In September 2022, prompted by the donation of one of the very few existing Urania Propitia copies to the Society, the LMS jointly with the IMA and the BSHM organised their 2022 Joint Meeting around the work of women astronomers.

Computer Science

The LMS/BCS-FACS (British Computer Society-Formal Aspects of Computing Science) Evening Seminar, held in collaboration with the FACS Specialist Group, was held on 17 November 2022 via Zoom. The speaker was Professor Sam Staton (Oxford). The talk was filmed and later posted to the Society’s YouTube channel. The Computer Science Committee awarded two Scheme 7 grants to facilitate collaborations in research at the interface of mathematics and computer science, to a total of £1,495.

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2022–23 highlights

2023–24 plans

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REPRESENTING AND PROMOTING MATHEMATICS

Objective: to promote widely mathematical sciences research and its broad benefits to decision makers, policy advisers, funders, and users of mathematics.

Through its external and public relations. the Society aims to ensure that the centrality of mathematics to so many aspects of society is represented to Government, other national policymakers and influential organisations and individuals in order to inform debate and improve decision-making. The Society undertakes significant collaborative work advocating for mathematics both individually and through the Council for the Mathematical Sciences (CMS).

Public affairs

The Society continued to partner with XTX Markets, who generously fund the campaign to Protect Pure Maths. Working closely with Connect Public Affairs, the campaign focused on the following: to ensure that maths funding properly reflects the value of maths to society, to ensure that maths is represented and understood in the UK’s parliaments, to strengthen the voice of industry in maths policymaking, and to stop any further cuts to pure maths in universities. Over the last year the campaign has had several notable successes including securing the first ever parliamentary debate dedicated to mathematics in November 2022 and the LMS President being quoted in the Science and Technology Select Committee’s report on diversity and inclusion in STEM in March 2023.

The LMS Research Policy Committee has continued to seek robust evidence to inform its policy contributions. With the Committee for Women and Diversity in Mathematics, the Committee received updated benchmarking data showing gender distribution in UK mathematics departments. This was published on the LMS website. The Committee continues to cultivate its relationship with the Engineering and Physical Sciences Research Council (EPSRC), working closely with EPSRC representatives to keep informed of the latest developments relating to mathematics research funding and to advocate on behalf of the community.

For the tenth year the mathematical sciences, through the CMS, were represented in the prestigious STEM for Britain poster competition, which brings together

young researchers across all STEM disciplines and Members of Parliament. On behalf of the CMS, the LMS President presented medals for mathematics. The event was held at the House of Commons.

Within the mathematics research community, the LMS President has represented the Society widely at various events, ensuring national and international recognition for the Society and for UK mathematics as a whole, and ensuring the Society’s and the UK’s input into international discussions. Amongst the many events which she has attended the President has represented the Society at CMS Board meetings, the British Mathematical Colloquium, the presentation of the Bachelier Prize in Paris and the Abel Prize award ceremony at the University Aula, Oslo. The President also attended the joint LMS–IMA Black Heroes of Mathematics event (online) and the LMS–IMA–BHMS Women in Astronomy event.

Council for the Mathematical Sciences

The Society is a founding member of the CMS, which aims, through its member bodies, to draw together the mathematical community to speak with one voice on national issues of mutual concern. The CMS provides a forum for the consideration of matters of joint interest; it responds and makes representations to Government and others.

The primary focus for the CMS in 2022–23 has been supporting the establishment of of the proto-Academy Executive Committee. The CMS now meets quarterly with the Chair to receive updates on progress. In addition to supporting the work on the Academy, the CMS has commissioned interim reports on the impact of the additional £124 million spent on mathematical sciences over five years (announced by government in

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Gustavo Rodrigues-Ferreira and Prachi Sahjwani at Voice of the Future

2020). The CMS also commissioned a report into the graduate outcomes for students who study mathematics at university. This report was jointly commissioned with the Heads of Departments of Mathematical Science (HoDoMS).

The CMS was represented by two early career researchers, Prachi Sahjwani (University of Cardiff) and Gustavo Rodrigues-Ferreira (Open University), at Voice of the Future in March 2023. Voice of the Future offers young scientists and engineers the chance to put their burning science policy questions to key political figures.

The CMS was represented at Parliamentary Links Day in June 2023 by Professor David Leslie, Lancaster University, who spoke about his area of expertise: Artificial Intelligence (AI). The theme for this year was science and economic development. More details on the panels and discussions are available at bit.ly/pld2023.

LMS President Ulrike Tillmann at at STEM for Britain 2023

Collaborative working

The Society works actively and collaboratively through its membership of, and funding for, a number of mathematics and science organisations. This ensures the interests of mathematics are represented in national policy and public debates, and the Society is kept informed of external policy issues. The Society is a member of the UK Parliamentary and Scientific Committee, the British Science Association, the Joint Mathematical Council, the Campaign for Science and Engineering (CaSE) and the Foundation for Science and Technology. The Society also works in association with the Heads of Departments of Mathematical Sciences (HoDoMS) and is a member of the Parliamentary Affairs Committee (run by the Royal Society of Biology, on behalf of other STEM learned bodies). The Society maintains representation within a number of other organisations, including the Programme and Scientific Committees of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute (INI). This year the Society provided funding for the Royal Society ACME Mathematics Futures Programme.

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2022–23 highlights

2023–24 plans

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DISSEMINATING MATHEMATICS

Objective: to disseminate mathematical knowledge and make it available worldwide.

The Society has been a publisher of academic content since the first issue of the Proceedings of the London Mathematical Society in 1865 and continues to publish high quality content in order to advance mathematics and enhance the mathematical research community. Society Meetings and Lecture Series enable both members of the community and the wider public to meet, hear about and discuss current mathematical thinking and developments.

Academic Publications

Through its publications the Society aims to disseminate high-quality mathematical research and thinking worldwide. The Society’s publications serve a dual purpose, in not only disseminating mathematical research but providing the Society with an income, which it utilises entirely in furtherance of its other charitable activities. The broad and developing portfolio of highquality journals and books serve our authors through transparent, timely and professionally managed editorial and production processes, and serve our readers by providing content of wide interest and high quality. The Society seeks to maintain sustainable and ethical pricing for its publications, including the offer of free online access to LMS members and institutions in developing countries.

The Society currently publishes ten peer-reviewed journals, five of which are in collaboration with other learned societies and institutions, as well as two book series and individual book titles. During the year, the Society agreed with Cambridge University Press to publish the new open access journal Moduli on behalf of the Foundation Compositio Mathematica. Moduli will provide a unified forum for significant new results in moduli theory and related fields. The first published articles will appear in 2024.

In March 2023, the Society, IOP Publishing and the Russian Academy of Sciences jointly terminated the agreements to publish the journals Sbornik: Mathematics, Izvestiya: Mathematics, and Russian Mathematical Surveys in English translation. This decision was due to the continuation of sanctions and the closure of the IOP Publishing Moscow office, which effectively brought a permanent halt to operations, and was made in full recognition of the regrettable detrimental effects on the

dissemination of mathematics and loss of income to the Society.

The Transactions of the London Mathematical Society acquired its first Impact Factor, a measure of how well cited the journal is. At 0.8, it is comparable to the Bulletin or Mathematika . The Transactions is a fully open access journal with emphasis on exploring the interconnectedness of pure mathematics and the boundaries of its applicability.

Survey articles in the Bulletin are published open access using a legacy provided by Frank Gerrish to support publication charges where institutional funds are not available to the authors. All obituaries published in the Bulletin are freely available online.

The publications income to the Society has continued to decrease due to the widespread move from subscriptionbased sales to open access; however, the decline is slower than in past years and is beginning to show signs of levelling out. This is partly due to recent growth of the research content published by the Society, especially in the Journal and Bulletin . The Journal increased the annual number of issues from 8 to 12 in 2023, and a similar increase is planned for the Bulletin in 2024.

The Society is continuing work to ensure that there are compliant options available to authors whose funders have mandated that they publish with immediate open access. In 2022, 37% of papers in the Society’s hybrid journals were published open access, compared to 24% in 2021.

The Society continues to develop strategies, identify risks and opportunities and to engage with wider developments that may affect its publishing programme.

Society Lectures and Meetings

Meetings

Society Meetings enable both members of the mathematical community and the wider public to meet, hear about and discuss current mathematical thinking and developments. In 2022–23, the Society continued to host some of its meetings as hybrid events, with participation from attendees both remotely and inperson, while other Society Meetings were held online, with support from the host institutions and the ICMS.

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2022 – 23 Programme of Society Meetings:

Date Venue Meeting Speakers
16 September 2022 De Morgan House, London,
and Zoom		 Joint LMS-IMA-BSHM Meet-
ing: Women in Astronomy		 Meg Schwamb (Queen’s
University Belfast)
Isabelle Lémonon Waxin (Cermes3)
Isobel Falconer (University of
St Andrews)
Suzanne Aigrain (Oxford Univer-
sity)
Mathilde Jauzac (Durham
University)
4-5 October 2022 Zoom, hosted by the ICMS Black Heroes of
Mathematics		 Sophie Dabo-Niang (Université de
Lille)
Toluope Fadina (Essex)
Tosin Babasola (Bath)
John Urschel (MIT)
Aris Winger (Georgia Gwinnett
College)
Nandi Leslie (AIMS Senegal)
Ejay Nsugbe (Nsugbe Research
Labs)
Franck Kalala Mutombo (AIMS
Cameroon)
18 November 2022 Goodenough College,
London, and online		 LMS Annual General
Meeting & Naylor Lecture
2022		 Naylor Lecturer:Endre Suli
(Oxford)
Josef Malek(Charles University)
17 January 2023 Southampton South West & South Wales
Regional Meeting &
Workshop 2023.
The topic for this meet-
ing was_Geometric Group_
Theory.		 Peter Kropholler (University of
Southampton.
Karen Vogtmann (University of
Warwick).
Ian Leary (University of
Southampton)
27 March 2023 Warwick LMS Midlands Regional
Meeting
The topic for this meet-
ing was_Geometric Group_
Theory.		 Viveka Erlandsson (Bristol
University)
Michael Magee (Durham
University)
Mark Pollicott (Warwick
University).
4 April 2023 Bath Society Meeting at the BMC
2023		 Tim Browning (IST Austria)
30 June 2023 Mary Ward House, London,
and online via Zoom.		 General Meeting & Hardy
Lecture 2023		 Hardy Lecturer:Eva Miranda
(UPC-Barcelona)
Sir Roger Penrose FRS(Oxford)

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Lecture series

The Society’s funding for visiting international lecturers helps UK-based mathematicians to keep engaged in dialogue with current mathematical thinking from across the world. In 2022–23, there was a Hardy Lecture Tour by Professor Eva Miranda (EPC-Barcelona) who visited Birmingham, Cambridge, Loughborough, Oxford, the Royal Institution in London, Warwick and gave the Hardy Lecture at the General Meeting in London on 30 June. Professor Miranda will return to the UK to give lectures in Edinburgh and Glasgow in September 2023.

Eva Miranda, Hardy Lecturer 2023, and Roger Penrose

There was the LMS Invited Lecture Series 2023, which was hosted at the University of Durham in July 2023. Professor Filippo Santambrogio, (Université Lyon 1) gave the invited lectures on Optimal transport and its applications .

2022–23 highlights

2023–24 plans

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ENGAGING WITH EDUCATION AND THE PUBLIC

Objective: to support mathematical education in schools, colleges and universities, and to encourage the public and young people to appreciate and engage with mathematics.

The Society wants the wider public and young people in particular to have the opportunity to engage with and appreciate mathematics and recognise its contributions to society. It operates a number of initiatives that aim to achieve this.

Education

The Education Committee works on a number of different activities and schemes, including grants for education, public lectures and responses to consultations.

Mathematics Education Policy

The Committee continues to work closely with other groups and societies in the area of mathematics education, including the Advisory Committee on Mathematics Education (ACME), the Joint Mathematical Council of the UK (JMC) and the Heads of Departments of Mathematical Sciences (HoDoMS). In June 2023, the LMS Education Secretary attended a Future Skills roundtable discussion at the House of Lords on gender parity of students taking mathematics at A-level. In July 2023, members of the Education Committee wrote a letter to the Maths to 18 Advisory Group stating the LMS position on the Prime Minister’s proposal for all students to study some form of mathematics to age 18. In May 2023, the Education Committee held its annual Education Day as an in-person event at De Morgan House. The day included discussions and presentations around diversifying the undergraduate mathematics curriculum. The event included lively discussion. Presentations were later posted on the LMS website, and a report included in the LMS Newsletter .

Education Committee Grants

This year the Society awarded 3 grants under its ‘Mathematics Education Conference Grants’ scheme, totalling £3.3k. The scheme provides support to organisers of regular mathematics education conferences and is intended to contribute to the travel/ subsistence expenses of attendees at the event in question. The Society also awarded £1,000 under its

‘Grants for Teaching and Learning in HE’ scheme, which partially funds one-day workshops disseminating good practice in teaching undergraduate mathematics. In addition, 15 awards totalling £6k, were made under the Small Grants for Education scheme, in support of events or activities that stimulate interest and enable involvement in mathematics from primary school to undergraduate level and beyond.

Outreach and Mathematics

The Education Committee continues to run the Holgate Session Leader Scheme. The scheme provides session leaders who give talks or run workshops on a mathematical subject to groups of students or teachers. The sessions are specifically mathematical in content (rather than, say, career talks) and are intended to enrich and enhance mathematical education, looking both within and beyond the curriculum.

The Education Committee held the third Mathematics Communication Workshops in June 2023. Two daylong workshops were held, one at a beginners’ level and one at an advanced level. The workshops were limited to 20 attendees and received much positive feedback. The Society was delighted to be able to hold the Joint LMS/Gresham College Lecture once again, which was presented by Professor Holly Krieger (Cambridge).

Levelling Up: Maths

Over the past year the Society continued to work on the Levelling Up: Maths scheme, which was made possible by continuing donations from Tony Hill and Simon Godwin. The Scheme seeks to widen participation of students from under-represented backgrounds in mathematics. Working together with the IMA, the scheme now operates across 12 English universities and 6 Scottish universities. The Society works directly with eight universities: University of Coventry; University of Durham; University of East Anglia; University of Kent; and the University of Hertfordshire; University of Southampton, Queen Mary University of London; University of Warwick. The LMS has commissioned an

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evaluation framework for universities participating in the scheme. The overall Levelling Up: STEM scheme aims to nurture A-level students from underrepresented groups in Maths, Physics and Chemistry who may be planning to study a STEM subject at university. The LMS supported the introduction of Levelling Up: Maths for Computer Science, a new programme led by the British Computer Society.

Teaching Mathematics as a Career

The Education sub-committee, ‘Teaching Mathematics as a Career’ (TeMaC), continues to work towards formulating and implementing the Society’s response to the national shortage of suitably qualified

mathematics teachers in the UK. The TeMaC subcommittee continued to build its network of TeMaC representatives in universities across the UK, which now stands at 40. A TeMaC Reps survey to find out what activities departments were undertaking to promote maths teaching was undertaken in May 2023. There was a good response and the answers to some of the questions will be developed into case studies to be posted on the LMS website. This year, the subcommittee agreed an annual action plan, which will involve sending resources about teaching mathematics and other useful information to TeMaC Reps in September. A second TeMaC Reps networking day will be held in early 2024.

