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2022-07-31-accounts

London Mathematical Society Report of the Trustees for the period 1 August 2021 – 31 July 2022

INTRODUCTION

At its Annual General Meeting in November 2021, the Society welcomed Professor Ulrike Tillmann as President and said farewell to Professor Jon Keating who piloted the Society so successfully through the worst of the pandemic.

This year, the Society has been delighted to be able to re-establish many of its in-person activities. We have applied the lessons learnt during the pandemic about more effective ways of working while also launching entirely new areas of activity. We have sought to balance the tactical with the strategic, as we recover from the pandemic, deal with the challenges created by current events and plan carefully for the future.

We have returned to our programme of in-person Society meetings and events. We held our first ever ‘hybrid’ Annual General Meeting in November 2021 which was followed by a very successful Annual Dinner. Another highlight of our events calendar was our Society meeting focused on the life and work of Alan Turing — and how this is celebrated in the design of the UK’s new £50 bank note. We held inperson regional meetings in Birmingham and Leeds, we welcomed the 2021 International Mathematical Olympiad team to De Morgan House and, together with the Institute of Mathematics and its Applications (IMA), we held the Crighton medal award event at the Royal Society to honour the achievements of Professor Ken Brown (winner of the 2019 medal) and Professor Caroline Series (winner of the 2021 medal). It was also a pleasure to be able in April to take part in the first in-person Heads of Departments of Mathematical Sciences (HoDoMS) conference for three years.

Work continued this year to ensure that the Society’s finances are on a solid and sustainable footing for the future. Funds were allocated for ‘Covid catch-up’ activities, recognising that there would be costs this year for activities and grants that were postponed during the pandemic, in addition to the costs of the Society’s normal programme of work. While the Society’s conference room business is beginning to show promising signs of recovery, the Society’s income from commercial lettings at De Morgan House has been lower than hoped as the market for central London office space remains difficult. Following key Council decisions last year, the Society also implemented a programme of budget reductions in its 2021-22 financial year. This has ensured that

the balance between the Society’s income and expenditure is maintained, particularly as the income from the Society’s publishing activities reduces due to changes in academic publishing, including the move to open access. A Publications Retreat was held in June to develop the Society’s strategic response to these significant changes in the publishing market.

We are very grateful for the support from our donors both small and large. Two of the Society’s key projects to promote diversity in the mathematical community have benefited from the generosity of our benefactors. Dr Tony Hill, Simon Godwin and the Heilbronn Institute for Mathematical Research (HIMR) together have supported our work on the Levelling Up: Maths online tutorial scheme for A-level mathematics students from under-represented backgrounds. The Liber Foundation has continued to fund the Society’s Emmy Noether Fellowships in 2022 for research mathematicians with caring responsibilities. HIMR has provided additional funding for the Society’s summer schools, undergraduate research bursaries and Early Career Fellowships. XTX Markets continues to fund the Protect Pure Maths (PPM) campaign, founded by the Society to ensure that the mathematical sciences are understood, valued and properly funded and to prevent further cuts to pure mathematics in universities. The Isaac Newton Institute has provided funding for LMS activities that support early career researchers in mathematics and the Society has received a generous bequest from the estate of a Member of the Society towards its work of advancing the development of mathematical knowledge.

In response to the devastating Russian invasion of Ukraine, the Society launched several strands of work in its areas of activity. The Society introduced two grant schemes to support members of the mathematical community who have had to leave their homes and who are seeking refuge in the United Kingdom. These schemes have been made possible thanks to a donation from XTX Markets’ ‘Academic Sanctuaries Fund’ which is supporting students and academics impacted by the war in Ukraine. While the Society reaffirmed its support for all individual mathematicians within the international community, irrespective of nationality, we were clear that collaborations with Russian government institutions or agencies were no longer acceptable or appropriate. The Society welcomed the decision of the International Mathematical Union (IMU) not to hold the 2022 International Congress

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of Mathematicians (ICM) in St Petersburg in summer 2022, as had previously been planned. The Society also ceased its journal exchanges with Russian and Belarusian institutions and has suspended for the time being 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.

Alongside re-establishing a fuller programme of activities following the pandemic and responding to in-year developments, the Society has continued to plan for the future. 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 travel-free alternatives such as online participation - for the Society’s events and lectureships.

In December 2021, the Council for Mathematical Sciences (CMS) consulted on a proposal for a National Academy for Mathematical Sciences, which would focus on external advocacy and enhancing connections across the mathematical sciences community. Following the consultation, the CMS proceeded — with support from CMS members including the Society — to a set-up phase including the appointment of a CEO and President for a proto-

Academy. A ‘go/no go’ decision for the Academy is to be taken within three years. In May 2022, the Society sought the views of its members on these proposals through a membership survey. The survey showed general support for an Academy although a range of specific concerns were raised. The anonymised results of the survey were published in September 2022 and have helped guide the Society’s Council in its discussions of the Academy.

The Protect Pure Maths (PPM) campaign has grown in reach and impact this year. One of its key achievements was the confirmation by the Chancellor in his Spring Statement that tax relief for research and development will be expanded to include research into pure mathematics, something which had previously been explicitly excluded. In May, President Tillmann gave oral evidence to the House of Commons Science and Technology Select Committee on diversity in STEM. The Society is delighted to be working alongside the IMA on the Steering Group of this important campaign.

Lastly, the Society is looking forward to welcoming a new Executive Secretary, Simon Edwards, in November 2022, having said farewell and thank you to the outgoing Executive Secretary, Caroline Wallace, earlier in the year.

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.

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MISSION

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 mathematics through our members and the broader scientific community worldwide.

The Membership

Around 3,100 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. Following feedback from the Society’s network of LMS Reps that tiered Ordinary memberships rates would be welcomed by the mathematical community Council agreed to offer three tiers of Ordinary membership rates from 1 November 2021 onwards. Members who pay the Ordinary membership rate can confirm which membership rate they wish to pay based on whether their annual professional income falls within the following ranges:

The Society does not collect any data on members’ actual professional income nor require proof of earnings. Instead, Ordinary members are asked to advise either via their online member record or the subscription form which tier of Ordinary membership subscription they will be paying.

In 2022, the Society was delighted to elect Professor Jennifer Tour Chayes (University of California, Berkeley, USA) and Professor Vladimir Drinfeld, (University of Chicago, Illinois, USA), as Honorary Members.

2022 Honorary Members Jennifer Tour Chayes and Vladimir Drinfeld

Communications and Engagement

The Society continues to work to the Communications Strategy and Operation Plan agreed in 202021, with Vice-President Cathy Hobbs as the Council member leading on communications matter. As part of the strategy, communications has become a standing item on the agendas of the Society’s Council and key committees, to ensure that newsworthy developments are picked up and shared through the most appropriate communications channels.