2022–23 highlights

2023–24 plans

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SUSTAINING THE MATHEMATICAL COMMUNITY

Objective: to promote equality of opportunity and a culture of fairness across all career stages, ensuring the long-term sustainability of the mathematical research community.

Ensuring that as much mathematical talent as possible is discovered and developed regardless of background is critical both in the interests of fairness and in the interests of academia, industry and society as a whole. This objective guides the Society’s work, particularly with respect to the transitions between the early career stages (undergraduate to postgraduate and postgraduate to postdoctoral) and with respect to women in mathematics and diversity more broadly. The Society has also recognised concerns regarding career progression, particularly for Early Career Researchers, and during the year redistributed funding from undersubscribed grant schemes to enhance the funding of its Early Career Fellowships.

Early career progression

The Society operates a number of schemes which provide support for the early career progress of mathematicians at undergraduate, postgraduate and postdoctoral level as well as for women in mathematics. A brief summary of the key Society schemes is given below, with further details contained in Annex 5.

For undergraduates, there are Undergraduate Research Bursaries (now in their ninth year), Undergraduate Summer Schools, and the new International Centre for Mathematical Sciences and London Mathematical Society (ICMS-LMS) UK Undergraduate Mathematics Colloquia.

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In 2022–23:

Women and Diversity in Mathematics

For postgraduates, there are LMS Research Schools, Cecil King Travel Scholarships to fund study or research abroad and Postgraduate Conference Grants. In 2022–23:

For post-docs and those starting new lecturer positions, there are LMS Early Career Fellowship and Celebrating New Appointment Grants. In 2022–23:

For Early Career Researchers (ECR) at both postgraduate and post-doc level, there are the ECR Travel Grants and the new online ECR Professional Development Panel discussions session. In 2022–23:

Committee for Women and Diversity in Mathematics

The Society focuses on diversity within the mathematical community through the Committee for Women and Diversity in Mathematics (CWDM). The Committee has representatives from the Institute of Mathematics and its Application (IMA), the Royal Statistical Society (RSS), the Operational Research Society (OR), the Edinburgh Mathematical Society (EMS) and European Women in Mathematics (EWM).

In 2022–23 the Committee focussed on underrepresentation in the mathematical sciences community, looking at the evidence coming from HESA data and other sources. One particular focus was on the under-representation of Black academics. Greater visbility at the professorial level will help ensure that the UK excels in attracting and supporting Black staff and students as well as those from other minority ethnic backgrounds. Another area of activity has been in addressing the underrepresentation of women and nonbinary people at PhD level; work in this area has led to the co-creation of initiatives with two PhD student led-networks: the Piscipia initiative and the PhD your Way network. We want to support the creation of an environment that encourages an open discussion of race-related issues and challenges racism. The Society, through the Committee’s leadership, is committed to celebrating, recognising and supporting a diverse mathematical community of individuals across the spectrum of age, race, gender, gender identity and expression, national or ethnic origin, religion and religious belief, marital status, parental status, body shape or size, sexual orientation, disability, socioeconomic status, employment status and other aspects of diversity. The LMS is among the organisers of the yearly conference on Black Heroes of Mathematics, which the Committee promotes and supports.

In addition to support for running Women and NonBinary People in Mathematics Days and Girls in Mathematics Days, CWDM now offers support for events focused on other aspects of Diversity in Mathematics and has become a regular contributor to the annual LGBT+ STEMinar and STEM, LGBTQ and You events (cross discipline conferences that bring together LGBTQ+ people working in STEM). CWDM has also collaborated with Numberfit in a project to amplify the profiles of mathematicians from underrepresented groups. The Society took steps to improve its collection of diversity data, for example by expanding the list of gender options available on members’ website user records, and revising its form used to capture diversity data at events and for other activities.

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Activities to Support Equality, Diversity and Inclusion in 2022–23

The Society continues to work to improve the proportion of women in mathematics, including through activities led by CWDM. For example, the Society has championed the embedding of equal opportunities and broader issues around diversity within the working practices of UK university mathematics departments.

The Society operates the LMS Good Practice Scheme, a sub-committee of CWDM, which aims to help mathematics departments to take practical actions to improve the participation of women and to share examples of good practice with other departments. The Scheme offers support in applying for an Athena SWAN award for those departments seeking recognition for their work in this area. In 2022–23, two Good Practice Scheme Workshops were held. The first, held online in January 2023, was on Promotions Practices and the second, held as a hybrid meeting in April 2023, was on Diversity and Good Practice in PhD Recruitment.

Thanks to donations from the Liber Stiftung, the Society

awards Emmy Noether Fellowships, which enhance the mathematical sciences research of holders either reestablishing their research programme after returning from a major break associated with caring responsibilities or maintaining their research programme while dealing with significant ongoing caring responsibilities. The total grant award under this scheme was £51k of which £17.5k has been paid in 2022–23, and the remaining is expected to be claimed next financial year. The awards were made predominently to women but were open to all genders.

Applicants for Research Grants across Schemes 1-9, and/ or who will run Society Meetings can request funding to help mathematicians with caring responsibilities to participate in their activities. In addition, the Society has a separate Caring Supplementary Grants scheme which provides caring support to individuals attending conferences, workshops, research schools and other events not necessarily organised by the LMS. The Society also awards Grace Chisholm Young fellowships to mathematicians who needs support when their mathematical careers are interrupted by family responsibilities, relocation of partner, or other similar circumstance.

2022–23 highlights

2023–24 plans

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MANAGING THE SOCIETY EFFECTIVELY

Objective: to manage the Society’s affairs and resources effectively and efficiently, operating where appropriate to make a not-for-profit financial return on activities, and to seek a variety of funding sources to support the Society’s work.

The Society aims to ensure that its resources are put to best possible use in achieving its mission and objectives. In all its operations it aims to ensure the longevity of the Society and plan for future circumstances, while also meeting the current needs of mathematics and its community.

In doing so the Society ensures it follows best governance practices by operating in accordance with its Charter, Statutes and By-Laws and by referring to guidance from the Charity Commission and, where appropriate, professional advisors (Annex 1).

The Society is governed by a Council of Member Trustees, elected by the membership from the mathematical community (Annex 1). Day-to-day operations are undertaken by a full-time equivalent (FTE) staff of 13.4 at the time of writing (Annex 4). Council has chosen to delegate decision making on a number of matters to 18 standing committees and has also set up a number of temporary ad-hoc committees to deal with specific items of business (Annex 2). Council also maintains and reviews annually a Risk Register with respect to all activities undertaken by the Society.

The Society runs its financial operations in accordance with best accounting practices and ensures that all its plans and activities are underpinned by a sound financial structure. The Society’s financial and governance affairs are externally audited on an annual basis.

Development Activities

In 2022–23, the Society received a number of notable donations. Dr Tony Hill, joined in 2022 by a second donor, Simon Godwin, continued with their generous donation enabling the expansion of the Levelling Up: Maths scheme, which originally went live in March 2021. The Society is now acting as the hub for eight participating universities.

The Society would once again like to thank XTX Markets for its very generous donations in funding the Protect Pure Maths campaign and also the LMS Solidarity Grants to support those academics fleeing from the war

in Ukraine.

In 2022–23, the Heilbronn Institute for Mathematical Research (HIMR) also contributed £20,000 towards the Undergraduate Research Bursaries, £15,000 towards the LMS Research Schools and, with funding from UKRI/EPSRC’s Additional Funding Programme, HIMR also offered £30,000 towards the LMS Early Career Fellowships, and £3,000 towards Women/Girls/ Diversity in Mathematics events.

In 2022–23, the Issac Newton Institute (INI) contributed funding support to the LMS-Bath Mathematical Symposia and the associated summer school. The INI supported the two summer symposia and summer schools with funding of £80,000.

The De Morgan Donation Scheme continues to thrive, with the number of members or supporters who have made a De Morgan Donation of £1,865 or more to the Society (1865 being the year of the Society’s foundation by Augustus de Morgan of University College, London) growing to 16. Professor F. OliveiraPinto became the 16th De Morgan Friend in 2022–23 through his generous donation of £2,000 to the Society in honour of his 80th Birthday.

The Society was humbled to receive donations in memoriam of one its members, the late Professor Garth Dales, from his friends and family. Professor Dales supported the Society in many ways, including serving on its Development Committee, and these gifts were a touching legacy to his memory.

The Society is most grateful to all donors for their gifts, which help ensure that the financial foundation of the organisation is as secure as possible for future generations, as well as making sure that the importance of the mathematical sciences is understood as widely as possible in industry and beyond.

The Society continued to offer the option for US taxpayers to make tax-deductible donations in US dollars or by other means to the LMS via the British Schools and Universities Foundation of which the LMS is an approved partner institution.

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In undertaking our fundraising activities, the Society does not raise funds from the public and does not work with professional fundraisers. Our fundraising activities are primarily focused on donations from our membership and corporate and charitable organisations closely aligned with mathematics. We are not currently registered with the Fundraising Regulator but work in line with best practice. We received no complaints related to our fundraising activity during the year.

Sustainability

The Society adopted a sustainability policy last year and energy efficiency and waste management improvements have been made at De Morgan House. This year, the Society began to review its charitable activities with a view to changes that could be made

to reduce their impact on the environment. This has included encouraging those in receipt of Society grants to take sustainability into consideration in their plans and working towards lower carbon travel — and travelfree alternatives such as online participation — for the Society’s events and lectureships. We also reduced the amount of printed promotional material displayed at LMS events and have instead been working to better integrate our print and online promotional channels.

More detailed information on how the Society operates is available in the sub-sections that follow:

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Governance and the Public Benefit

Governance

The Society’s governing body is its Council, members of which are also the Trustees of the charity. The Council consists of 20 members of the Society of whom 8 are Officers (including the President) and 12 are Members-at-Large, including one ‘Member-at-Large (Women and Diversity)’.

The Officers of the Society, together with the Executive Secretary, comprise the Finance and General Purposes Committee (F&GPC), which is responsible for providing advice to Council on a number of ad-hoc matters, implementing Council’s decisions and ongoing financial management.

All candidates for election to Council are provided with information on the roles and responsibilities of Trustees. Those elected attend an induction about the work of the Society and the responsibilities of a Trustee. All Council members are required to return a Declaration of Interests, a Declaration as a Fit and Proper Person, and to sign up to the Society’s AntiBribery policy. Staff in management positions also sign an annual Declaration of Interests.

Council met five times in 2022–23: in October and November 2022 and in February, April and June 2023 the Finance & General Purposes Committee met four times: in September 2022, January, March and June 2023. The Society holds an Annual General Meeting and a mid-year General Meeting each year; in 2022–23 these were held in November 2022 and June 2023 respectively.

Council has established several standing committees which advise Council and to which it has delegated some decision making. A list of all committees and committee membership is given in Annex 2.

As Trustees, Council members receive reimbursement only for expenses actually incurred in attending meetings or representing the Society. However, if a Trustee carries out work for the Society over and above normal Trustee’s duties, the Society may pay an honorarium for that service if there is a written agreement produced in advance between the Society and the Trustee outlining the work to be undertaken

and stating the exact or maximum amount. There was no paid work carried out by Trustees during the year.

The Society depends heavily on the unpaid voluntary work of many of its members and others across the mathematical community. This includes those who referee papers submitted to the Society’s publications, those who edit those publications or serve on the Society’s Editorial Advisory Boards, those who serve on the Society’s committees and those who represent the Society on other bodies, together with the members of the Council themselves, many of whom take on significant responsibilities for the Society. The Society appoints representatives on external bodies and committees; these are listed in Annex 3.

Public benefit

In shaping objectives for the year and planning activities, Council has considered the Charity Commission’s guidelines on Public Benefit, including the guidance, ‘Public benefit: running a charity’ (PB2).

Council holds that the development and extension of mathematical knowledge, expanding humanity’s ability to determine and affect the natural, artificial, and social worlds, leads overwhelmingly to public benefit, providing for improved health and wealth for nations and individuals and providing tools to understand and sustain the world in which we live. The Society’s activities directly correlate with its mission and its objectives and are focused on: supporting mathematicians in their endeavours through grants for research collaboration; sharing of knowledge through conferences and publications; improving the quality of mathematics education for people of all ages; promoting mathematics and its impact on everyday life to the general public; and encouraging policies that will benefit mathematics.

Members of the general public are able to participate without charge in all Society activities of a suitable level. Charges for events aimed at professional mathematicians, whether or not members of the Society, are kept low, a policy that is maintained when deciding on criteria for grant awards. Publications are sold at prices that keep them competitive in the academic publishing world.

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Financial Review

During the year, the value of the Society’s total assets rose from about £19.7m to £20m.

In the period 2022–23 the Society achieved a surplus of £335k (net movement in funds) despite the loss of £17k in the value of Society’s investments and an actuarial loss of £61k on defined benefit pension schemes. The surplus was mainly due to restricted donations that have not been fully spent for the Solidarity grants programme and the Protect Pure Maths Campaign (PPM) during the year. However, the fund for both is expected to be spent in the coming financial year. Continued robust financial management by staff and trustees ensured that operational income and expenditure are broadly in line.

Despite the surplus, the Society’s income from conference and venue-hire business in De Morgan House continues to be lower than pre-pandemic levels though it is showing a gradual return. This is partly mitigated by a reduction in operational costs for the conference business and anticipated cost savings arising from changes in levels of activity in some areas.

The Society has carefully monitored the performance of its investments in what has been a turbulent time for financial markets and is hopeful that its investment strategy, and its long-term investment horizon, will together mitigate the worst effects of both the pandemic and current and future changes to the publications landscape on the Society’s income. The Society continues to work on developing new sources of funding.

The LMS has relied largely on subscription income from its journals publishing programme to run its charitable objectives. However, it is facing enormous challenges as the academic journals publishing landscape becomes more complex and established revenues are threatened. Ongoing shifts in publishing business models and the transition to Open Access pose potential risks to publication income. The Society’s Publications

Committee keeps the publications landscape under review and looks to propose strategies to minimise losses in income. The Society signed a new agreement with Wiley for the publication of Bulletin, Journal, Proceedings, Transactions, the Journal of Topology and Mathematika. This contract runs from January 2022 to December 2026 and its terms are less financially advantageous to the Society than previous agreements. The Society has taken steps to manage the impact of these changes to its finances.

The Society remains in a strong position financially and has significant reserves readily available to fund future activities, although the current high-inflation situation is clearly a big concern in terms of increasing costs and the relatively rapid rise in interest rates in recent months is a stress factor that could prolong market volatility. Given the continuing volatility in the economic climate, the Society will keep under review the possibility of using resources to further the Society’s aims.

The sources of income (Figure 1, page 23) were:

Publications: 43.3% Investments: 20.1% Conference facilities and rentals: 8.5% Members’ subscriptions: 5.0% Grants and Contracts: 5.8% Advertisements in LMS Newsletter : 0.1% Donations: 17.1% Other: 0.1%

Figure 2 (page 24) shows expenditure (including governance and support costs) broken down by objective.

These were:

Advancing mathematics (e.g. membership, links with the mathematics community, library, prizes): 11.6%

Enabling mathematics (e.g. grants, and training courses): 30.0%

Disseminating mathematics (e.g. publishing, meetings and lectures): 25.9%

Promoting mathematics (e.g. decision/policy makers, education, public, media): 19.8%

Other (e.g. conference facilities costs, managing residential properties, Investment management fees): 12.7%

Budgets are set by Council on the recommendation of F&GPC, based on bids from budget holders, in line with the strategic objectives of the Society. Expenditure is

Figure 1: Income sources

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monitored quarterly by F&GPC, which is responsible for recommending any variation in the budgets set by Council.

The full audited accounts of the Society, including the accounting policies, are annexed to this report.

Risk management

Council and F&GPC annually review the Society’s Risk Register with the aim of ensuring that it identifies and quantifies potential risks to the Society and its plans and objectives, and that it lays out systems and strategies for mitigating those risks. Risks are addressed under the following headings: Governance and Management, Law and Regulation, Reputation, External and Environment, Financial, and Operational. In certain cases, Council has established Designated Funds to set against potential risks (see Reserves below); the risks or commitments that are covered by each fund are reviewed and revised annually.

The Covid-19 pandemic has had an impact on many areas of the Society’s activities and has increased the probability of a number of existing risks in the risk register materialising. Indeed, some of these risks (for example, the loss of access to De Morgan House) did materialise, although it was rightly anticipated that this was temporary. The impact of the virus has been reflected in changed risk ratings and commentaries against relevant risks. All Covid-19 adjustments to the risk register have been reviewed and removed where appropriate.

The current high inflation environment is a concern in that the Society’s costs may rise excessively. Controls are in place to minimise inflationary pressures.

The Risk Register includes the potential threat to publications income, which as noted earlier will have a significant adverse effect on the income which the Society derives from its learned journals.

Reserves

Council reviews its policy on reserves on an annual basis. The unrestricted reserves comprise a General Fund and other Designated Funds. In addition, there are several Restricted Funds. Council has several specific Designated Funds to meet the potential costs of activities, to set against risks relating to the building and to publishing (see above) and to meet grant awards made for projects or activities which span a number of years – these are given at Annex 6. The Society has a broad-ranging programme of activities in support of its strategic objectives as described in this report. While some activities are supported from

Figure 2: Expenditure

Restricted Funds, all need continuity of funding. Due to the scale and future risks to academic publishing, Council continues to operate from the basis that it is prudent to hold a General Fund from which income can be drawn to maintain and extend its charitable activities. The General Fund acts both to provide income for activities not funded from Designated or Restricted Funds, and incorporates a ‘free reserve’, providing adequate working capital for the Society to operate effectively and efficiently, and for the pursuit of the Society’s objectives as Council may from time to time determine. A full explanation of the Society’s free reserves is given in Annex 6.

The Society holds several Restricted Funds, as described in the audited accounts. These originate from various donations and bequests and are invested and accounted for on an aggregated ‘total return’ basis.

Grant Awards and Commitments

Where the Society has contractual or constructive obligations to make grant payments these amounts are accrued in the accounts in accordance with the requirements of the Statement of Recommended Practice (SORP). Resources expended on grants shown in the Statement of Financial Activity (SoFA), therefore, recognise (within the year the grant is awarded) both liabilities and provisions for grant commitments. Normally grant commitments will be claimed by the end of the financial year, although the claim period may be extended by a further year where the start or end date of the grant so requires.

The Society also awards some grants with conditions for payment (such as delivery of a specific level of service or other specific output). Such commitments are reserved in the Designated Funds, and the grants are only recognised in the SoFA when the recipient of the grant has provided evidence of the specific service or output.

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Investments

The Society decided to invest up to 30% of its relevant assets in residential property, as valued at the time of purchase, with the remainder given over to the Society’s investment managers. Investment in such residential property is directly managed by the Society. The percentage calculation excludes the value of De Morgan House. Also excluded are any investments made by the investment managers in the property area of asset classes.

1. Quoted investments

The Society believes that in investing its funds, regard must be made to environmental, social and governance (ESG) issues. In line with its general investment strategic direction, the Society believes that its investments should mirror its own desire to be sustainable, and currently about 50% of its quoted investment is allocated in a Sustainable Multi-Asset Fund tailored to optimize ESG indices (see below). Council had previously indicated that this percentage should rise to 100% by 2025.

The investment strategy for the portfolio, which is managed by Cazenove Capital (part of the Schroders group), is modelled to achieve CPI + 4% per annum nominal return over rolling 10-year periods. However, Council recognises that current levels of inflation will likely make it impossible to achieve this goal in the short to medium term.

Drawdown form the portfolio, as agreed by Council, follows the ‘Yale model’ and consists of 50% of the previous year’s drawdown together with 3.5% of 50% of the current value of the portfolio. Thus, the drawdown is determined by a formula and so may be less or greater than the dividends and interest received: it is shown in the SoFA as Investment Income. The growth in the value of the Society’s investments (capital plus income) is the sum of this drawdown and the figure shown in the SoFA for Gains on investment assets. The scale of the Society’s activities is designed to match this level of return through the annual budgeting process.

It is Society policy to review on a regular basis the performance of those professional bodies it employs. Close attention is paid to our investment policy and to the performance of Schroders, with whom we have regular meetings. Accordingly, Council has an Investment Sub-Committee, which includes up to six external financial experts, to provide professional advice on the Society’s investments and on Schroders’ performance. Council has confirmed an investment

mandate with discretionary powers with Schroders, based on a ‘total return’ basis, designed to maximise investment income while maintaining the real value of the investments.

The investment managers have discretion in both the mix and selection of investments in order to meet the growth targets for the portfolio, without exposing to undue risk the Society’s reserves, both Restricted and Unrestricted Funds, on which its future capacity to maintain its activities depends. The portfolio has exposure to a range of equity, cash, fixed-interest investments and alternative asset classes in both UK and overseas markets, accessed via two Schroders common investment funds: S U T L Cazenove Charity Multi-Asset Fund and Cazenove Sustainable Charity Multi-Asset Fund. A summary of the main categories of investments and the geographical split is provided in the notes to the financial statements in accordance with the Charities’ SORP. Both Multi-Asset funds are designed for charities seeking to maintain the real value of their capital over the medium to long term whilst generating a sustainable and reliable distribution level (from income and capital). The portfolio which aims to deliver returns similar to equity markets but with a lower level of volatility, is well diversified across asset classes. This approach is considered by the trustees to give optimum total return without exposing the Society’s investments to undue risk; it is consistent with the principles set out in the Charity Commission guidelines Investment of Charitable Funds, Basic Principles (CC14) and conforms with the Trustee Act 2000.

2. Residential property investments

As a safeguard against fluctuating performance of the stock exchange, the Society expanded its investments portfolio to include residential property and owns seven long lease residential properties (four in Central London and three in the Birmingham area), all of which are rented out. The rental derived is shown on the SOFA under ‘Investment Income’. The growth in the value of the Society’s residential property investment will be shown in the SOFA as Gains on investment assets. The primary long-term target of the Society’s residential property is to produce a yield of 4% pa and to provide an increase in capital value by at least the rate of inflation. The residential property investment is valued at the balance sheet date using the local estate agent’s guidance on the current housing market within the area where the properties are located.

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De Morgan House

Staff management

The Society currently employs a team of full and part time staff. These staff are predominantly based in De Morgan House, currently working three days a week there and two days a week from home. A list of staff in post during the period can be found in Annex 4.

The Executive Secretary is responsible for staffrelated issues with strategic overview provided by the Society’s Personnel Committee.

The remuneration of all staff within the Society is considered in detail by Personnel Committee and set against the salary scales of the University of London. Any recommendations from the Personnel Committee regarding remuneration are then formally approved by the Trustees (the governing Council). The pay ranges for key management personnel (Senior Management Team) are determined and set by Trustees following analysis of roles and performance by the Personnel Committee. The Personnel Committee will also, as appropriate, compare the Society’s pay ranges with those of similar roles in other similar organisations.

De Morgan House

The Society holds a long lease (to 2109) from Bedford Estates on De Morgan House, 57-58 Russell Square, London, WC1. It uses these premises: (a) to house its administrative headquarters; (b) to hold its meetings and conferences in the promotion of mathematics; (c) to let out offices on the upper floors to other organisations on a commercial basis; and (d) for function rooms that it lets to other organisations for their own purposes. This last category includes other

mathematical and charitable organisations, where there is both a mathematical and financial benefit; discounts are available, and some rooms are offered at either reduced rates or at no charge as part of the Society’s charitable giving.

The Conference Centre has seen a continued increase in bookings throughout 2022–23 with the return of many clients post pandemic, although overall booking levels have yet to return to those achieved pre-pandemic.

Office space remains available to rent commercially, with a new tenant moving into rooms on the third floor in late 2023. There continues to be 4 other commercial spaces let to external organisations, and a room sponsorship agreement has been agreed with the IMA.

LMS Website

The Society’s website is a key part of its data management infrastructure. Using a Drupal Content Management System, underpinned by a CiviCRM database, the website is not only a channel for communicating the Society’s activities but is also a key interface between the Society, its members and the mathematical community more broadly. It enables prospective members and grant holders to submit applications, it allows current members to manage and pay for their membership online and it allows audiences to register for Society events. Use of the website for these key business processes requires careful management and innovative design to ensure that the functionality benefits the Society and its stakeholders while protecting their data.

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Statement of Trustees’ Responsibilities

The trustees are responsible for preparing the Trustees Report and the financial statements in accordance with applicable law and United Kingdom Accounting Standards (United Kingdom Generally Accepted Accounting Practice).

The law applicable to charities in England and Wales requires the trustees to prepare financial statements for each financial year which give a true and fair view of the state of the affairs of the charity and of the incoming resources and application of resources of the charity for that period. In preparing these financial statements, the trustees are required to:

accuracy at any time the financial position of the charity and enable them to ensure that the financial statements comply with the Charities Act 2011, the Charity (Accounts and Reports) Regulations 2008 and the provisions of the Royal Charter. They are also responsible for safeguarding the assets of the charity and hence for taking reasonable steps for the prevention and detection of fraud and other irregularities.

For and on behalf of the Council of the London Mathematical Society:

The trustees are responsible for keeping proper accounting records that disclose with reasonable

Professor Ulrike Tillmann (President)

20/10/2023

Date

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ANNEX 1: COUNCIL, EXECUTIVE TEAM AND PROFESSIONAL ADVISERS

Membership of Council during the period 1 August 2022 to 31 July 2023

President: Ulrike Tillmann Vice-Presidents: Iain Gordon Cathy Hobbs Treasurer: Simon Salamon General Secretary: Robb McDonald Programme Secretary: Chris Parker Publications Secretary: Niall MacKay Education Secretary: Kevin Houston Members-at-Large: Sara Lombardo (Women and Diversity) Peter Ashwin Elaine Crooks Andrew Dancer Anne-Christine Davis (until November 2022) Jessica Enright Minhyong Kim Jason Lotay (from November 2022) Frank Neumann Rachel Newton Brita Nucinkis (until November 2022) Anne Taormina Amanda Turner Sarah Whitehouse (from November 2022)

Executive Management Team during the period 1 August 2022 to 31 July 2023

Executive Secretary (CEO): Simon Edwards (from 1 October 2022) Interim Executive Secretary (CEO): Fiona Nixon (1 August 2022 - 30 September 2022 Head of Finance and Accounting: Ephrem Abate Head of Society Business: Lindsay Walsh (until 17 November 2022) Head of Society Business: Jennifer Gunn (from 1 December 2022) Head of Conferences and Buildings: Andrew Dorward

External advisors

Auditor: Moore Kingston Smith LLP, 9 Appold Street, London, EC2A 2AP Investment Advisers: Cazenove Capital (part of the Schroders group), 12 Moorgate, London, EC2R 6DA Bankers: National Westminster Bank plc, 208 Piccadilly, London, W1J 9HE Solicitors: Bates Wells, 2-6 Cannon Street, London, EC4M 6YH

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Registered address

London Mathematical Society, De Morgan House, 57-58 Russell Square, London, WC1B 4HS https://www.lms.ac.uk

Charity registration number

252660

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ANNEX 2: COMMITTEE MEMBERSHIP (as at July 2023)

Membership of Committees as at 31 July 2023

Computer Science Committee: P. Wong (Chair), P. Ashwin, A. Beckmann, M. Cryan, O. Dardha, J. Davenport (Institute of Mathematics and its Applications (IMA)), A. Popescu (British Computer Society-Formal Aspects of Computing Science (BCS-FACS)), C. Kestner, B. Martin, S. Zivny.

Development Committee: President (Chair), Treasurer, General Secretary, Executive Secretary, Past President, President-Elect, A. Dancer. J. Rodrigo, C. Roney-Dougal.

Early Career Research Committee: C. Parker (Chair), S. Beheshti, E. Crooks, J. Grbic, T. Kempton, A. Lecuona (ECRCDWM Liaison) R. Newton (Deputy Chair), M. Ptashnyk, I. Short (Climate Working Group Rep), B. Singh, and EPSRC Observer.

Education Committee: Education Secretary (Chair), T. Crawford, J. Enright, P. Glaister, Vice-President C. Hobbs, J. Parker (Heads of Departments of Mathematical Sciences (HoDoMS)), J-A Lees, M. McCartney, T. Roper, C. Saker.

Finance and General Purposes Committee: President (Chair), Vice-Presidents, General Secretary, Treasurer, Programme Secretary, Publications Secretary, Education Secretary, Executive Secretary.

International Affairs Committee: President (Chair), Publications Secretary, P. Glaister (IMA), D. Evans, J. Fraser (Edinburgh Mathematical Society (EdMS)), R. Norman (EdMS President), M. Mathieu, B. Nucinkis, J. Parker, S. Schroll.

Investment Sub-Committee: Treasurer (Chair), all other Members of Finance and General Purposes Committee, R. Bogni, J. Dodd, A. Harrington, J. Horn-Phathanothai, G. Keniston-Cooper.

IT Resources Committee: President (Chair), Vice-President Hobbs, Executive Secretary, F. Clarke, J. Cremona, K. Gillow, I. Stewart.

Library Committee: D. Kent (Chair), LMS Archivist, Publications Secretary, I. Falconer, A. Rice, Tony Mann.

Newsletter Editorial Board: A. Vdovina (Editor-in-Chief), J. Barrow-Green, D. Chillingworth, J. Enright, J. Fraser, S. Huggett, Vice-President C. Hobbs, A. Johansen, R. Laking, T. Kempton, S. Oakes M. Whittaker, A. Wilson, General Secretary, Publications Secretary.

Nominating Committee: T. Brendle (Chair), C. Budd, N. Chamberlain, P. Maini, , B. Pelloni, M. Rees, G. Stallard. L. Ciobanu, H. Wilson, S. Whitehouse (Council Representative), S. Lombardo

Personnel Committee: Vice-President C. Hobbs (Chair), Publications Secretary, Executive Secretary, A. Belton, A. Taormina, P. Ashwin.

Prizes Committee: President (Chair), J. Bennett, T. Bridgeland, P. Cameron, A. Caraiani, J. Marklof, C. Ortner, A. Teckentrup, C. Stroppel, M. Wemyss.