Communication with its members and other audiences, including the wider mathematics and STEM communities, policy makers and the general public, is key in ensuring that the Society keeps abreast of the most interesting and exciting developments in mathematics and the mathematicians associated with this work. The Society acknowledges achievements in mathematics through prize-giving, Honorary Memberships and invitations to give lectures.

Effective communication also ensures that the Society can identify the current concerns within the community and can

work to help address them. This year, the Society has continued to work closely with the Protect Pure Maths (PPM) campaign to advance the mathematical sciences in the UK. The campaign has been particularly effective in engaging with media (leading to several letters and

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articles by members of the mathematical community, including the LMS President, being published in the mainstream press) and government. The focus of the campaign’s activities this year has been on asking the Government to both deliver and report on the £300m funding for mathematical sciences research announced in the January 2020 budget. The status of the additional funding was discussed at a Science and Technology (S&T) Select Committee hearing on 15 June. The campaign has also been instrumental in highlighting diversity in STEM to government; in May, the LMS President gave evidence to an S&T Select Committee on the chronic underrepresentation of women at every level of mathematics education. In addition, the campaign is working to secure a parliamentary inquiry on mathematics, ensuring PPM representatives are called to give input, and has taken steps towards its aim to strengthen the business community, particularly AI businesses, to become a stronger voice on the importance of mathematics and investing in mathematical research.

We are grateful for the assistance of the 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 communicates via monthly emails and, from 2022-23 onwards, a biennial LMS Reps Day at which the Society can engage with and obtain feedback from the Reps.

In addition to the LMS Representatives there is also a network of Good Practice Scheme (GPS) Representatives who provide contact points between GPS Supporter departments and the Society. The GPS is a Society initiative which encourages mathematics departments to embed equal opportunities for women within their working practices. There are currently 64 GPS Representatives at departments across the UK. The Society also engages with equality and diversity issues in mathematics more broadly and this work will continue over the coming year.

The regular mid-month LMS e-Update keeps members informed of upcoming events and grant deadlines as well as other Society news, reminders of how to “Maximise Your Membership” and links to recent

articles from journals within the LMS Publications portfolio.

The LMS has an active Twitter account, @LondMathsoc, which is used to advertise Society events and activities, highlight awards and promote news of interest to the mathematical community, as well as share news relevant to its Publications latest updates, such as Issue releases. Since August 2021 the Society’s Twitter account has gained over 3000 new followers, bringing its total number of followers to 23.4K. In order to bring further focus to the LMS library and increase its membership, the Book of the Month initiative was launched, where once a month the Publications Assistant posts photographs and information of a selected work that is part of the Philippa Fawcett collection and to which members have access. The Society continues to be active on YouTube and its account now regularly features recordings from online and hybrid meetings. Finally, the main LMS LinkedIn account was recently reviewed and updated and we are currently working on populating the account with Society news and updates. The UK Women in Mathematics LinkedIn Group has remained constant at around 130 followers.

The Society’s Newsletter continues to function as a central resource for mathematical and Society news and events. In 2021-22, the Newsletter has included mathematical feature articles on a diverse range of topics such as Mathematical Jigsaws, Watson’s Bessel Functions and Guesswork. In May, the Newsletter published its 500th issue, which featured mathematical articles from prominent UK and international mathematicians, as well as recollections from former Editors-in-Chief (from 1973 to the present day) from their time in the role. The Society has undertaken a number of successful collaborations in 2021-22, including with Plus Magazine during the 2022 ICM. Plus Magazine took over the LMS Twitter account on one of the days and live tweeted several of the Fields Medal Lectures. The Society has improved its engagement with other mathematics organisations and now liaises regularly with, for example, the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) to organise mutual promotion of activities.

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2021–22 highlights

2022–23 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.

As well as its publishing activities the Society supports mathematical research by making grants, awarding prizes, maintaining and making available the Society’s Library and through its support for computer science initiatives.

Grants

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

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 schemes the Society has continued to provide support to many mathematicians and their research. In 2021-22 the Society’s Research Grants Committee awarded a total of £275,489 via 118 grants through its core grant schemes which represented a 95% success rate of the 124 applications received under these grant schemes. 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. Three rounds of applications resulted in £4,785 being granted to support 8 researchers to reboot their research. The Research Grants Committee also incorporated the successful online lecture series grant scheme into Scheme 3.

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 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.

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 problem(s) 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 online Summer Schools took place in 2021 and, due to the Covid-19 pandemic, the associated workshops were postponed to 2022:

A further LMS-Bath Mathematical Symposium, with funding from the Isaac Newton Institute, also took place in 2022:

The 73rd British Mathematical Colloquium was held at Kings College London on 6-9 June 2022. This was the first time the event had been held in-person since before the Covid-19 pandemic, and it was a great success. The Society contributed a grant of £20,000 towards the organisation of the Colloquium, and held

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its Society Meeting there on 7 June, where Isabelle Gallagher (École Normale Supérieure) gave a lecture on The Dynamics of Dilute Gases .

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 and its secretariat. The Society also offers travel grants to support attendance of UK-based mathematicians at the European Congress of Mathematics (ECM) and the International Congress of Mathematicians (ICM).

Following discussions at the 2022 IMU General Assembly 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. The Society also agreed to an IMU request that the $20k given over the last four years by the Society to the IMU Special Development Fund for the promotion of mathematics in developing countries be used instead to cover the cost of running ICM 2022 online.

In 2021-22, the Society and the AUB ran a third 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. One Fellowship was awarded in 2022-23 to support visits by Dr Rémi Mokdad Mokdad (University of Burgundy, France) to the Queen Mary, University of London for several months in 2022-23. He also hopes to visit CAMS in Beirut during his tenure. Due to the Covid-19 pandemic, the planned visits by the two previous Atiyah Fellows were postponed from 2021: a visit by Mark Wildon (RHUL) to the AUB, which is planned to take place in Spring 2023, and a visit by Ahmad Sabra of the AUB to the University of Sussex, which took place from June-August 2022.

Through its Scheme with AMMSI, the Society normally supports postgraduate student attendance at mathematical conferences held in Africa. However, there were no applications to the scheme in 2021-22.

In 2021-22, 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 2021-22, the IMU Panel awarded seven Fellowships.

Four partnerships were awarded a 1-year extension on grants under the Mentoring African Research in Mathematics (MARM) programme in 2021-22, and the grant periods for these partnerships end in December 2022. 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: in Cameroon, Congo, Ethiopia, Ghana, Côte d’Ivoire, Kenya, Malawi, Morocco, Nigeria, Rwanda, South Africa, Tanzania and Uganda. The programme continues to inspire a high application rate from both African institutions and potential European partners and the Society hopes that funding for the scheme will continue into the future, for the benefit of mathematics across the two continents.

Through its ICM Travel Grant schemes to support early career researchers and established researchers, the Society awarded 40 grants to support attendance by UK-based mathematicians at the ICM 2022, which was due to be held in St. Petersburg, Russia, in July 2022. The grants for Early Career Mathematicians were to include financial support from EPSRC. However, the ICM 2022 was held as a virtual event, due to the Russian invasion and ongoing war in Ukraine.