Publications Committee: Publications Secretary (Chair), Vice-President C. Hobbs, Treasurer, M. Brown, E. Crooks, H. Harrington, R. Kessar, A. Lazarev, I. Leary, N. O’Connor, C. Parker, O. Randal-Williams, A. Turner.

Research Grants Committee: A. Dancer (Chair), J. Brodski, H. Bui, S. Connor, I. Kyza, A. Lazarev, F. Neumann, B. Nucinkis, N. Peyerimhoff, M. Ptashnyk, A. Turner, P. Milewski (Bath Symposia Representative).

Research Policy Committee: Vice-President I. Gordon (Chair), P. Ashwin, A. Caraiani, S. Gutierrez, J. van den Heuvel (HoDoMS), T. Liverpool, H. Krieger, D. Smith.

Society Lectures and Meetings Committee: B. Nucinkis (Chair), G. Evans, M. Kambites, J. Lotay (Council Rep on SLAM), K. Leschke, N. Petrovskaya, M. Todd, V. Styles.

Committee for Women and Diversity in Mathematics: S Lombardo (Chair), L. Bandara, A. Davis, C. Garetto, VicePresident I. Gordon, L. Hakim, H. Herrera (ORS), T. Kelly, S. Lawrence (IMA), A. Lecuona (EdMS), A. Madzvamuse, K. Severn (RSS), M. Sommacal.

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Sub-Groups, Ad-hoc Committees and LMS appointments as at 31 July 2023

Publications Nominating Group: Publications Secretary (Chair), T. Browning (Managing Editor, Proceedings of the LMS), M. Hairer, J. Maynard (Managing Editor, Journal of the LMS), A. Lazarev (Managing Editor, Bulletin of the LMS), O. Randal-Williams (Publications Committee), J. L. Rodrigo (Managing Editor, Transactions of the LMS), R. Sharp.

Education sub-Committee (Teaching Mathematics as a Career): J. White (Chair), Education Secretary, K. Golden, T. Roper, C. Saker, N. Steele (IMA).

Atiyah Fellowship Panel: Caroline Series (Chair), Minhyong Kim, Edriss Titi (Cambridge), Jihad Touma (Director, Centre for Advanced Mathematical Sciences (CAMS), American University of Beirut), Fida El Chami (Lebanese University), Bassam Shayya (American University of Beirut).

Good Practice Scheme Steering Group: A. Davis (Chair), S. Lombardo (Chair, Committee for Women and Diversity in Mathematics), N. Mazza, J. van den Heuvel (HoDoMS).

LMS-IMA Joint Working Group (LMS members): President (Chair), Vice-President I. Gordon, Executive Secretary.

LMS–IMA Zeeman Medal Committee 2022 (LMS Members): President, A-C Davis, K. Brown.

Mentoring African Research in Mathematics (MARM) Board: F. Neumann, A-S Kalaghiros, T. Liverpool, A. Madzvamuse, M. Roberts, B. Szendroi.

Undergraduate Summer School Scientific Committee: A. Hone, F. Kirwan, A. Veselov.

Council Diarist: various Council members.

Council Webmaster: General Secretary.

LMS/EMS Newsletter Correspondent: D. Chillingworth.

Election Scrutineers: C. Goldie and C. Chu.

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ANNEX 3: EXTERNAL REPRESENTATIVES (as at July 2023)

Representatives on external committees and boards as at 31 July 2023

Athena Forum: Chair, Committee for Women and Diversity in Mathematics.

British Science Association Mathematics Section: Education Secretary.

British Mathematical Colloquium Scientific Committee: M. Devisscher, S. Rees, C. Roitzheim.

Council for the Mathematical Sciences Board: President, Vice-President C. Hobbs, Vice-President I. Gordon, Executive Secretary (any 3 of).

Council for the Mathematical Sciences-Engineering and Physical Sciences Research Council (CMS-EPSRC Liaison Sub-Group: Vice-President C. Hobbs, Vice-President I. Gordon, Executive Secretary (any 2 of).

European Mathematical Society (EMS) Council: President, F. Neumann, A. Turner, A. Vdovina.

Heads of Departments of Mathematical Sciences Committee: J. Parker

International Centre for Mathematical Sciences (ICMS Board: S. Rees.

International Centre for Mathematical Sciences (ICMS Programme Committee: C. Drutu, J. Gog.

International Commission on Mathematical Instruction (ICMI UK representative: P. Glaister.

Joint Mathematical Council (JMC: Education Secretary.

Parliamentary and Scientific Committee: President, Vice-President I. Gordon, Vice-President C. Hobbs, Executive Secretary.

STEMM Disability Advisory Committee: Chair, Committee for Women and Diversity in Mathematics.

Teaching Training Scholarships Management Group: Education Secretary.

32

ANNEX 4: STAFF

Staff in post in the period 1 August 2022 to 31 July 2023

Executive Secretary’s Office

Executive Secretary (CEO): Interim Executive Secretary (CEO): PA to the Executive Secretary: Head of Finance and Accounting: Accounts Assistant: Administrative Editor, LMS Newsletter:

Simon Edwards (from October 2022) Fiona Nixon (August 2022 to September 2022) Clare Ralphs Ephrem Abate Valeriya Kolesnykova Susan Oakes

Publications

Head of Academic Publications: Publications Development Manager: Editorial Manager: Publications Assistant:

Simon Buckmaster (from August 2023) Suzanne Abbott (until May 2023) Ola Törnkvist Anna Agathopoulou

Society Business

Head of Society Business: Head of Society Business: Membership and Grants Manager: Society Governance Officer: Society Governance Officer: Society Business, Research & Communications Officer: Events Co-ordinator: Grants and Membership Administrator:

Lindsay Walsh (until November 2022) Jennifer Gunn (from December 2022) Elizabeth Fisher James Taylor (until November 2022) Lesley Campbell (from January 2023)

Katherine Wright Kieran O’Connor Lucy Covington

Conferences and Building Group

Head of Conferences and Buildings: Andrew Dorward

33

ANNEX 5: GRANT SCHEMES

General policy on grant-making

The grant schemes are funded from the Society’s resources received from its endowments, investments and publishing activities and are one of the primary mechanisms through which the Society achieves its central purpose, namely to promote and extend mathematical knowledge. The principles governing its grant-giving are:

The Society’s committees that assess applications for grants are made up of mathematicians with a wide spread of research interests. Under most schemes, proposals are judged by the committees themselves, although they may seek advice. Each committee judges each application on its merits.

Any mathematician working in the UK is eligible to apply for a grant but, for some schemes, if they are not a member of the Society, then the application must be countersigned by a member who is prepared to support the application.

34

Summary of main grants and training schemes

Conference Grants (Scheme 1)

Grants are made to the organisers of conferences to be held in the UK. Priority is given to the support of meetings where an LMS grant can be expected to make a significant contribution to the viability and success of the meeting. Support of larger meetings of high quality is not ruled out, but for such meetings an LMS grant will normally cover only a modest part of the total cost.

Visitors to the UK (Scheme 2)

The aim of the Scheme is to provide grants to mathematicians based within the UK to partially support visitors to the UK; the visitors are expected to give lectures in at least three separate institutions.

Support of Joint Research Groups (Scheme 3)

The Scheme is to provide support for groups of mathematicians, working in at least three different locations (of which at least two must be in the UK), who have a common research interest and who wish to engage in collaborative activities. The grant award covers two years and is expected that a maximum of four meetings (or an equivalent level of activity) will be held per academic year.

Research in Pairs (Scheme 4)

The Scheme is to provide small grants to UK-based mathematicians to help support short visits of intensive collaborative research with colleagues in other institutions, both in the UK and abroad.

Research Reboot (Scheme 4)

This scheme is to help restart research activity. It offers funding for the applicant to leave their usual environment to focus entirely on research for a period from two days to a week, in order to restart their research activity.

Collaborations with Developing Countries (Scheme 5)

The Scheme is to provide grants to mathematicians within the UK to support visits for collaborative research, or academic activities that will benefit the country concerned. Countries considered to be eligible for Scheme 5 funding are those contained within (but not exclusively limited to) the International Mathematical Union Commission for Developing Countries (IMU CDC) Definition for Developing Countries: https://www.mathunion.org/cdc/about-cdc/definition-developing-countries

Workshop Grants (Scheme 6)

The Society supports research workshops, which may be held anywhere in the UK and are an opportunity for a small group of active researchers to work together for a concentrated period on a specialised topic. Applications to support the development of research in an area not ready for a larger-scale application are welcomed; applications for partial support for larger events will only exceptionally be supported.

Computer Science Small Grants (Scheme 7)

The aim of the Scheme is to provide small grants to researchers based within the UK to help support visits for collaborative research at the interface of Mathematics and Computer Science.

Caring Supplementary Grants

The Society recognises that parents and carers are sometimes prevented from attending conferences and meetings and making research visits because there is no provision for the extra costs incurred in caring for dependants. It is the LMS’ view that institutions should make provision for caring costs but, while this is not largely the case, the Society is willing to make a supplementary grant as a contribution to the costs.

35

Grace Chisholm Young Fellowship

This fellowship aims to provide some support when a mathematical career is interrupted by family responsibilities, relocation of partner, or other similar circumstance, making possible some continuous mathematical activity and so enabling the fellow to be in a position to apply for posts when circumstances allow. The holder will be based in a specific Mathematics Department in a University or Research Institute in the UK; the host is expected to provide an email address, use of library and IT facilities and access to research literature. The normal duration of the fellowship is one year.

Emmy Noether Fellowships

These Fellowships are designed to enhance the mathematical sciences research, broadly construed, of holders, either re-establishing their research programme after returning from a major break associated with caring responsibilities or those requiring support to maintain their research programme while dealing with significant ongoing caring responsibilities.

Small Education Grants

These grants support such activities as popular lectures, exhibitions, masterclasses, mathematical competitions, etc., that help to encourage joint mathematical ventures between higher education institutions and schools, or the development of projects that would improve the public image of mathematics.

Mathematics Education Conference Grants

This scheme offers funding to organisers of regular mathematics education conferences and is intended to contribute to the travel/subsistence expenses of attendees of the event in question.

Grants for Teaching and Learning in HE

This scheme offers partial funding of one-day workshops disseminating good practice in teaching undergraduate mathematics.

Mentoring African Research in Mathematics (MARM)

The aim of the programme is to enable all mathematicians in Africa to pursue academic careers of the highest standard. The Society believes that enhancing and developing academic research and research institutions in Africa will help ensure that pursuing world-class mathematical careers within Africa will be both achievable and a more attractive option than moving permanently to the developed world. Over time, the strengthening of the mathematical community within Africa will benefit not only the African community but mathematics as a whole. Grants are awarded for two-year academic partnerships between European and African institutions for activities including exchange visits, lectures and workshops, conferences, PhD supervision and mentoring support.

Support for Mathematics in Africa

The Society awards grants to contribute to the travel costs of postgraduates attending conferences in Africa, organised or supported by the African Mathematics Millennium Science Initiative (AMMSI).

Atiyah UK–Lebanon Fellowships

This scheme was set up in memory of Sir Michael Atiyah (1929–2019) and operated in partnership with the Centre for Advanced Mathematical Sciences at the American University of Beirut. It provides for an established UK based mathematician to visit the Lebanon as an Atiyah Fellow for a period of between one week up to 6 months, or alternatively for a mathematician from the Lebanon of any level, in particular promising advanced level students from the AUB, to visit the UK to further their study or research for a period of up to 12 months.

Solidarity Grant Programme

This programme is designed for the purpose of giving refuge to researchers in the mathematical sciences who have had to leave their country of residence. The aim is not only to offer participants a safe home but also to enable them to continue their work and start new scientific collaborations in the UK. Participants can be hosted for up to 12 months in the UK whilst on the programme. The programme is administered by the Issac Newton Institute with support for the Society.

36

Summary of grants and training schemes supporting Young Mathematicians and Early Career Researchers

Undergraduate Research Bursaries in Mathematics

The Scheme aims to give training in research to undergraduates with research potential to encourage them to consider a career in scientific research. Grants are awarded for a six-to-eight week summer research project undertaken with the guidance of a research supervisor. The Undergraduate Research Bursaries are often supported by funding from HIMR.

Undergraduate Summer Schools

The goal of the Summer Schools is to introduce exceptional pre-final year undergraduates to research mathematics and, in particular, to make them think seriously about an academic career at this stage. The Summer Schools are a combination of short lecture courses with problem-solving sessions and colloquium style talks. Talks are given by lecturers mostly (though not exclusively) from the UK, including high-profile speakers. The Schools are for around 50 students and involve 10 lecturers. The event is hosted by a UK university for a period of 10 days in summer.

LMS Prospects in Mathematics

The Society provides support for this annual event, primarily for final year undergraduates and Masters’ Students who are considering applying for a PhD after they have completed their studies to discuss current research and potential career opportunities.

LMS Research Schools Programme

The purpose of the Research Schools, including Research Schools on Knowledge Exchange, is to provide training for young researchers in a core area of mathematics. Students and post-docs can meet a number of leading experts in the topic as well as other young researchers working in related areas. The series aims at the highest international standing of these research schools, allowing for support of both international lecturers and participants. The main criteria for funding are the topicality and the mathematical significance of the course material, the general alignment with the mission of the LMS and the likely demand for places nationally and internationally, and the standing of the proposed lecturers in the international mathematical community. The Research Schools are often supported by funding from HIMR.

Cecil King Travel Scholarship

The London Mathematical Society administers two £6,000 travel awards funded by the Cecil King Memorial Foundation for early career mathematicians, to support a period of study or research abroad, typically for a period of three months. One Scholarship will be awarded to a mathematician in any area of mathematics and one to a mathematician whose research is applied in a discipline other than mathematics.

Postgraduate Research Conferences (Scheme 8)

The aim of this Scheme is to support postgraduate research conferences, organised by and for postgraduate research students, to be held in the UK.

Early Career Researchers in Mathematics Conference (formerly Young Researchers in Mathematics Conference)

The Society provides a grant for the Early Career Researchers in Mathematics Committee to help support the Early Career Researchers in Mathematics Conference; a mathematics conference specifically targeting early career researchers.

LMS Early Career Fellowships

To support early career mathematicians in the transition between PhD and a postdoctoral position, the London Mathematical Society offers up to 8 Fellowships of between 3 and 6 months to mathematicians who have recently or will shortly receive their PhD. In 2021-22, the award was calculated at £1,300 per month plus a travel allowance. The fellowships may be held at one or more institutions but not normally at the institution where the fellow received their PhD. The Early Career Fellowships are often supported by funding from HIMR/EPSRC-UKRI.

37

Celebrating New Appointments (Scheme 9)

Grants are made to provide partial support for meetings held in the UK to celebrate the appointment of a new lecturer in mathematics at a UK institution. The aim of the grant award is to embed the new lecturer in their home institution and the local mathematical community, and to allow the new appointment to create useful and lasting relationships with the local mathematical community. It is expected that the new appointment themselves will present a lecture at the meeting.

Travel Grants for Early Career Researchers

The Travel Grant Scheme provides partial support for UK-based early career researchers to attend conferences or undertake research visits either in the UK or overseas. Grant holders are early career researchers in mathematics, based in the UK, defined as a PhD/research student or anyone who has completed their PhD in the last five years (excluding academic career breaks). The scheme is open to both members and non-members of the LMS.