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 Christopher Zeeman Medal. The De Morgan Medal, the Society’s premier award, was awarded to Professor Sir John Ball FRS FRSE for his multi-faceted and deep contributions to mathematical research and the mathematical community over many years. The Zeeman Medal was awarded to Dr Simon Singh for his outstanding contributions to public outreach in mathematics. The Society also awarded the Louis Bachelier Prize to Professor Beatrice Acciaio, for her broad contributions to mathematical finance. The Louis Bachelier Prize is awarded jointly with the Natixis Foundation for Quantitative Research and the Société de Mathématiques Appliquées et Industrielles (SMAI). The Society extends warmest congratulations to all prize winners.

Library

The Society’s Library is housed at University College London (UCL). The Library Committee meets annually with representatives from the Science Library at

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UCL to review the Society’s 85 international journal exchange agreements, and to review the services offered by the UCL Library to members of the Society. This year, the Society received a donation from Jane Vaucher, a descendant of Augustus De Morgan, of a portrait of De Morgan which will be displayed in the LMS Members’ Room. Additionally, Sylvia Neumann gifted the Society several papers of her late husband, Dr Peter Neumann, and items that were relevant to his work within the LMS, over the long years of his contribution.

Computer Science

The 2021 Computer Science Colloquium was held on 17 November 2021 with the topic Mathematical Foundations for Machine Learning. The event was held online, via Zoom. Speakers were Benjamin Guedj (UCL

and Inria), Alexandros Hollender (Oxford), Aretha Teckentrup (Edinburgh) and Peter Tino (Birmingham). The event, aimed at PhD students and post-docs, was very successful, with over 100 attendees.

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 18 November 2021 at De Morgan House as a hybrid event. The speaker was Professor Peter Sewell (Cambridge). 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 £1,410 (95% of its allocated budget).

2021–22 highlights

2022–23 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 policy-makers 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 has partnered with XTX Markets, who have generously agreed to fund a campaign to Protect Pure Maths. Working closely with Connect Public Affairs, the campaign focuses 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 successfully targeted the media and parliamentarians with key messages regarding each of these aims.

The LMS Research Policy Committee has continued to seek robust evidence to inform its policy contributions. The Committee is working with the Women in Mathematics and Diversity Committee to request updated benchmarking data from JISC, which will include statistics relating to ethnicity as well as gender. 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 ninth 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 (Science, Engineering, Technology and Mathematics) disciplines and Members of Parliament. It was a welcome return to an in-person event 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 a CMS Board meeting, the British Mathematical Colloquium, an EPSRC meeting on strategic priorities funding and joint meetings with the Institute of Mathematics and its Applications and the Royal Statistical Society, as well as the International Mathematical Union’s General Assembly in Helsinki and the meeting of the European Mathematical Society’s Council in Bled, Slovenia. During the year the President also gave evidence to a hearing of the House of Commons Science and Technology Select Committee, a video clip of which has received a wide viewership.

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 on relevant issues. The new CMS Chair, Professor Alison Etheridge FRS, was appointed in September 2021 for a three-year term.

The CMS represents the mathematical sciences to government, meets regularly with the EPSRC in full) and aims to have similar interaction with UK Research and Innovation (UKRI). The key focus of these meetings has continued to be the additional government funding committed to the mathematical sciences in 2020 and when this is likely to come into effect. The CMS is also a member of the Parliamentary Collaboration Steering Group for STEM learned societies.

The CMS has continued to support the Royal Society Advisory Committee on Mathematics Education (ACME), chaired by Sir Martin Taylor FRS and its oversight of the Mathematical Futures Programme, which aims to build

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a new vision of mathematics education that anticipates and supports the role of mathematics for individuals, economies and society, strengthening diversity and reducing inequity.

The primary focus for the CMS in 2021-22 has been the establishment of a National Academy for Mathematical Sciences. Following the CMS consultation on the National Academy for Mathematical Sciences and Connected Centres Network in December 2021, the CMS Chair convened a Task and Finish Group to consider feedback and propose next steps for a proto academy. This envisages employing an Executive Director and setting up a focused Executive Committee, to be in place by Autumn 2022. A go/no-go decision for the Academy would be taken at the end of the period (two and a half years).

The CMS Societies have agreed that the Operational Research Society (ORS) will become a full member of CMS alongside the Royal Statistical Society (RSS), IMA and LMS, paying an equal annual contribution.

Collaborative working

The Society works actively and collaboratively through its membership of and funding for a number of mathematics and science organisations to ensure the interests of mathematics are represented in national policy and public debates and to ensure 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 UK 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). The Society had previously worked individually with both the Athena Forum (run by the Royal Society) and the STEMM Disability Advisory Committee. In July 2020, the Athena Forum agreed to merge with the STEMM Disability Advisory Committee (STEMM-DAC), with the merger taking effect in January 2021.

This year the Society provided funding for the Royal Society ACME Mathematics Futures Programme.

The Society and the IMA have continued their collaborations throughout the year, including a joint LMS-IMA meeting on Maths in Human Society (bit. ly/3qDzkYA) held online, hosted by ICMS in full),

in September 2021 and the award of the LMS-IMA Zeeman Medal in 2022. A joint award ceremony for the winners of the 2019 and 2021 Crighton Medals (Ken Brown and Caroline Series, respectively) took place in May 2022. A joint award ceremony for the 2020 and 2022 Zeeman Medal winners (Matt Parker and Simon Singh, respectively) is currently being planned for spring 2023. The Society is also working in partnership with the IMA to extend the national Levelling Up: Maths Scheme.

The Society has worked with the ICMS to launch the new UK Undergraduate Mathematics Colloquia. The Society has also engaged with the ICMS and INI in preparing the Call for Institutions to host the LMS Mathematical Symposia from 2026 onwards.

Development Activities

In 2021-22, the Society received a number of notable donations. Dr Tony Hill continued with his 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 five participating universities, including the pilot universities, Durham and Leicester who have been joined by the University of East Anglia, the University of Greenwich and the University of Southampton. Dr Hill has now been joined by co-funder Simon Godwin in supporting this scheme. In addition the Heilbronn Institute for Mathematical Research (HIMR) contributed £10,000 towards this scheme as well as providing funding for Early Careers activities. 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 15.

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 implemented 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, which was previously an issue for some potential donors.

The Society would once again like to thank XTS 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.

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2021–22 highlights

2022–23 plans

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DISSEMINATING MATHEMATICS

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

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 in providing the Society with an income which it utilises entirely in furtherance of its other charitable activities. The broad and developing portfolio of high-quality 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 nine peer-reviewed journals, four of which are in collaboration with other learned societies and institutions, as well as two book series and individual book titles. From 1 July 2022 the Society and IOP Publishing have suspended for the time being the publication of three mathematics journals translated from Russian to English ( Sbornik: Mathematics, Izvestiya: Mathematics and Russian Mathematical Surveys ) which operate in partnership with the Russian Academy of Sciences.

The decision to suspend the publication of the three journals was taken jointly by the Society and the Institute of Physics, after financial sanctions on Russia had made it impossible to fulfil obligations under the contract, and was made in full recognition of the regrettable detrimental effects on the dissemination of mathematics and potential loss of income to the Society.

This year has seen significant work to secure renewed contracts for the publication of some of the Society’s key journals.

A contract was signed with Wiley in September 2021 for the continued publication of the Bulletin, Journal, Proceedings, Transactions, the Journal of Topology and Mathematika for the period 2022-26. This followed a tendering process during which the Society invited bids from academic publishers and carefully reviewed its publishing requirements and ambitions. The terms of

Wiley’s winning bid reflect major changes to publishing. From 2022, the journals are no longer printed and are typeset in a new format and style In addition, the Society has seen a reduction in the income from its publications caused by the continuing move towards more content being published Open Access, which produces lower income per article, and greater access to free content. It is expected that the changing nature of publishing will reduce the Society’s income from its publications in future years. The Society has taken steps to respond to these changes (see ‘Managing the Society Effectively’ below).

From August 2021, all Obituaries in the Bulletin have been made freely available online. 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.

A Publications Strategic Retreat was held in June 2022 bringing together members of Publications Committee, Editors of the LMS journals, representatives of Wiley and other key stakeholders.

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. More than a quarter of all papers in the Society’s hybrid journals were published open access 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 2021-22, the Society was pleased to be able to host some of its meetings as hybrid events, with participation from attendees both remotely and in-person, while other Society Meetings were held online, with support from the host institutions and the ICMS. Meetings during 2021-22

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were the Northern Regional Meeting 2021 (organised by University of Manchester and hosted online by the University of Bielefeld in September 2021, the Joint IMA/LMS Meeting (hosted in September 2021 online by the ICMS), the Black Heroes of Mathematics Conference (in conjunction with the IMA and the BSHM, and hosted in October 2021 online by the ICMS), the Annual General Meeting & Presidential Address (Goodenough College, London and online in November 2021), the South West and South Wales Regional Meeting 2022 (hosted online by the University of Swansea in January 2022), a Society Meeting to celebrate the work of Alan Turing (De Morgan House and online in March 2022), the LMS Midlands Regional Meeting 2022 (University of Birmingham in April 2022), the LMS Hirst Lecture and Society Meeting

Executive Secretary Caroline Wallace and LMS President Jon Keating at the LMS AGM in November 2021

(De Morgan House and online in May 2022), the Northern Regional Meeting 2022 (University of Leeds and online in May 2022), the Society General Meeting & Aitken Lecture (BMA House, London and online in June 2022) and Society Meetings as part of the British Mathematical Colloquium (King’s College London in June 2022) and the virtual International Congress of Mathematicians 2022 (University of Copenhagen in July 2022).

Attendees at the Hirst Lecture and Society Meeting sign the Members’ Book

2021–22 highlights

2022–23 plans

13

into account the evolving scholarly publishing landscape in light of discussions at the Publications Retreat.

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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 recognised increasing concern among the mathematical community regarding career progression, particularly for Early Career Researchers at a time when some universities face

an uncertain financial future in light of the Covid-19 pandemic. To address this immediate concern, the Society 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.

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For undergraduates, there are Undergraduate Research Bursaries (now in their ninth year), Undergraduate Summer Schools, Prospects in Mathematics Meeting and the new International Centre for Mathematical Sciences and London Mathematical Society (ICMSLMS) UK Undergraduate Mathematics Colloquia. In 2021-22:

For postgraduates, there are LMS Research Schools, Cecil King Travel Scholarships to fund study or research abroad and Postgraduate Conference Grants. In 2021-22:

For post-docs and those starting new lecturer positions, there are LMS Early Career Fellowship and Celebrating New Appointment Grants. In 2021-22:

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 2021-22:

Women and Diversity in Mathematics

The Society continues to seek to improve the proportion of women in mathematics, including through activities led by its Committee for Women and Diversity in Mathematics. 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 Committee continues to have as part of its membership representatives from all five constituent mathematical bodies of the CMS as well as from the Standing Committee of European Women in Mathematics, ensuring it speaks for the entire UK

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and wider mathematical community. The Chair of the Committee for Women and Diversity in Mathematics represents the Society on the Athena Forum.

The Society recently amended its By-Laws to dedicate a place on Council specifically to women and diversity. The postholder of the LMS Council role of Member-at-Large (Women and Diversity) now chairs the Committee for Women and Diversity in Mathematics.

The Society operates the LMS Good Practice Scheme,

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. The Society continues to run Good Practice Scheme workshops that aim to cover a wide variety of Good Practice issues. In November 2021 the Society held an online workshop focusing on the Athena SWAN Charter.

2021–22 highlights

2022–23 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 which aim to achieve this.

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), Heads of Departments of Mathematical Sciences (HoDoMS) and the Higher Education Academy (HEA).

Education

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

Over the past year the Society continued to work on the Levelling Up: Maths Scheme, made possible by a generous donation from Dr Tony Hill. The Scheme seeks to widen participation of students from underrepresented backgrounds in mathematics. Working together with the IMA, the scheme is now supporting eight English universities for the second cohort (a further university has committed to join the next tranche) which started in Spring 2022, with the LMS acting as the hub for five of these participating universities. The overall 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.

This year the Society awarded 2 grants under its ‘Mathematics Education Conference Grants’ scheme, totalling £4,000. The scheme provides support to organisers of regular mathematics education conferences and is intended to contribute to the travel/subsistence expenses of attendees of the event in question. The Society also awarded £997 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, 13 awards, totalling £6,300 (100% of the committee’s allocated budget), 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.

The Committee continues to work closely with other

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 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. At the start of the year, 36 mathematics departments across the UK signed up to the TeMaC code of practice and provided the name of a contact in their department to be a TeMaC representative. A networking day for TeMaC representatives was held at De Morgan House on 6 June. The event was an excellent opportunity for representatives to meet each other and discuss the aims of the TeMaC project in more depth. Participants were encouraged to give their ideas about how the project can be most effective. The key themes were summarised in a short document sent after the meeting, and an action plan for the future will be agreed by the TeMaC sub-committee in September 2023.

The Education Committee held the second Mathematics Communication Workshops in July 2022. Two workshops were held, at a beginners’ and an advanced level, over two days. The workshops were limited to 20 attendees and received much positive feedback.

Popularisation

The Society was delighted to be able to hold the Joint LMS/Gresham College Lecture once again, which was presented by Professor Hugh Hunt (Cambridge).

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2021–22 highlights

2022–23 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.

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.

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 12.6 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 continues to update its Data Protection Policy, Privacy Notice and Procedures as new legislation is released. When the UK left the European Union, the Society faced some new obligations in relation to the data of EU citizens that it holds and processes. The Society is very grateful to the European Mathematical Society, which has agreed to act as the Society’s EU GDPR Representative, to help the Society comply with these obligations.