Women and Non-Binary People in Mathematics Events

These events are aimed at academic mathematicians (from at least postgraduate level and up and may include undergraduates). The events are intended to help early career women and non-binary mathematicians when considering the next stages in their careers and typically have included mathematical talks combined with panel discussions, social opportunities and networking. Individuals or groups are able to express interest in organising and hosting an event.

Girls in Mathematics Events

Events are aimed at schoolgirls, up to and including A-levels or equivalent, with mathematics as a main focus. Individuals or groups are able to express interest in organising and hosting an event.

Diversity in Mathematics Events

Diversity in Mathematics Days support aspects of diversity beyond gender. The events are expected to focus on some aspect of diversity in the Mathematical Sciences. One of the events is expected to feature both the work of people in the Mathematical Sciences, whether in industry or academia, who come from that diversity group, and also offer opportunities for mathematicians from that diversity group to receive mentoring and networking opportunities.

38

ANNEX 6: GENERAL AND RESERVE FUNDS

For the purposes of financial planning the Society has chosen to define Relevant Funds to consist of Quoted Investments + Residential Properties + Cash at bank. The Society’s target returns on its investment portfolio of CPI + 4% in the long-term, in order to guarantee its value in real terms, Council considered that the present level of the Relevant Funds should reach £20m by 2025, and with the current valuation of around £19m it is well on target to achieve that. At present, Residential Properties are making a gross rent return of 4% as well as increasing in market value which is reflected in the Relevant Funds.

General Fund

This provides for the general operation of the Society including its charitable activities not funded from Designated or Restricted Funds. Within the Society’s reserves, the General Fund is deemed an expendable reserve to be used in pursuit of the Society’s objectives as Council may from time to time determine. At present the fund exists to assure the availability of resources for the Society’s grant schemes and other continuing charitable activities in future years. This manages the risk to the Society’s ability to generate income to provide for such activities and offers a contingency against threats such as open access.

The Society normally maintains £600k free reserve as cash at bank to ensure that there is enough operating capital to stabilise the Society’s finances. It provides contingency against unexpected events, as well as allowing the Society to deal with losses in income and large unbudgeted expenses. The latter includes the potential requirement by future donors that the Society is able to equally match the donated funds to be used for major specific and unexpected projects. The actual level of free reserves consists of the unrestricted net current assets less long- term liabilities shown in note 22 to the financial statements which amounted to £1,172k at 31 July 2023. During this financial year, the Society decided to invest in short term deposits to benefit from high interest rate gains. The free reserve is higher than we aim for, but due to the continued impact of pandemic and publication income shortfall, the trustees have decided to maintain higher reserves to support the transition of our income stream. However, the trustees will continue to keep this under review.

General Fund £15,650,336

Building and Development Reserve Fund

This reserve, originally built up for the Society to purchase or rent its own property was utilised in part in the purchase of a leasehold property. This reserve fund exists to maintain the property in a state of good repair as required by the Lease holder, including in the case of disaster recovery should any major incident affect the physical aspects of the Society’s offices. The agreed purposes and recommended levels as from the next financial year will be:

the Society’s offces. The agreed purposes and recommended levels as from the next fnancial year will be:
Rehousing and re-establishing the administration for one year should De Morgan House (DMH)
be lost through fre etc		 £195,000
Costs of venue hire for all LMS meetings held in DMH £15,000
Costs of re-establishingour work £13,000
Dilapidations,were the Societyto leave DMH £23,000
External and Internal redecoration £79,000
Major modifcations and developments,unexpected repairs/replacement £275,000
£600,000

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Publication Reserve Fund

This fund is to provide a reserve to meet the costs of producing and publishing the Society’s LMS journals, including where the Society’s income from these journals is unable to cover such commitments. It is intended that the reserve will be reviewed as circumstances arise each year. The agreed purposes and recommended levels are:

be reviewed as circumstances arise each year. The agreed purposes and recommended levels are:
Repayingsubscriptions income if we ceased to trade,and other commitments £1,725,000
Buffer against over/under shootingthe budget £175,000
New ventures. Based on the costs of launchingandproducinga newjournal £750,000
Special strategic and commercial initiatives £75,000
Insurance against breach of copyright and libel(includinglegal fees) £275,000
£3,000,000

Grants Payable Reserve Fund

This fund is set aside for grant awards to mathematical projects or activities which span a number of years. Such grants are reviewed annually and are paid once the recipient of the grant has provided a progress report with satisfactory performance of the project.

Grants awarded and approved by Council to be paid in future accounting periods £7,000

Global Engagement Fund

This fund has been set aside to allow the Society to develop and fund activities to support its global ambitions in line with the updated strategic direction. The fund will allow the Society to support relationships and programmes in line with the Society’s objectives to promote and extend mathematical knowledge. The fund will initially operate for the next five years but will be reviewed annually as the global aspects of the strategy are implemented.

Funds available to develop the Society’s global ambitions in line with the updated strategy and £100,000 strategic objectives

Funds to develop the Society’s updated strategy and strategic objectives

This fund is set aside to allow the Society to develop and fund activities to embed the updated strategy. The fund will ensure the Society can look beyond current ways of working to change and make a difference over the next five years. It is intended that the reserve will be reviewed as circumstances arise each year.

Funds available to developthe Society’s updated strategyand strategic objectives £50,000
Restricted Funds
Prizes Fund(for Berwick/De Morgan/Lord Rayleigh’s/Fröhlich/Shephard Prizes) £207,927
A.J. Cunningham Research Fund(forpublication of work on the factorisation of large numbers £103,931
Zeeman Fund (for Undergraduate Research Bursaries named in honour of Prof. Sir Christopher
Zeeman		 £221
Frank Gerrish Fund (for promotion of expository articles and surveys within the Society's
publications		 £25,419
Emmy Noether Fellowship Fund (for those re-establishing their research after a break or ongoing
caringresponsibilities		 £32,457
Levelling Up Scheme Fund (for tutorial of A-level maths students from under-represented
backgrounds)		 £12,754
Campaign for Pure Mathematics Fund (for campaigning to protect and promote pure
mathematics)		 £142,389
SolidarityGrant Fund(for mathematicians who are feeingtheir countries) £105,947
£631,045

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ANNEX 7: AUDITOR’S REPORT

Opinion

We have audited the financial statements of The London Mathematical Society for the year ended 31 July 2023 which comprise the Statement of Financial Activities, the Balance Sheet, the Cash Flow Statement and notes to the financial statements, including a summary of significant accounting policies. The financial reporting framework that has been applied in their preparation is applicable law and United Kingdom Accounting Standards, including FRS 102 ‘The Financial Reporting Standard Applicable in the UK and Republic of Ireland’ (United Kingdom Generally Accepted Accounting Practice).

In our opinion the financial statements:

Basis for opinion

We conducted our audit in accordance with International Standards on Auditing (UK) (ISAs(UK)) and applicable law. Our responsibilities under those standards are further described in the Auditor’s Responsibilities for the audit of the financial statements section of our report. We are independent of the charity in accordance with the ethical requirements that are relevant to our audit of the financial statements in the UK, including the FRC’s Ethical Standard, and we have fulfilled our other ethical responsibilities in accordance with these requirements. We believe that the audit evidence we have obtained is sufficient and appropriate to provide a basis for our opinion.

Conclusions relating to going concern

In auditing the financial statements, we have concluded that the trustees’ use of the going concern basis of accounting in the preparation of the financial statements is appropriate.

Based on the work we have performed, we have not identified any material uncertainties relating to events or conditions that, individually or collectively, may cast significant doubt on the charity’s ability to continue as a going concern for a period of at least twelve months from when the financial statements are authorised for issue.

Our responsibilities and the responsibilities of the trustees with respect to going concern are described in the relevant sections of this report.

Other information

The other information comprises the information included in the annual report, other than the financial statements and our auditor’s report thereon. The trustees are responsible for the other information. Our opinion on the financial statements does not cover the other information and, except to the extent otherwise explicitly stated in our report, we do not express any form of assurance conclusion thereon.

In connection with our audit of the financial statements, our responsibility is to read the other information and, in doing so, consider whether the other information is materially inconsistent with the financial statements or our knowledge obtained in the audit or otherwise appears to be materially misstated. If we identify such material inconsistencies or apparent material misstatements, we are required to determine whether there is a material misstatement in the financial statements or a material misstatement of the other information. If, based on the work we have performed, we conclude that there is a material misstatement of this other information, we are required to report that fact.

We have nothing to report in this regard.

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Matters on which we are required to report by exception

We have nothing to report in respect of the following matters where the Charities Act 2011 requires us to report to you if, in our opinion:

Responsibilities of trustees

As explained more fully in the trustees’ responsibilities statement, the trustees are responsible for the preparation of the financial statements and for being satisfied that they give a true and fair view, and for such internal control as the trustees determine is necessary to enable the preparation of financial statements that are free from material misstatement, whether due to fraud or error.

In preparing the financial statements, the trustees are responsible for assessing the charity’s ability to continue as a going concern, disclosing, as applicable, matters related to going concern and using the going concern basis of accounting unless the trustees either intend to liquidate the charity or to cease operations, or have no realistic alternative but to do so.

Auditor’s responsibilities for the audit of the financial statements

We have been appointed as auditor under section 144 of the Charities Act 2011 and report in accordance with regulations made under section 154 of that Act.

Our objectives are to obtain reasonable assurance about whether the financial statements as a whole are free from material misstatement, whether due to fraud or error, and to issue an auditor’s report that includes our opinion. Reasonable assurance is a high level of assurance, but is not a guarantee that an audit conducted in accordance with ISAs (UK) will always detect a material misstatement when it exists. Misstatements can arise from fraud or error and are considered material if, individually or in aggregate, they could reasonably be expected to influence the economic decisions of users taken on the basis of these financial statements.

Irregularities, including fraud, are instances of non-compliance with laws and regulations. We design procedures in line with our responsibilities, outlined above, to detect material misstatements in respect of irregularities, including fraud. The extent to which our procedures are capable of detecting irregularities, including fraud is detailed below.

Explanation as to what extent the audit was considered capable of detecting irregularities, including fraud

The objectives of our audit in respect of fraud, are; to identify and assess the risks of material misstatement of the financial statements due to fraud; to obtain sufficient appropriate audit evidence regarding the assessed risks of material misstatement due to fraud, through designing and implementing appropriate responses to those assessed risks; and to respond appropriately to instances of fraud or suspected fraud identified during the audit. However, the primary responsibility for the prevention and detection of fraud rests with both management and those charged with governance of the charity.

Our approach was as follows:

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As part of an audit in accordance with ISAs (UK) we exercise professional judgement and maintain professional scepticism throughout the audit. We also:

We communicate with those charged with governance regarding, among other matters, the planned scope and timing of the audit and significant audit findings, including any significant deficiencies in internal control that we identify during our audit.

Use of our report

This report is made solely to the charity’s trustees, as a body, in accordance with Chapter 3 of Part 8 of the Charities Act 2011. Our audit work has been undertaken so that we might state to the charity’s trustees those matters we are required to state to them in an auditor’s report and for no other purpose. To the fullest extent permitted by law, we do not accept or assume responsibility to any party other than the charity and charity’s trustees as a body, for our audit work, for this report, or for the opinion we have formed.

James Cross Statutory auditor, Moore Kingston Smith LLP

9 Appold Street London EC2A 2AP

Date .....................................................................

Moore Kingston Smith LLP is eligible to act as auditor in terms of Section 1212 of the Companies Act 2006.

43

ANNEX 8: STATEMENT OF FINANCIAL ACTIVITIES

Page
45 Statement of fnancial activities
46 Balance sheet
47 Cash fow statement
48 Accounting policies
52 Investment income
53 Income from other tradingactivities
53 Costs of raisingfunds
53 Charitable activities: Advancingthe interests of mathematics
54 Charitable activities: Enablingmathematicians to undertake research and collaboration
55 Charitable activities: Disseminatingmathematical knowledge – Publications
56 Charitable activities: Disseminatingmathematical knowledge – Conference and meeting programmes
56 Charitable activities: Promotingmathematical research and its benefts
57 Governance and other committees’ costs
57 Analysis ofgeneral support andgovernance costs
58 Allocation of support andgovernance costs byactivity
59 Employment costs
60 Pension costs
61 Fixed asset investments
61 Gains and losses on investment assets
62 Tangible fxed assets
62 Debtors
62 Creditors and deferred income
63 Restricted funds
64 Unrestricted funds
65 Analysis of net assets between funds
65 Grants and contracts management account
65 Transactions with Trustees and connectedpersons
66 Comparison fgures of each fund(2019/20 fnancial statements)

44

STATEMENT OF FINANCIAL ACTIVITIES For the year ended 31st July 2023

Notes
Income and endowments:
Donations and legacies
Income from charitable activities:
Membership subscriptions
Publications – LMS Periodicals
7a
Publications – Ventures and Royalties
7c,d
Grants and contracts
23
Total income from charitable activities
Income from other trading activities
3
Income from Investments
2
Other income		 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
7,210
-
529,000
156,937
-
-
858,650
-
5,820
234,748
260,562
-
94,866
-
87,600
_______
1,345,201
260,562
93,420
269,454
-
-
621,847
-
9,125
3,040
-
-
__		 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
7,210
-
529,000
156,937
-
-
858,650
-
5,820
234,748
260,562
-
94,866
-
87,600
_______
1,345,201
260,562
93,420
269,454
-
-
621,847
-
9,125
3,040
-
-
__		 2023
Total
Funds
£
536,210
156,937
864,470
495,310
182,466
1,699,183
269,454
630,972
3,040		 2022
Total
Funds
£
260,432
155,158
1,079,185
599,702
150,682
1,984,727
142,861
531,719
3,782
Total Income 2,246,752
260,562		 631,545 3,138,859 2,923,521
Expenditure:
Costs of raising funds
4
Expenditure on charitable activities:
Advancing the interests of mathematics
5
Enabling mathematicians to undertake research
and collaboration
6
Disseminating mathematical knowledge:
- Costs of publications
7b,c,d
- Conferences and meeting programmes
8
Promoting mathematical research and its benefits
9
Total expenditure on charitable activities		 __
346,901
-
__
313,078
-
620,140
7,000
377,845
168,929
153,772
-
336,643
-
__
1,801,478
175,929
__		 -
4,000
191,096
4,440
-
201,976
401,512		 346,901
317,078
818,236
551,214
153,772
538,619
2,378,919
270,512
286,752
529,109
522,628
154,949
516,293
2,009,731
Total expenditure 2,148,379
175,929		 401,512 2,725,820 2,280,243
Net income before gains and losses on
investment
Net (losses)/ gains on investment assets
16
Net Income for the year
Transfers between funds
20,21
Actuarial loss on defined benefit
pension schemes
14,19		 __
98,373
84,633
(11,083)
-
__
87,290
84,633
(15,283)
58,367
(61,172)
-
__		 230,033
(5,907)
224,126
(43,084)
-		 413,039
(16,990)
396,049
-
(61,172)
643,278
(299,946)
343,332
-
(227,987)
Net movement in funds for the year 10,835
143,000		 181,042 334,877 115,345
Reconciliation of funds:
Total funds brought forward
1		 5,639,501 3,614,000 450,003 19,703,504 19,588,159
Fund balances carried forward
1		 5,650,336
3,757,000		 631,045
20,038,381
19,703,504

The comparative figures for each fund are shown in the notes to the accounts, (see note 25).