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 normally in advance of their first Council meeting, which includes information on the work of Council, its strategies and plans, the operation of the financial systems, the administration 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; these declarations must be renewed by all Trustees on an annual basis. Staff in management positions also sign an annual Declaration of Interests.

Council met five times in 2021-22: in October and November 2021 and in February, April and July 2022. The Finance & General Purposes Committee met four times: in September 2021 and in January, March and June 2022. The Society holds an Annual General Meeting and a mid-year General Meeting each year; in 2021-22 these were held in November 2021 and July 2022 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.

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.

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.

The Society depends heavily on the unpaid voluntary work of many of its members and others across the

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Financial Review

During the year, the value of the Society’s total assets rose from £19.6m to £19.7m, despite an unrealised loss of £300k in the value of its investments.

In the period 2021-22 income (excluding gains on investment assets) exceeded expenditure by £643k, against an expected budget forecast of £183k deficit. This was mainly due to cost savings and underspends in activities which were largely down to the Coronavirus pandemic. Some meetings and events being moved to a virtual platform has also led to significant cost savings. While fewer in-person activities have meant less expenditure for the Society, the Society deeply regrets that this is because it has provided less support to the mathematics community than it had planned.

and has significant reserves readily available to fund future activities, although the current emergency with inflation is clearly a bigger concern in increasing costs. Given the continuing volatility in the economic climate, the Society will keep under review where resources might best be used to further the Society’s aims.

Despite the surplus, the Society’s conference and venue-hire business in De Morgan House has been one of the hardest hit by the impact of the pandemic.

The sources of income (see Figure 1, above) were:

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 also continues to work on developing new sources of funding.

Publications: 57.4% Investments: 18.2% Conference facilities and rentals: 4.8% Members’ subscriptions: 5.3% Grants and Contracts: 5.2% Advertisements in LMS Newsletter: 0.1% Donations: 8.9% Other: 0.1%

The Society relies largely on subscription income from its journals publishing programme to run its charitable objectives. However, the Society 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 the publications programme. The Society’s Publications Committee keeps the scholarly 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.

Figure 2 (p.23) 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): 12.6% Enabling mathematics (e.g. grants, and training courses): 23.2%

Disseminating mathematics (e.g. publishing, meetings and lectures): 29.7%

Promoting mathematics (e.g. decision/policy makers, education, public, media): 22.6% Other (e.g. conference facilities costs, managing residential properties, Investment management fees): 11.9%.

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

The Society remains in a strong position financially

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

in this report, the Society has taken steps to manage the impact of these changes to its finances. Renewed agreements for the publication of Compositio Mathematica also came into force from January 2022.

Risk management

Ongoing shifts in publishing business models and the transition to open access pose potential risks to the publications programme. The Society’s Publications Committee keeps the scholarly publications landscape under review and looks to propose strategies to minimise losses in income.

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.

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 Restricted Funds, all need continuity of funding. Due to the scale and future risks to academic publishing (a key part of the Society’s income), 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 also as 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.

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 reviewed and removed where appropriate.

The current emergency with inflation is a concern such that the Society’s costs rise excessively.

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. As noted elsewhere in this report, in September 2021 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. As also noted elsewhere

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

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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.

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 would be directly managed by the Society rather than the investment managers. The percentage calculation excludes the value of De Morgan House, though this could be reviewed at any point. Also excluded are any investments made by the investment managers in the property area of asset classes.

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 one-third of its quoted investment is allocated in Responsible/Sustainable funding.

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 recognise that current levels of inflation will likely make it impossible to achieve this goal in the short to medium term.

Due to the change in the investment climate Council agreed to accept a lower than 4% return in order to reduce risks. The drawdown each year, 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: Schroder Charity Multi-Asset Fund and Schroders Responsible 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. The Cazenove/Schroders Charity Multi-Asset Fund (and Responsible Multi-Asset Fund) is a common investment fund 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.

Residential property investments

As a safeguard against fluctuating performance of the stock exchange, the Society expanded its investments portfolio to include residential property and now 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 increase in capital value by at least the rate of inflation.

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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 normal circumstances within De Morgan House. As a result of the Covid-19 pandemic, staff largely worked from home from March 2020 until July 2021. Since July 2021, the lifting of government restrictions has allowed a return to more in-person working at De Morgan House. At the time of writing, staff are working three days a week at De Morgan House and two days a week from home. A list of staff in post during the period is at 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 which 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 full reopened in 202122 following Covid-19 restrictions. Due to space reconfiguration at De Morgan House, more office space is available for commercial tenancies. Room 11 was let in 2021-22, with other spaces being advertised with the Society’s commercial estate agent.

LMS Website

The Society’s website is a key part of its data management infrastructure. Using a Drupal Content Management System, which is 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. In 2021-22, the Society undertook two development projects to expand the operational functionality of the website. In particular, streamlining the processes for assessing grant applications received via the LMS website, thereby saving time for both staff and volunteers, and producing online nomination forms for the LMS Prizes, which will be available to use in 2022-23. There have also been changes to grant application forms to include questions for applicants to consider how they would ensure their activities are environmentally sustainable and, from 2022-23, there will be new questions on the application forms for Conference Grants (Scheme 1) and Joint Research Group grants (Scheme 3) so that applicants can outline how they would manage the hybrid formats of their events (if applicable) and request funding to support these formats.

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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:

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:

Professor Ulrike Tillmann (President)

The trustees are responsible for keeping proper accounting records that disclose with reasonable accuracy at any time the financial position of the

21/10/2022

Date

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ANNEX 1: COUNCIL, EXECUTIVE TEAM AND PROFESSIONAL ADVISERS

Membership of Council during the period 1 August 2021 to 31 July 2022

President: Jon Keating (until November 2021)
Ulrike Tillmann (from November 2021)
Vice-Presidents: Iain Gordon
Cathy Hobbs
Treasurer: Simon Salamon
General Secretary: Robb McDonald
Programme Secretary: Chris Parker
Publications Secretary: John Hunton (until November 2021)
Niall MacKay (from November 2021)
Education Secretary: Kevin Houston
Members-at-Large: Mark McCartney (Librarian) (until November 2021)
Sara Lombardo (Women and Diversity) (from November 2021)
Peter Ashwin
Elaine Crooks
Andrew Dancer
Anne-Christine Davis
Jessica Enright (from November 2021)
Tony Gardiner (until November 2021)
Minhyong Kim
Niall MacKay (until November 2021)
Frank Neumann
Brita Nucinkis
Rachel Newton (from November 2021)
Anne Taormina
Amanda Turner
In attendance: Eugenie Hunsicker (Chair, Committee for Women and Diversity in
Mathematics)
Executive Management Team during the period 1 August 2021 to 31 July 2022
Executive Secretary: Caroline Wallace
Head of Finance and Accounting: Ephrem Abate
Head of Society Business: Lindsay Walsh
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, W1A 2DG
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 2022)

Membership of Committees as at 31 July 2022

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, G. Dales, A. Dancer. J. Rodrigo, C. Roney-Dougal.