45

BALANCE SHEET

as at 31st July 2023

Notes
Fixed Assets
Fixed Asset Investments
Quoted Investments
15a
Residential Property
15b
Tangible Fixed Assets
Leasehold Property
17
Fixtures, Fittings and Equipment
17
Current Assets
Debtors
18
Current Asset Investment

Cash at bank and in hand
Liabilities:
Creditors: Amounts falling due within one year
Creditors
19
Deferred Income
19
Net current assets
Creditors: Amounts falling due after more than one year
Provision of Pension Liability
19
Total Net Assets
Represented by:
General Funds
21
Designated Funds
21
Restricted Funds
20		 2023
£
£
13,440,223
3,938,750
17,378,973
1,075,618
30,881
1,106,499
18,485,472
179,768
1,310,811
1,231,354
2,721,933
670,183
-
670,183
2,051,750
(498,841)
20,038,381
15,650,336
3,757,000
631,045
20,038,381		 2022
£
£
13,766,170
3,713,950
17,480,120
1,120,435
37,014
1,157,449
18,637,569
241,375
2,113,763
2,355,138
803,647
47,887
851,534
1,503,604
(437,669)
19,703,504
15,639,501
3,614,000
450,003
19,703,504

The notes on pages 48 to 66 form part of these financial statements.

Approved by the trustees on 20 October 2023 and signed on their behalf by:

Professor Simon Salamon (Treasurer)

46

Cash Flow Statement

For the year ended 31 July 2023

2023 2022
£
£		 £ £
Cash flow from operating activities
Net movements in funds 334,877 115,345
Add / (Deduct) gains/(losses) on investments (note 16) 16,990 299,946
Add back re-invested gains (note 2) 109,865 97,110
Add back investment management fees (note 4) 80,758 59,870
Add back VAT on investment management fees 3,399 2,458
Deduct investment income (note 2) (630,972) (531,719)
Add back depreciation charge (note 17) 59,136 62,939
Decrease / (Increase) in debtors (note 18) 61,607 71,072
Decrease / (Increase) in medals in stock - 1,531
(Decrease)/increase in creditors (note 19) (120,179) 10,089
Net cash (used in) provided by operating activities (84,519) 188,641
Cash flow from Investing activities
Acquisition of fixed deposit (1,310,811) -
Purchase of tangible fixed assets (note 17) (8,186) (17,504)
Purchase of fixed asset investments (note 15) (117,288) (2,096,909)
Proceeds on disposal of fixed assets investments (note 15) 16,214 -
Investment income (note 2) 630,972 531,719
Net cash (used in) provided by investing activities (789,099) (1,582,694)
Change in cash and cash equivalents in the year (873,618) (1,394,053)
Cash and cash equivalents at the beginning of the year
Cash at bank 2,113,763 3,508,017
Cash held in investments 301 100
2,114,064 3,508,117
Cash and cash equivalents at the end of the year
Cash at bank 1,231,354 2,113,763
Cash held in investments 9,092 301
1,240,446 2,114,064

47

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

1. Accounting Policies

The accounting policies adopted by the Society are as detailed below:

a) Basis of accounting

The London Mathematical Society meets the definition of a public benefit entity under FRS 102. Assets and liabilities are initially recognised at historical cost or transaction value unless otherwise stated in the relevant accounting policy note(s).

The trustees have assessed whether the use of going concern basis is appropriate and have considered possible events or conditions that might cast significant doubt on the ability of the Society to continue as a going concern. The trustees have made this assessment for a period of at least one year from the date of approval of the financial statements. In particular, the trustees have considered the residual impact of COVID-19 pandemic and the expected decline in the Society’s income from its publishing activities.

In relation to the residual impact of the pandemic, the conference income from De Morgan House continues to be lower than pre-pandemic though is showing a gradual return. This is partly mitigated by a reduction in operational costs for the conference business and anticipated cost savings arising from changes in levels of activity in some areas. For example, some grant schemes will reduce the number of grants available, and some events will continue to take place online rather than face-to-face.

As noted earlier in this report, the Society is set to lose a significant part of its income from its publications activities. However, the Society has in place plans to increase the number of articles published in the Bulletin and Journal which will help mitigate some of the decline in subscription income. Council is actively exploring other sources of income. Pending the development of additional income streams, Council has reviewed all the Society’s activities in order to identify savings.

On this basis, and the level of reserves held, the trustees consider that the Society has adequate resources to continue in operational existence for the foreseeable future. The Society therefore continues to adopt the going concern basis in preparing its financial statements.

The financial statements are prepared in sterling, which is the functional currency of the company. Monetary amounts in these financial statements are rounded to the nearest pound.

In the application of the Society’s accounting policies, the trustees are required to make judgement, estimates and assumptions about the carrying amount of assets and liabilities that are not readily apparent from other sources. The estimates and associated assumptions are based on historical experience and other factors that are considered to be relevant. Actual results may differ from the estimates.

The estimates and underlying assumptions are reviewed on an ongoing basis. Revisions to accounting estimates are recognised in the period in which the estimate is revised where the revision affects only that period, or in the period of the revision and future periods where the revision affects both current and future periods.

The most significant estimates and assumptions which affect the carrying amount of assets and liabilities in the accounts relate to:

48

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

c) Financial Instruments

The Society has elected to apply the provision of Section 11 ‘Basic Financial Instrument’s and Section 12 ‘Other Financial Instruments Issues’ of FRS 102 to all of its financial instruments. Financial Instruments are recognised in the Society’s balance sheet when the Society becomes party to the contractual provisions of the instrument. Financial assets and liabilities are offset, with the net amounts presented in the financial statements, when there is a legally enforceable right to set off the recognised amounts and there is an intention to settle on a net basis or to realise the asset and settle the liability simultaneously.

With the exceptions of prepayments and deferred income all other debtor and creditor balances are considered to be basic financial instruments under FRS 102. (See notes 18 and 19 for details)

d) Members’ Subscriptions

Subscription income from members is recognised in the year to which it relates. Members who joined during the year are allowed to pay pro-rata subscription fees depending on when they are elected during the membership year.

e) Donations

f) Investments

The Society in its total returns policy treats all cash withdrawals from the investment portfolio as investment income. This is analysed in the notes to the financial statements as investment income split between the various categories of investment based on information provided by the investment managers and the proportion of total return drawn down relating to gains. The balance of unrealised gains and losses on revaluation of investments and realised gains and losses arising on disposal of investments are separately identified in the notes to the Financial Statements and on the SoFA.

Residential property investment

The rental derived is shown on the SoFA under ‘Investment Income’. The growth in the value of the Society’s residential property investment will be shown in the SoFA as Gains on investment assets. The residential property investment is valued at balance sheet date using the local estate agent’s guidance on the current housing market within the area where the properties are located.

Depreciation is provided on all tangible fixed assets at rates calculated to write off, on a straight-line basis, the cost less estimated residual value over their expected useful lives as follows:

Leasehold Property Over 50 years
Fixtures, Fittings and Office Equipment 20%
Computer equipment 33.33%

The Society operates a policy of capitalising assets whose unit cost exceeds £1,000, with expenditure below this level written off as incurred.

h)

Publications

49

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

1. Accounting Policies (continued)

iv) No valuation for accounting purposes is taken of any stocks of publications unsold at the Balance Sheet date.

v) The cost of publishing rights and subscribers’ lists are written off in the year of acquisition.

vi) Royalties are taken into the Statement of Financial Activities as declared due by the relevant publishers.

i) Joint Ventures

The results of joint ventures are included in the accounts up to the year- end indicated.

j ) Grants and Contracts

The Society has been awarded contracts and grants for some of its activities. These comprise: a contribution from IMU to support mentoring activities for mathematicians in Africa; shared costs of some activities with sister societies. The income and expenditure relating these are handled through this Fund.

k) Recognition of grant liabilities

Where the Society has contractual or constructive obligations to make grant payments these amounts are accrued in the accounts in accordance with the requirements of the SORP. The liability will be recognised within the year the grant is awarded and communicated to the recipient. The unpaid grant commitments should normally be claimed by the end of the following financial year. However, the claim period may need to be extended for a further year (award year + 2) if the grant cannot be claimed by the end of the year following the award due to constraints on the start or end date of a grant, or due to other circumstances outside the control of the Society.

The Society also awards some grants with conditions for payment being a specific level of service or specific output to be delivered. Such grant awards (commitments) will be reserved in the Designated funds, and the grants are only recognised in the SoFA once the recipient of the grant has provided evidence of the specific service or output. Such grants are therefore reviewed annually and the grant payments subject to the condition of a progress report with satisfactory performance. If the project spans a number of years and satisfactory progress reports are received after year one, the first stage of the grant will be released from the Designated fund and that part of the grant expenditure will be recognised in the SoFA at that point.

Grants unclaimed by the end of award year +2 will be released back to the Society’s general funds.

l) Grants payable

m) Taxation

The Society is a registered charity and no liability to taxation arises on the results of its business activities in support of its charitable purposes.

The Society has partial exempt status in respect of VAT, based on the split of its business and non-business activities. The proportion of VAT that cannot be recovered because of partial or fully exempt status of the activity is redistributed to the activities. The basis on which irrecoverable VAT have been allocated to the activities is set out in note 12.

n) Foreign currencies

Monetary assets and liabilities denominated in foreign currencies are translated at the rate of exchange ruling at the Balance Sheet date. Transactions in foreign currencies are recorded at the rate ruling at the date of the transaction. All differences are taken to the Statement of Financial Activities.

o) Medals in stock

The medal stock for the prize is stated at the lower of cost and net realisable value.

The Unrestricted reserves are analysed between the General Fund and other Designated Funds. The General Fund, detailed in note 21 to the financial statements, is to provide for the general operation of the Society including its charitable activities not funded from Designated or Restricted Funds. Within the Society’s reserves the General Fund is deemed an expendable reserve to be used in pursuit of the Society’s objectives as Council may from time to time determine. At present it is managed to provide the income to be used to ensure the availability of resources for its grant schemes and other charitable activities in future years.

q) Designated Funds

(i) Building & Development Reserve Fund

This reserve is to meet the costs of (a) consequences of the temporary loss of De Morgan House, (b) periodic internal and external decoration and maintenance, (c) major modifications or repairs.

50

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

(ii) Publication Reserve Fund

This fund has been established to cover grants awarded and approved by Council to be paid in future accounting periods, subject to available finance and satisfactory report.

This fund is set aside to help mitigate the impact of the COVID-19 pandemic on mathematical research, including the ‘people pipeline’ of early career researchers.

This fund holds the transaction relating to, and any year-end excess of income over expenditure, relating to the Society’s joint venture with the Foundation Compositio to produce the journal Compositio.

This fund is set aside to allow the Society to develop and fund activities to support the Society’s global ambitions in line with the updated strategic direction. The fund will allow the Society to support relationships and programmes in-line with the Society’s objectives to promote and extend mathematical knowledge. The fund will initially operate for the next five years but will be reviewed annually as the global aspects of the strategy are implemented.

r) Restricted Funds

The income of these restricted funds is to be used for the following purposes:

51

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

1. Accounting Policies (continued)

s) Support and governance costs

Support costs are those functions that assist the work of the charity but do not directly undertake charitable activities. Support costs include back-office costs, finance, personnel, payroll and governance costs which support the Society’s Mathematical Sciences programmes and activities. The Governance costs include external audit, legal advice and the costs of trustee and committee meetings, as well as costs associated with constitutional and statutory requirements. Support and governance costs have been allocated between the costs of raising funds and charitable activities. The bases on which support and governance costs have been allocated to activities are set out in note 12.

t) Employee benefits

Termination benefits are recognised immediately as an expense when the Society is demonstrably committed to terminate the employment of an employee through, for example, redundancy, or to provide termination benefits.

u) Heritage assets

The Society holds an archive of historical material, known as the LMS Archive. The purpose of the Society’s Archive is to provide a permanent historical record of the activities of the London Mathematical Society. The Society’s Archive also provides protection for other significant material relating to mathematics in the UK that might otherwise be lost or destroyed, for the purposes of bibliographic reference and further study by historians of mathematics. No value is attributed to the Archive in the financial statements. From time to time, items may be added to the Archive and again no value is attributed to these items in the financial statements. The cost of regular valuations of items in the archive would not be justified.

v) Cash and Cash Equivalents

Cash and cash equivalents include cash in hand and current and fixed term bank deposits maturing in less than 90 days.

2. Investment Income

2023
Unrestricted Designated Restricted
£
£
£
a) Investment income receivable:
Total returns/ Unit Trust Distribution
(Bond interest, Equities dividends, etc.)
545,186
-
8,399
Re-invested total returns
(109,865)
-
-
Net investment income receivable
435,321
-
8,399
b) Residential property rental income
146,423
-
-
c) Interest receivable (Treasury Reserve and Bank deposits)
40,103
-
726
Total investment income 2023
621,847
-
9,125
2022
Unrestricted Designated Restricted
£
£
£
a) Investment income receivable:
Total returns/ Unit Trust Distribution
(Bond interest, Equities dividends, etc.)
477,115
-
8,371
Re-invested total returns
(97,110)
-
-
Net investment income receivable
380,005
-
8,371
b) Residential property rental income
142,240
-
-
c) Interest receivable (Treasury Reserve and Bank deposits)
964
-
139
Total investment income 2022
523,209
-
8,510		 Total
2023
£
553,585
(109,865)
443,720
146,423
40,829
630,972
Total
2022
£
485,486
(97,110)
388,376
142,240
1,103
531,719

52

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

3. Income from other trading activities


a) DMH Conference facilities
b) DMH Rental income
c) Advertising in Newsletter
Total		 2023

£
175,214
91,762
2,478

269,454
 2022
£
53,520
86,071
3,270

142,861

4. Costs of raising funds

2023
£
£
a)
Conference facilities
General expenditure
43,137
Apportioned support and governance costs
74,232

117,369
b)
Services for tenants
96,964
c)
Investment Management fees
80,758
d)
Residential Investment Property costs
51,810

Total
346,901

5.
Charitable activities: Advancing the interests of Mathematics
2023
£
£
Members’ services:
LMS Newsletter
22,806
Other costs
3,858
Unrecoverable subscriptions
3,485

30,149
Activities to support Women in Mathematics
1,208
Activities to support Maths -Computer Sciences
-
Library, binding and archives
4,373
EMS, IMU, ICIAM subscriptions & ICM costs
11,170
Prizes
10,461
Apportioned support and governance costs (note 12)
259,717

Total
317,078
2022
£
£
15,812
63,825

79,637
85,590
59,870
45,415

270,512

2022
£
£
24,579
3,773
5,219

33,571
-
464
5,042
23,928
10,381
213,366

286,752

53

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

6. Charitable activities: Enabling Mathematicians to undertake research and collaboration

2023
Grant Schemes
£
£
Research Grants (Schemes 1 – 6 and MIA AMMSI)
328,225
Early Career Support (Schemes 8 and 9/ECR travel grants)
50,439
Research School Grants(incl. £20k HIMR Fund)
45,000
Early Career Fellowship Grants(incl. £30k HIMR Fund)
69,695
Undergraduate Bursaries
34,440
Undergraduate Summer School
24,000
Computer Science Grants
1,470
Small Education grants (incl. Teachers CPD)
10,324
Women in Mathematics scheme(incl.£3k HIMR Fund)
5,950
Atiyah UK-Lebanon Fellowships
8,000
Isaac Newton Institute (INI) Grants
30,000