Early Career Research Committee: C. Parker (Chair), S. Beheshti, E. Crooks, J. Grbic, H. Johnston, A. Lecuona (ECRCDWM Liaison) R. Newton (Deputy Chair), M. Ptashnyk, S. Roy, I. Short (Climate Working Group Rep), 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: 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: Librarian (Chair), LMS Archivist, I. Falconer, Publications Secretary, S. Hart, A. Rice.

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

Nominating Committee: T. Brendle (Chair), I. D. Abrahams, C. Budd, N. Chamberlain, P. Maini, F. Neumann (Council), B. Pelloni, M. Rees, G. Stallard.

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, A. Teckentrup, D. Vella, M. Wemyss, B. Wingate.

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, 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, K. Brown, A. Caraiani, S. Gutierrez, J. van den Heuvel (HoDoMS), O. Jensen, T. Liverpool, H. Krieger, D. Smith.

Society Lectures and Meetings Committee: B. Nucinkis (Chair), G. Evans, M. Kambites, 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, S. Pumpluen, K. Severn (RSS), C. Smith, M. Sommacal.

29

Sub-Groups, Ad-hoc Committees and LMS appointments as at 31 July 2022

Publications Nominating Group: Publications Secretary (Chair), G. Brown, , M Hairer, J. Maynard (Managing Editor, Journal of the LMS), A. Lazarev (Managing Editor, Bulletin of the LMS, , J. L. Rodrigo (Managing Editor, Transactions of the LMS), R. Sharp, C. Tretter.

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), C. Marr, N. Mazza, C. Smith, 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, H. Fry, C. Roney-Dougal.

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: R. McDonald.

LMS/EMS Newsletter Correspondent: D. Chillingworth.

Election Scrutineers: C. Goldie and C. Lance.

30

ANNEX 3: EXTERNAL REPRESENTATIVES (as at July 2022)

Representatives on external committees and boards as at 31 July 2022

Athena Forum: A. Davis.

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: John 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.

Isaac Newton Institute (INI) Scientific Steering Committee: M. Harris, V. Isham.

Isaac Newton Institute (INI) Correspondent: N. MacKay.

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.

31

ANNEX 4: STAFF

Staff in post in the period 1 August 2021 to 31 July 2022

Executive Secretary’s Office

Executive Secretary: Caroline Wallace PA to the Executive Secretary: Clare Ralphs Head of Finance and Accounting: Ephrem Abate Accounts Assistant: Valeriya Kolesnykova Administrative Editor, LMS Newsletter: Susan Oakes

Publications

Publications Development Manager: Editorial Manager: Publications Assistant:

Suzanne Abbott Ola Törnkvist Georgina Gale (until September 2021) Anna Agathopoulou (from January 2022)

Society Business

Head of Society Business: Lindsay Walsh Membership and Grants Manager: Elizabeth Fisher Society Communications Officer: John Johnston (until December 2021) Society Governance Officer: James Taylor Society Business, Research & Communications Officer: Katherine Wright Grants and Membership Administrator: Lucy Covington

Conferences and Building Group

Head of Conferences and Buildings: Andrew Dorward

32

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.

33

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.

Online Lecture Series (Scheme 3)

The Scheme is to provide support to mathematicians, or groups of mathematicians, delivering online lecture series in mathematics.

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, if they have been prevented from doing so by the adverse conditions of the Covid-19 crisis.

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/ defnition-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.

British Colloquium for Theoretical Computer Science

The Society supports the annual meeting which provides a forum in which researchers in theoretical computer science can meet, present research findings, and discuss developments in the field. Specifically, the Society funds the costs of a speaker who is ordinarily from overseas and who is introduced as the ‘LMS Keynote Lecturer in Discrete Mathematics’.

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.

34

Grace Chisholm Young Fellowship

These fellowships aim 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. Each 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 a 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.

35

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.

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 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.

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.

Young Researchers in Mathematics Conference

The Society provides a grant for the Young Researchers in Mathematics Committee to help support the Young 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. The award will be calculated at £1,200 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.

LMS Early Career Fellowships (Covid-19 Response)

Recognising that one impact of the Covid-19 pandemic on Early Career Researchers is the unexpected turbulence in the job market, to support early career mathematicians in the transition between positions, the London Mathematical Society offers a number of Early Career Fellowships of between 3 and 6 months to mathematicians who have recently or will shortly receive their PhD. The award will be calculated at £1,000 per month and offers no travel allowance. An additional scholarship of approximately £1,000 (dependent on uptake) is also available and funded by the HIMR.

36

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 Masters student, 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 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 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. Two such days will be supported each year. 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. For the first time the London Mathematical Society will also support a Diversity in Mathematics Day in schools. One such day will be supported each year that encourages racially diverse students to become more involved in mathematics. The event will be aimed at school students up to and including A-level or equivalent. Individuals or groups are able to express interest in organising and hosting these events.

37

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 is in the process of rebuilding the investment portfolio and guaranteeing a real return, hence the aim of CPI + 4% as the primary long-term target. In order to maintain its value in real terms, Council considers that the present level of the Relevant Funds should (if possible) be increased to at least £20m by 2025. Despite current economic uncertainty, the Society is on target to achieve that. At present Residential Properties are making a return of 4% through rent.

General Fund

The General Fund 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 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 (operating reserve) as cash at bank to ensure that there is enough working 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 donated funds to be used for specific initiatives and unexpected projects.

The actual level of free reserves consists of the unrestricted net current assets less the liabilities shown in note 22 to the financial statements which amounted to £865,399 at 31 July 2022. This is not significantly in excess of the minimum level of free reserves according to the policy. The trustees will continue to keep the level of unrestricted net current assets under review.

General Fund £15,639,501

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 would be:

the Society’s offces. The agreed purposes and recommended levels as from the next fnancial year would be:
Rehousing and re-establishing the administration for one year should De Morgan House (DMH) to
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

38

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.

satisfactory performance of the project.
Grants awarded and approved byCouncil to bepaid in future accounting periods £14,000
Restricted Funds
Prizes Fund(for Berwick/De Morgan/Lord Rayleigh’s/Fröhlich/Shephardprizes) £208,190
A.J. Cunningham Research Fund(forpublication of work on the factorisation of large numbers £102,903
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		 £23,836
Emmy Noether Fellowship Fund (for those re-establishing their research after a break or ongoing
caringresponsibilities		 £25,000
Levelling Up Scheme Fund (for tutorial of A-level maths students from under-represented
backgrounds)		 £49,664
Campaign for Pure Mathematics Fund (for campaigning to protect and promote pure
mathematics)		 £30,689
SolidarityGrant Fund(for mathematicians who are feeingtheir countries) £9,500
£450,003

39

ANNEX 7: AUDITOR’S REPORT

Opinion

We have audited the financial statements of The London Mathematical Society for the year ended 31 July 2022 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.

40

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 set out on page 27, 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:

41

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

9 Appold Street London EC2A 2AP

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

42

ANNEX 8: STATEMENT OF FINANCIAL ACTIVITIES

Page
44 Statement of fnancial activities
45 Balance sheet
46 Cash fow statement
47 Accounting policies
51 Investment income
52 Income from other tradingactivities
52 Costs of raisingfunds
52 Charitable activities: Advancingthe interests of mathematics
53 Charitable activities: Enablingmathematicians to undertake research and collaboration
54 Charitable activities: Disseminatingmathematical knowledge – Publications
55 Charitable activities: Disseminatingmathematical knowledge – Conference and meeting programmes
55 Charitable activities: Promotingmathematical research and its benefts
56 Governance and other committees’ costs
56 Analysis ofgeneral support andgovernance costs
57 Allocation of support andgovernance costs byactivity
58 Employment costs
59 Pension costs
60 Fixed asset investments
60 Gains and losses on investment assets
61 Tangible fxed assets
61 Debtors
61 Creditors and deferred income
62 Restricted funds
63 Unrestricted funds
64 Analysis of net assets between funds
64 Grants and contracts management account
64 Transactions with Trustees and connectedpersons
65 Comparison figures of each fund(2020/21 financial statements)

43

STATEMENT OF FINANCIAL ACTIVITIES For the year ended 31st July 2022

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
£
£
£
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
 2021
Total
Funds
£
144,236

146,062
1,424,264
649,088
133,449

2,352,863
124,417
502,606
24,969
Total Income 2,322,183
285,865
 315,473 2,923,521 3,149,091
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
9,333
327,745
185,683
154,949
-
330,570
-


__
1,529,261
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
275,867

346,071
682,184
602,193
103,744
354,218
2,088,410
Total expenditure 1,799,773
195,016
 285,454 2,280,243 2,364,277
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
__
522,410
90,849
(291,813)
-

__
230,597
90,849
113,362 (125,100)
(227,987)
-

__
30,019
(8,133)

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

343,332
-
(227,987)
784,814
1,421,884

2,206,698
-
(38,952)
Net movement in funds for the year 115,972
(34,251)		 33,624 115,345 2,167,746
Reconciliation of funds:
Total funds brought forward
1
 5,523,529 3,648,251
416,379 19,588,159 17,420,413
Fund balances carried forward
1		 5,639,501
3,614,000
 450,003
19,703,504
19,588,159


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

44

BALANCE SHEET

as at 31st July 2022

Notes
Fixed Assets
Fixed Asset Investments
Quoted Investment
15a
Residential Property
15b
Tangible Fixed Assets
Leasehold Property
17
Fixtures, Fittings and Equipment
17
Current Assets
Medals in stock
Debtors
18
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		 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
 2021
£
£
12,153,444
3,688,950

15,842,394
1,165,252
37,632
1,202,884

17,045,278
1,531
312,447
3,508,017

3,821,995

962,083
107,349

1,069,432

2,752,563
(209,682)

19,588,159
15,523,529
3,648,251
416,379

19,588,159
 2021
£
£
12,153,444
3,688,950

15,842,394
1,165,252
37,632
1,202,884

17,045,278
1,531
312,447
3,508,017

3,821,995

962,083
107,349

1,069,432

2,752,563
(209,682)

19,588,159
15,523,529
3,648,251
416,379

19,588,159
19,588,159

The notes on pages 47 to 65 form part of these financial statements.

Approved by the trustees on 21 October 2022 and signed on their behalf by:

-------------------------------------------Professor Simon Salamon (Treasurer)

45

Cash Flow Statement

For the year ended 31 July 2022

2022 2021
£ £ £
£
Cash flow from operating activities
Net movements in funds 115,345 2,167,746
Add / (Deduct) gains/(losses) on investments (note 16) 299,946 (1,421,884)
Add back re-invested gains (note 2) 97,110 89,612
Add back investment management fees (note 4) 59,870 53,063
Add back VAT on investment management fees 2,458 2,231
Deduct investment income (note 2) (531,719) (502,606)
Add back depreciation charge (note 17) 62,939 60,783
Decrease / (Increase) in debtors (note 18) 71,072 (168,314)
Decrease / (Increase) in medals in stock 1,531 -
(Decrease)/increase in creditors (note 19) 10,089
 87,723
Net cash provided by operating activities 188,641 368,354
Cash flow from Investing activities
Purchase of tangible fixed assets (note 17) (17,504) (25,623)
Purchase of fixed asset investments (note 15) (2,096,909) (89,612)
Investment income (note 2) 531,719
 502,606
Net cash provided by investing activities (1,582,694)
 387,371
Change in cash and cash equivalent in the year (1,394,053)
 755,725
Cash and cash equivalent at the beginning of the year
Cash in bank and deposit 3,508,017 2,752,292
Cash held in investments 100
 100
3,508,117
 2,752,392
Cash and cash equivalent at the end of the year
Cash in bank and deposit 2,113,763 3,508,017
Cash held in investments 301
 100
2,114,064
 3,508,117

46

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

1. Accounting Policies

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

a) Basis of accounting

The financial statements have been prepared in accordance with Accounting and Reporting by Charities: Statement of Recommended Practice (SORP) applicable to charities preparing their accounts in accordance with the Financial Reporting Standard applicable in the UK and Republic of Ireland (FRS 102) (effective 1 January 2015) and the Charities Act 2011.

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 impact of COVID19 pandemic and the forthcoming reduction in the Society’s income from its publications activities.

In relation to the pandemic, the conference income from De Morgan House continues to be affected. This is partly mitigated by anticipated cost savings due to changes in levels of activity in some areas. For example, it is likely that there will continue to be fewer applications than usual for certain grant schemes 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. 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 and decided on reductions in its budget for this financial year accordingly.

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.

b) Judgements and key sources of estimation uncertainty

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:

47

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

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. During the year new members are allowed to pay pro-rata subscription fees depending on when they are elected during the membership year.

e)

Donations

Cash donations are credited to the General Fund in the year of receipt but donations in kind are not recognised in these financial statements.

f) Investments

• Quoted investments

All quoted investments are valued at their market value at the balance sheet date, giving rise to unrealised gains and losses which are included in the Statement of Financial Activities. The market value is determined as follows:

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.

g) Fixed Assets

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

48

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

1. Accounting Policies (continued)

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. 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

Grants payable out of existing revenues are provided for in full in the accounts. Those payable out of future resources are held in the Grant payable Reserve Fund (see also note ‘1i ’ )

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 are 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.

p) General Fund

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.

49

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

1. Accounting Policies (continued)

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

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.

50

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

t) Employee 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.