607,543
Covid response Fund(Designated)
-
Mentoring African Research in Mathematics (MARM)(Restricted)
4,000
Cecil King Grants (Restricted)
18,000
Emmy Noether Fellowship (Restricted)
17,543
ACME Grants (Designated)
7,000
Solidarity Grants(Restricted)
83,553
Ad hoc Grants to Mathematical Bodies (UK & International)
11,200

Total Grants before cancellation/refunds and Support costs
748,839
Less: Grants cancellation and refunds
(132,290)
Charitable giving of LMS rooms
22,880
Apportioned support and governance costs (note 12)
178,807

Total Grants after cancellation/refunds and Support costs
818,236

2023
ANALYSIS OF GRANT AWARDS
£
a) Grants: contractual commitments
Royal Society (ACME grant)
7,000
b) Other grant awards to institutions
543,159
c) Other grant awards to individuals
198,680

Total grant awards
748,839

_ Grant awards to each institution can be up to a maximum of £35k_
2023
GRANT REFUNDS AND CANCELLATION
£
Grant refunds
(66,887)
Grants not taken up (‘out of date’)
(65,403)

Total grant refunds and cancellation
(132,290)

2023
MOVEMENT IN OBLIGATION GRANT COMMITMENTS
£
Grant recognised at the start of the year
341,389
New grants charged to the SoFA in year
748,839
Grants paid during the year
(750,934)
Grants not taken up (‘out of date’)
(65,403)

Amount of grant recognised at the end of the year
273,891**
 2022
£
£
275,489
44,275
30,000
76,900
44,308
32,612
1,410
10,130
2,009
8,000
30,000

555,133
2,333
16,000
24,000
-
7,000
10,500
20,289

635,255
(280,613)
7,737
166,730

529,109

2022
£
7,000
488,610
139,645

635,255

2022
£
(28,059)
(252,554)

(280,613)

2022
£
540,934
635,255
(582,246)
(252,554)

341,389

54

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

7. Charitable activities: Disseminating Mathematical Knowledge - Publications

a) Net Income from LMS journals
b) Direct costs of Publications
Journal of Computation and Mathematics
Costs of Expository Surveys project
Other Operational Costs
Net LMS periodicals surplus
before Support and governance costs
Apportioned support and governance costs (note 12)
Net LMS periodicals surplus
after Support and governance costs
c) Ventures & Royalties (net income)
Nonlinearity
Russian journals (Turpion/RAS/LMS joint venture)
TMMS (AMS/LMS joint venture)
LMS Books and Royalties
Compositio
Profit share & Management fee (see 7d)
Costs of_Compositio_(LMS - only)
Mathematika
NET PUBLICATIONS SURPLUS		 2023
£
£
864,470
(500)
(4,440)
(20,388)
(25,328)
(356,701)
482,441
170,844
-
-
17,978
188,822
91,633
(10)
91,623
45,680
808,566		 2022
£
£
1,079,185
(500)
(9,200)
(14,361)
(24,061)
1,055,124
(312,874)
742,250
178,560
56,359
10,700
16,753
262,372
100,182
(10)
100,172
51,465
1,156,259		 2022
£
£
1,079,185
(500)
(9,200)
(14,361)
(24,061)
1,055,124
(312,874)
742,250
178,560
56,359
10,700
16,753
262,372
100,182
(10)
100,172
51,465
1,156,259
1,055,124
(312,874)
742,250
262,372
100,172
51,465
1,156,259

The Society was involved in the following publishing ventures in the year:

Income
Expenditure
Direct costs
Profit share to_Compositio_Foundation
NetCompositio surplus before LMS fees and Profit share
Management fee to LMS
Profit share to LMS
Balance C/fwd onCompositio Fund		 2023
£
260,562
(46,117)
122,812
168,929
91,633
(39,000)
(52,633)
-		 2022
£
285,865
(42,926)
(142,757)
(185,683)
100,182
(39,000)
(61,182)
-

55

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

8. Charitable activities: Disseminating Mathematical Knowledge

– Conference and meeting programmes

Society meetings and regional workshops
Aitken/Forder Lectures
Invited Lectures
Hardy Lecturer
Caring costs for Lecturers visiting UK
Apportioned support and governance costs (note 12)
Total		 2023
£
£
32,220
1,512
4,518
3,618
1,182

43,050
110,722

153,772		 2022
£
£
28,407
5,768
14,500
-
2,807

51,482
103,467

154,949

9. Charitable activities: Promoting Mathematical Research & its benefits

Policy
CMS
Communication and External Relations
Research Policy Activities
Annual dinner
Subscriptions to UK organisations
Education and young people, public engagement
Holgate Lecturers
Popular Lectures
Other educational activities (MCTD/Education Day/etc)
Levelling Up Scheme
Campaign for Pure Mathematics
Apportioned support and governance costs (note 12)
Total		 2023
£
£
24,764
3,868
4,613
5,493
2,233

40,971
1,800
1,376
6,847

10,023
13,676
158,300
315,649

538,619
 2022
£
£
25,763
6,477
7,000
8,313
1,770

49,323
2,250
-
5,708

7,958
29,652
127,852
301,508

516,293

56

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

10. Governance and other committees’ costs

Professional services
Solicitors fees
Audit and accountancy fees
Audit and accountancy fee over accrual
Other professional fees
Costs of meetings (Catering/Accommodation/Travel/Subsistence)
Governance(Council/F&GPC/Nomination, etc.)
Other Committees
Election of Trustees
General office and staff costs (apportioned)(note 11_)_
Total		 2023
£
£
1,081
18,000
900
35
20,016
15,411
2,439
17,850
4,558
247,750
290,174		 2022
£
£
6,805
14,000
950
35
21,790
5,903
2,519
8,422
3,723
210,496
244,431

11. Analysis of general support and governance costs

2023
Governance and
Committee related
£
Staff costs
172,727
Office and Premises costs
44,344
IT costs
12,381
Depreciation
13,755
Irrecoverable VAT
4,543
Professional services
20,016
Costs of meetings
17,850
Elections of Trustees
4,558
Total 2023
290,174
2022
Governance and
Committee related
£
Staff costs
169,881
Office and Premises costs
10,587
IT costs
11,918
Depreciation
13,811
Irrecoverable VAT
4,299
Professional services
21,790
Costs of meetings
8,422
Elections of Trustees
3,723
Total 2022
244,431		 Other general
support
£
786,588
173,458
57,491
45,381
48,121
-
-
-
1,111,039
Other general
support
£
818,545
42,055
58,100
49,128
41,971
-
-
-
1,009,799		 Total
2023
£
959,315
217,802
69,872
59,136
52,664
20,016
17,850
4,558
1,401,213
Total
2022
£
988,426
52,642
70,018
62,939
46,270
21,790
8,422
3,723
1,254,230

57

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

12. Allocation of support and governance costs by activity

2023
Raising funds
Conference facilities (DMH)
Services for tenants (DMH)
Managing Residential Property
Total support costs for raising funds
Charitable activities
 Advancing the interest of Mathematics
 Enabling Mathematicians to undertake
research and collaboration
 Disseminating Mathematical Knowledge
– Publications
 Disseminating Mathematical Knowledge
– Conference and meeting programmes
 Promoting Mathematics research and
its benefits
Total support costs for Charitable activities
Total 2023
2022
Raising funds
Conference facilities (DMH)
Services for tenants (DMH)
Managing Residential Property
Total support costs for raising funds
Charitable activities
 Advancing the interest of Mathematics
 Enabling Mathematicians to undertake
research and collaboration
 Disseminating Mathematical Knowledge
– Publications
 Disseminating Mathematical Knowledge
– Conference and meeting programmes
 Promoting Mathematics research and
its benefits
Total support costs for Charitable activities
Total 2022		 Direct
Staff
£
24,316
15,075
9,241

48,632

104,533
73,604
188,416
30,626
120,901

518,080

566,712

Direct
Staff
£
25,779
8,593
8,593

42,965

97,076
80,822
187,335
33,346
166,020

564,599

607,564		 General
Office
General
Management
and Finance
Governance
and
Committee
£
£
£
38,429
10,998
489
75,420
1,848
489
1,396
1,427
489



115,245
14,273
1,467



40,655
56,494
58,035
22,217
46,374
36,612
48,035
62,215
58,035
8,939
20,263
50,894
67,021
42,596
85,131



186,867
227,942
288,707



302,112
242,215
290,174



General
Office
General
Management
and Finance
Governance
and
Committee
£
£
£
34,444
3,195
407
72,044
655
407
1,149
612
407



107,637
4,462
1,221



39,247
28,401
48,642
21,146
16,120
48,642
46,306
30,591
48,642
10,222
11,257
48,642
62,559
24,287
48,642



179,480
110,656
243,210



287,117
115,118
244,431

Basis of apportionment

Support costs include (a) Staff costs (salaries, benefits, training, H&S, recruitment, etc. of staff directly attributable to each of the above Society’s activities); (b) General Office Costs (rent, rates, services, cleaning, equipment, maintenance, telephones, postage, equipment, stationery, etc., depreciation and Irrecoverable VAT, and IT costs such as computer hardware and software, network, internet access, websites, software development, etc.), (c) General management and finance (cost of services that cannot be directly attributed to an activity, i.e. general accounting and financial controls, HR and Executive Secretary’s general management, etc.) ( d) Governance costs (costs of meetings, trustees’ expenses, and costs associated with constitutional and statutory requirements).

The costs of these are attributed across all the activities of the Society in proportion to (a) salary or f.t.e., (b) space occupied in De Morgan House, and (c) f.t.e. respectively, based on a time analysis undertaken by all staff.

58

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

12. Allocation of support and governance costs by activity (continued)

Support and governance costs have been allocated between the costs of raising funds and charitable activities as:

The Society has partial exempt status in respect of VAT, based on the split of its business and non-business activities. The proportion of VAT that cannot be recovered because of partial or fully exempt status of the activity is redistributed to the activities on the same basis as the original elements (i.e. staff time and space occupied, IT and office use etc.), under General Office costs.

Support costs for each area of the above activities can be higher or lower than last year due to staff time allocation. This changes from year to year and will have an effect on direct staff costs, general office costs, general management costs and governance costs.

13.
Employment Costs
Total employment costs of all staff including taxable benefits for the year comprise:
Salaries and Wages
Redundancy
Employer’s National Insurance Contributions
Less HMRC employment allowance
Employer’s Pension Contributions
Total		 2023
£
703,509
-
80,781
(5,000)
128,826
908,116		 2022
£
711,962
18,360
82,595
(4,000)
142,724
951,641

The total employment costs (Salaries/NIC /Pension) for the Executive Management Team amounted to £390,827 (2022: £399,502). This team is considered to be Key Management Personnel and consists of the Executive Secretary, Head of Finance, Head of Society Business, and the Head of Conference and Building .

The number of employees earning £60,000 per annum or more was:

2023 2022
No. No.
£60,000 - £70,000 1 2
£70,000 - £80,000 1 1
£80,000 - £90,000 1 -
£100,000 - £110,000 - 1

The pension payments for the above members of staff amounted to £62,168 (2022: £63,958). These contributions were paid into a defined benefits pension scheme.

The average number of employees over the year (and full time equivalent) was:

Management and administration
Publishing and editorial
Total		 2022/2023
Total
FTE
12.4
9.8
2.8
2.8
15.2
12.6		 2021/2022
Total
FTE
12.8
10.5
2.8
2.8
15.6
13.3

59

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

14. Pension costs

The Society participates in Universities Superannuation Scheme (USS). The assets of the scheme are held in a separate trustee-administered fund. Because of the mutual nature of the scheme, the assets are not attributed to individual institutions and a scheme-wide contribution rate is set. The Society is therefore exposed to actuarial risks associated with other institutions’ employees and is unable to identify its share of the underlying assets and liabilities of the scheme on a consistent and reasonable basis. As required by Section 28 of FRS 102 “Employee benefits”, the Society therefore accounts for the scheme as if it were a defined contribution scheme. As a result, the amount charged to the statement of financial activities (SoFA) represents the contributions payable to the scheme. Since the Society has entered into an agreement (the Recovery Plan) that determines how each employer within the scheme will fund the overall deficit, the Society recognises a liability for the contributions payable that arise from the agreement (to the extent that they relate to the deficit) with related expenses being recognised through the statement of financial activities.

The total movement to the profit & loss account is a loss of £61,172 (2022: loss of £227,987) as shown in note19.

The information provided is based on the last formal completed actuarial valuation of Universities Superannuation Scheme (the scheme) which was as at 31 March 2020 and completed in October 2021. The 2023 valuation is currently in progress and USS have been actively facilitating discussions with stakeholders with the aim of completing the valuation in time to implement any changes they decide to make by April 2024. Given the changes in market conditions since the 2020 valuation, it is likely that the 2023 valuation will show an improved funding position with the scheme expected to be in a surplus position.

Since the institution cannot identify its share of USS Retirement Income Builder (defined benefit) assets and liabilities, the following disclosures reflect those relevant for those assets and liabilities as a whole.

The 2020 valuation was the sixth valuation for the scheme under the scheme-specific funding regime introduced by the Pensions Act 2004, which requires schemes to have sufficient and appropriate assets to cover their technical provisions. At the valuation date, the value of the assets of the scheme was £66.5 billion and the value of the scheme’s technical provisions was £80.6 billion indicating a shortfall of £14.1 billion and a funding ratio of 83%.

The key financial assumptions used in the 2020 valuation are described below. More detail is set out in the Statement of Funding Principles.

key financial assumptions used in the
tement of Funding Principles.		 2020 valuation are described below. More detail is set out in th
CPI Term dependent rates in line with the difference between the Fixed Interest
and Index Linked yield curves, less:
1.1% p.a. to 2030, reducing linearly by 0.1% p.a. to a long-term
difference of 0.1% p.a. from 2040
Pension increases (subject to a floor of 0%) CPI assumption plus 0.05%
Discount rate (f/wd rates) Fixed interest gilt yield curve plus:
Pre-retirement: 2.75% p.a.
Post retirement: 1.00% p.a.

The main demographic assumption used relates to the mortality assumptions. These assumptions are based on analysis of the scheme’s experience carried out as part of the 2020 actuarial valuation. The mortality assumptions used in these figures are as follows:

2020 valuation
Mortality base table 101% of S2PMA “light” for males and 95% of S3PFA for
Future improvements to mortality CMI 2019 with a smoothing parameter of 7.5 an initial addition of
0.5% p.a. and a long-term improvement rate of 1.8% pa for males
and 1.6% pa for females

The current life expectancies on retirement at age 65 are:

2023 2022
Males currently aged 65 (years) 24.0 23.9
Females currently aged 65 (years) 25.6 25.5
Males currently aged 45 (years) 26.0 25.9
Females currently aged 45 (years) 27.4 27.3

A deficit recovery plan was put in place as part of the 2020 valuation, which requires payment of 6.2% of salaries over the period 1 April 2022 until 31 March 2024, at which point the rate will increase to 6.3%. The 2023 deficit recovery liability reflects this plan. The liability figures have been produced using the following assumptions:

umptions:
2023 2022
Discount rate 2.59% 2.59%
Pensionable salary growth 1% 1%

60

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

15. Fixed Asset Investments

2023
£
£
£
a) Quoted investments
Investment
Assets
in the UK
Investment
Assets
outside the
UK
Total
Total Market value at 31st July 2023
£670,630 £12,769,593 £13,440,223

In the prior year, £1,535,619 of investment assets were in the UK with the remaining £12,230,551 being outside t
Reconciliation of opening & closing market values:
£
Market value at 1stAugust 2022
13,766,170

Additions at cost
117,288
Disposal proceeds
(16,214)
Unrealised (losses)/gains (note 16a)
(241,790)
Movement in cash
(185,231)
Total Market value at 31st July 2023
13,440,223

Analysis by Fund:
Restricted Funds
249,710
Unrestricted Funds
13,190,513
 2022
£
Total
13,766,170
he UK.
£
12,153,444
2,096,909
-
(324,946)
(159,237)
13,766,170
249,467
13,516,703
The investments are entirely invested in the Schroder/Cazenove [49% in ordinary Charities Multi-Asset Fund The investments are entirely invested in the Schroder/Cazenove [49% in ordinary Charities Multi-Asset Fund The investments are entirely invested in the Schroder/Cazenove [49% in ordinary Charities Multi-Asset Fund
(CMAF) and 51% in Responsible Multi-Asset Fund (RMAF)] [Prior year: 68% in CMAF, 32% in RMAF)
b) Residential Property investments 2023 2022
£ £
Market value at 31st July 2023 3,938,750 3,713,950
Reconciliation of opening and closing market values:
Market value at 1st August 2022 3,713,950 3,688,950
Unrealised gains (note 16b) 224,800 25,000
Total Market value at 31st July 2023 3,938,750 3,713,950

Represents purchase of property for residential letting purposes to diversify the Society’s investment portfolio. The rental derived is shown on the SoFA under ‘Investment Income’.

16. Gains and losses on investment assets

2023
Unrestricted
funds

£
a. Unrealised losses in market value ofQuoted investments
(235,883)
b. Unrealised gains in market value ofResidential Properties
224,800
Total gains
(11,083)
2022
Unrestricted
funds

£
a. Unrealised losses in market value ofQuoted investments
(316,813)
b. Unrealised gains in market value ofResidential Properties
25,000
Total gains
(291,813)		 Restricted
funds
£
(5,907)
-
(5,907)
Restricted
funds
£
(8,133)
-
(8,133)		 Total
£
(241,790)
224,800
(16,990)
Total
£
(324,946)
25,000
(299,946)

61

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

17. Tangible Fixed Assets Leasehold Fixtures Total
Property Fittings and
Equipment
£ £ £
Cost
Brought forward at 1st August 2022 2,175,353 168,995 2,344,348
Additions - 8,186 8,186
Carried forward at 31st July 2023 2,175,353 177,181 2,352,534
Depreciation
Brought forward at 1stAugust 2022 1,054,918 131,981 1,186,899
Charge for the year 44,817 14,319 59,136
Carried forward at 31st July 2023 1,099,735 146,300 1,246,035
Net book value
At 31st July 2023 1,075,618 30,881 1,106,499
At 31stJuly 2022 1,120,435 37,014 1,157,449
Part of the leasehold property is let out and the rental derived is shown on the SOFA under ‘Activities for Generating Funds’.
18. Debtors 2023 2022
£ £
Publications 100,501 135,535
Conference facilities 6,280 10,356
Other debtors 28,482 55,918
Prepayments and accrued interest 44,505 39,566
179,768 241,375
19. Creditors and Deferred Income 2023 2022
£ £
Creditors: amounts falling due within one year
Accruals 41,333 38,650
Grant creditors 273,891 341,389
Taxation and other Social Security creditors 103,379 66,118
Other creditors 251,580 357,490
670,183 803,647
Deferred income:
Unexpired publications’ subscriptions:
Balance brought forward 47,887 107,349
Amount released in year (47,887) (107,349)
Income deferred to future years - 47,887
Balance carried forward - 47,887
Creditors: amounts falling due after more than one year
Brought Forward Pension Provision 437,669 209,682
Movement 61,172 227,987
Carried Forward Pension Provision 498,841 437,669

62

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

20.
Restricted Funds
2023
Prize (Capital) funds
Berwick Fund
De Morgan Medal & Larmor Fund
Prize (Income) funds
Berwick Fund
De Morgan Medal & Larmor Fund
Lord Rayleigh’s Fund
J.H.C. Whitehead Fund
Fröhlich Fund
Shephards Fund
Other funds
A.J. Cunningham Research Fund
Zeeman Fund
Frank Gerrish Fund
MARM Grant
Cecil King Grant
Emmy Noether Fellowship Fund
Levelling Up Scheme
Campaign for Pure Maths Fund
Solidarity Grant Fund
HIMR Fund
Total Funds

The transfer of £1,750 from the General Fund to Restricte

The transfer of £2,400 from General Fund to Grants and

The transfer of £47,234 from Levelling up scheme to Gen
2022
Prize (Capital) funds
Berwick Fund
De Morgan Medal & Larmor Fund
Prize (Income) funds
Berwick Fund
De Morgan Medal & Larmor Fund
Lord Rayleigh’s Fund
J.H.C. Whitehead Fund
Fröhlich Fund
Shephards Fund
Other funds
A.J. Cunningham Research Fund
Zeeman Fund
Frank Gerrish Fund
MARM Grant
Cecil King Grant
Emmy Noether Fellowship Fund
Levelling Up Scheme
Campaign for Pure Maths Fund
Solidarity Grant Fund
HIMR Fund
Total Funds		 Balance
at
1.08.22
Other &
Investment
Income
Expenditure
Investment
loss
Transfers
£
£
£
£
£
32,505
275
-
-
-
29,120
248
-
-
-
18,609
626
(2,250)
(441)
-
52,213
1,757
-
(1,236)
-
21,328
718
-
(505)
-
-
-
(1,750)
-
1,750
14,473
489
(343)
-
39,942
1,345
(946)
-
102,903
3,464
-
(2,436)
-
221
-
-
-
-
23,836
6,023
(4,440)
-
-
-
1,600
(4,000)
-
2,400
-
18,000
(18,000)
-
-
25,000
25,000
(17,543)
-
-
49,664
24,000
(13,676)
- (47,234)
30,689
300,000 (188,300)
-
-
9,500
180,000
(83,553)
-
-
-
68,000
(68,000)
-
-





450,003
631,545 (401,512)
(5,907) (43,084)





d Funds is to cover a shortfall in income for the Whitehead prizes.
Contracts represent LMS’s contribution for MARM grant.
eral fund is to cover Society’s staff time to deliver the project since inception.
Balance
at
1.08.21
Other &
Investment
Income
Expenditure
Investment
gain
Transfers
£
£
£
£
£
32,456
49
-
-
-
30,605
46
(1,531)
-
-
20,090
659
(1,500)
(640)
-
53,663
1,760
(1,500)
(1,710)
-
21,308
699
-
(679)
-
-
-
(1,500)
-
1,500
15,959
523
(1,500)
(509)
-
41,403
1,358
(1,500)
(1,319)
-
102,807
3,372
-
(3,276)
-
221
-
-
-
-
29,791
3,245
(9,200)
-
-
-
5,762
(16,000)
-
10,238
-
24,000
(24,000)
-
-
-
25,000
-
-
41,316
38,000
(29,652)
-
-
26,760
160,000 (156,071)
-
-
-
20,000
(10,500)
-
-
-
31,000
(31,000)
-
-





416,379
315,473 (285,454)
(8,133)
11,738




 Balance
at
31.07.23
£
32,780
29,368
16,544
52,734
21,541
-
14,619
40,341
103,931
221
25,419
-
-
32,457
12,754
142,389
105,947
-

631,045

Balance
at
31.07.22
£
32,505
29,120
18,609
52,213
21,328
-
14,473
39,942
102,903
221
23,836
-
-
25,000
49,664
30,689
9,500
-

450,003

The transfer of £1,500 from the General Fund to Restricted Funds is to cover a shortfall in income for the Whitehead prizes.

The transfer of £10,238 from General Fund to Grants and Contracts represent LMS’s contribution for MARM grant.

63

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2023

21. Unrestricted Funds

2023
General Fund:
(see note1(p))
Designated Funds:
a) Building & Development
Reserve Fund
b) Publication
Reserve Fund
c) Grants Payable
Reserve Fund
d) Compositio Fund
e) Global Engagement
Reserve Fund
f)Strategic objectives
Reserve Fund		 Balance
at
01.08.22
£
15,639,501


600,000
3,000,000
14,000
-
-
-

3,614,000

19,253,501
 Income
Expenditure Loss/(gain)
on
investments
£
£
£
2,246,752 (2,148,379) (11,083)



-
-
-
-
-
-
-
(7,000)
-
260,562
(168,929)
-
-
-
-
-
-
-



260,562
(175,929)
-



2,507,314 (2,324,308)
(11,083)


 Actuarial
gains
(losses) on
pension
scheme
£
(61,172)

-
-
-
-
-
-

-

(61,172)
 Transfer
Balance
at
31.07.23
£
£
(15,283) 15,650,336


-
600,000
- 3,000,000
-
7,000
(91,633)
-
100,000
100,000
50,000
50,000


58,367 3,757,000


43,084 19,407,336
2022
General Fund:
(see note1(p))
Designated Funds:
a) Building & Development
Reserve Fund
b) Publication
Reserve Fund
c) Grants Payable
Reserve Fund
d) Compositio Fund
e) COVID-19 Emergency
Fund		 Balance
at
01.08.21
£
15,523,529


600,000
3,000,000
21,000
-

27,251

3,648,251

19,171,780

 Income
Expenditure
i
£
£
2,322,183 (1,799,773)


-
-
-
-
-
(7,000)
285,865
(185,683)
-
(2,333)


285,865
(195,016)


2,608,048 (1,994,789)


Gain/(loss)
on
nvestments
£
(291,813)

-
-
-
-
-

-

(291,813)

 Actuarial
gains
(losses) on
pension
scheme
Transfer
Balance
at
31.07.22
£
£
£
(227,987) 113,362 15,639,501



-
-
600,000
-
- 3,000,000
-
-
14,000
-
(100,182)
-
-
(24,918)
-



-
(125,100) 3,614,000



(227,987)
(11,738) 19,253,501

64

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

22. Analysis of net assets between funds

2023
Fund balances are represented by
Tangible fixed assets
Investments
Current assets
Current liabilities
Long-term liabilities
Total net assets
2022
Fund balances are represented by
Tangible fixed assets
Investments
Current assets
Current liabilities
Long-term liabilities
Total net assets
Grants and Contracts Management account
CMS
Income(IMA/RSS/EdMS/ORS contributions)
Expenditure (including support costs)
LMS’s Contribution to the CMS
MARM
Income from IMU
Expenditure
LMS’s Contribution to the MARM		 Unrestricted funds
General
Designated
£
£
1,106,499
-
13,372,263
3,757,000
2,340,598
-
(670,183)
-
(498,841)
-
15,650,336
3,757,000
Unrestricted funds
General
Designated
£
£
1,157,449
-
13,616,653
3,614,000
2,154,602
-
(851,534)
-
(437,669)
-
15,639,501
3,614,000
2023
£
£
59,366
98,215
(38,849)
1,600
(4,000)
(2,400)		 Restricted
Total
Funds
Funds
£
£
-
1,106,499
249,710
17,378,973
381,335
2,721,933
-
(670,183)
-
(498,841)
631,045
20,038,381
Restricted
Total
Funds
Funds
£
£
-
1,157,449
249,467
17,480,120
200,536
2,355,138
-
(851,534)
-
(437,669)
450,003
19,703,504
2022
£
£
54,419
(87,874)
(33,455)
5,762
(16,000)
(10,238)

23. Grants and Contracts Management account

24. Transactions with Trustees and connected persons

Trustees receive reimbursement only for expenses actually incurred in attending meetings. No remuneration is paid to trustees except as disclosed below. The gross amount that has been reimbursed in respect of attendance of meetings in the period amounted to £4,856 for 13 Trustees (2022: £4,800 for 12 Trustees).

As disclosed in the Trustees’ Report, where grants are awarded to Trustees the payment is always made to the relevant institution.

65

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2023

25. Comparison figures of each fund (2021/22 financial statements)

Notes
Income and endowments:
Donations and legacies
Income from charitable activities:
Membership subscriptions
Publications – LMS Periodicals
7a
Publications – Ventures and Royalties
7c,d
Grants and contracts
22
Total income from charitable activities
Income from other trading activities
3
Income from Investments
2
Other income		 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
17,432
-
243,000



155,158
-
-
1,075,985
-
3,200
313,837
285,865
-
89,919
-
60,763

_______

1,634,899
285,865
63,963
142,861
-
-
523,209
-
8,510
3,782
-
-


 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
17,432
-
243,000



155,158
-
-
1,075,985
-
3,200
313,837
285,865
-
89,919
-
60,763

_______

1,634,899
285,865
63,963
142,861
-
-
523,209
-
8,510
3,782
-
-


 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
17,432
-
243,000



155,158
-
-
1,075,985
-
3,200
313,837
285,865
-
89,919
-
60,763

_______

1,634,899
285,865
63,963
142,861
-
-
523,209
-
8,510
3,782
-
-


 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
17,432
-
243,000



155,158
-
-
1,075,985
-
3,200
313,837
285,865
-
89,919
-
60,763

_______

1,634,899
285,865
63,963
142,861
-
-
523,209
-
8,510
3,782
-
-


 2022
Total
Funds
£
260,432

155,158
1,079,185
599,702
150,682

1,984,727
142,861
531,719
3,782
Total Income 2,322,183 285,865
 315,473 2,923,521
Expenditure:
Costs of raising funds
4
Expenditure on charitable activities:
Advancing the interests of mathematics
5
Enabling mathematicians to undertake research
and collaboration
6
Disseminating mathematical knowledge:
- Costs of publications
7b,c,d
- Conferences and meeting programmes
8
Promoting mathematical research and its benefits
9
Total expenditure on charitable activities
270,512

277,721
438,276
327,745
154,949
330,570

1,529,261
-
__
-
9,333
185,683
-
-

__
195,016
-

9,031
81,500
9,200
-
185,723

285,454
270,512

286,752
529,109
522,628
154,949
516,293

2,009,731
Total expenditure 1,799,773 195,016
 285,454 2,280,243
Net income before gains and losses on investment
Net gains on investment assets
16
Net Income for the year
Transfers between funds
20,21
Actuarial loss on defined benefit
pension schemes
14,19
522,410
(291,813)

230,597
113,362
(227,987)
90,849
-
__
90,849
(125,100)
-
__
30,019
(8,133)

21,886
11,738
-
643,278
(299,946)

343,332
-
(227,987)
Net movement in funds for the year
1		 15,972 (34,251) 33,624 115,345
Reconciliation of funds:
Total funds brought forward
1
 5,523,529
 3,648,251


 416,379 19,588,159
Fund balances carried forward
1		 5,639,501 3,614,000
 450,003
19,703,504


66