2. Investment Income

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

2021
Unrestricted Designated Restricted
£
£
£
a) Investment income receivable:
Total returns/ Unit Trust Distribution
(Bond interest, Equities dividends, etc.)
446,638
-
8,094
Re-invested total returns
(89,612)
-
-



Net investment income receivable
357,026
-
8,094
b) Residential property rental income
135,976
-
-
c) Interest receivable (Treasury Reserve and Bank deposits)
1,367
-
143



Total investment income 2021
494,369
-
8,237		 Total
2022
£
485,486
(97,110)

388,376
142,240
1,103

531,719

Total
2021
£
454,732
(89,612)

365,120
135,976
1,510

502,606

51

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

3.
Income from other trading activities
2022
£
a) DMH Conference facilities
53,520
b) DMH Rental income
86,071
c) Advertising in Newsletter
3,270

Total
142,861

4.
Costs of raising funds
2022
£
£
a)
Conference facilities
General expenditure
15,812
Apportioned support and governance costs
63,825

79,637
b)
Service for tenants
85,590
c)
Investment Management fees
59,870
d)
Residential Investment Property costs
45,415

Total
270,512

5.
Charitable activities: Advancing the interests of Mathematics
2022
£
£
Members’ services:
LMS Newsletter
24,579
Other costs
3,773
Unrecoverable subscriptions
5,219

33,571
Activities to support Women in Mathematics
-
Activities to support Maths -Computer Sciences
464
Library, binding and archives
5,042
EMS, IMU, ICIAM subscriptions & ICM costs
23,928
Prizes
10,381
Apportioned support and governance costs (note 12)
213,366

Total
286,752
2021
£
7,288
112,484
4,645

124,417

2021
£
£
11,030
83,845

94,875
69,831
53,063
58,098

275,867
2021
£
£
23,978
3,222
4,599

31,799
150
-
6,450
13,935
18,122
275,615

346,071

52

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

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

2022
Grant Schemes
£
£
Research Grants (Schemes 1 – 6)
275,489
Early Career Support (Schemes 8 and 9/ECR travel grants)
44,275
Research School Grants(incl. £16k HIMR Fund)
30,000
Prospects in Mathematics Grants
-
Early Career Fellowship Grants(incl. £15k HIMR Fund)
76,900

Undergraduate Bursaries
44,308
Undergraduate Summer School
32,612
Computer Science Grants
1,410
Small Education grants (incl. Teachers CPD)
10,130
Women in Mathematics Grants (Event/Childcare/Diversity)
2,009
Atiyah UK-Lebanon Fellowships
8,000
Isaac Newton Institute (INI) Grants
30,000
ECM/ICM travel Grants
-

555,133
Covid response Fund(Designated)
2,333
Mentoring African Research in Mathematics (MARM)(Restricted)
16,000
Cecil King Grants (Restricted)
24,000
Emmy Noether Fellowship (Restricted)
-
ACME Grants (Designated)
7,000
Solidarity Grants(Restricted)
10,500
Ad hoc Grants to Mathematical Bodies (UK & International)
20,289

Total Grants before cancellation/refunds and Support costs
635,255
Less: Grants cancellation and refunds
(280,613)
Charitable giving of LMS rooms
7,737
Apportioned support and governance costs (note 12)
166,730

Total Grants after cancellation/refunds and Support costs
529,109

2022
ANALYSIS OF GRANT AWARDS
£
a) Grants: contractual commitments
Royal Society (ACME grant)
7,000
b) Other grant awards to institutions
488,610
c) Other grant awards to individuals
139,645

Total grant awards
635,255

_ Grant awards to each institution can be up to a maximum of £35k_
2022
GRANT REFUNDS AND CANCELLATION
£
Grant refunds
(28,059)
Grants not taken up (‘out of date’)
(252,554)

Total grant refunds and cancellation
(280,613

2022
MOVEMENT IN OBLIGATION GRANT COMMITMENTS
£
Grant recognised at the start of the year
540,934
New grants charged to the SoFA in year
635,255
Grants paid during the year
(582,246)
Grants not taken up (‘out of date’)
(252,554)

Amount of grant recognised at the end of the year
341,389**
 2021
£
£
112,512
9,951
45,000
3,500
123,800
48,107
-
4,930
25,342
10,732
3,000
-
4,829

391,703
112,583
-
6,000
22,855
7,000
-
12,133

552,274
(65,623)
-
195,533

682,184
2021
£
7,000
297,620
247,654

552,274
2021
£
(10,288)
(55,335)

(65,623)
2021
£
473,406
552,274
(429,411)
(55,335)

540,934

53

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

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		 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
 2021
£
£
1,424,264
(500)
(6,000)
(20,639)


(27,139)

1,397,125
(358,966)

1,038,159
179,764
83,409
16,527
10,726

290,426
112,920
(10)

112,910
29,664

1,471,159

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

d) Compositio management account


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		 2022
£

285,865
(42,926)
(142,757)

(185,683)

100,182
(39,000)
(61,182)

-
 2021
£
328,998
(43,596)
(172,482)

(216,078)

112,920
(39,000)
(73,920)

-

54

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

8. Charitable activities: Disseminating Mathematical Knowledge

– Conference and meeting programmes

Society meetings and regional workshops
Aitken/Forder Lectures
Invited Lectures
Caring costs for Lecturers visiting UK
Apportioned support and governance costs (note 12)
Total		 2022
£
£
28,407
5,768
14,500
2,807

51,482
103,467

154,949
 2021
£
£
4,130
-
-
-

4,130
99,614

103,744

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
Levelling Up Scheme
Campaign for Pure Mathematics
Apportioned support and governance costs (note 12)
Total		 2022
£
£
25,763
6,394
7,000
8,313
1,770

49,240
2,250
-
5,708

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

516,210
 2021
£
£
15,257
8,479
-
-
2,136

25,872
1,800
905
4,000

6,705
23,684
13,240
284,717

354,218

55

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

10. Governance and other committees’ costs

2022 2021
£
 £
£
 £
Professional services
Solicitors fees 6,805 2,504
Audit and accountancy fees 14,000 13,550
Audit and accountancy fee over accrual 950 774
Other professional fees 35
 35
21,790 16,863
Costs of meetings (Catering/Accommodation/Travel/Subsistence)
Governance(Council/F&GPC/Nomination, etc.) 5,903 94
Other Committees 2,519
 31
8,422 125
Election of Trustees 3,723 3,677
General office and staff costs (apportioned)(note 11_)_ 210,496
 236,373
Total 244,431
 257,038
nalysis of general support and governance costs
Governance and Other general
 Total
2022 Committee related
support		 2022
£ £ £
Staff costs 169,881 818,545 988,426
Office and Premises costs 10,587 42,055 52,642
IT costs 11,918 58,100 70,018
Depreciation 13,811 49,128 62,939
Irrecoverable VAT 4,299 41,971 46,270
Professional services 21,790 - 21,790
Costs of meetings 8,422 - 8,422
Elections of Trustees 3,723
 -
 3,723
Total 2022 244,431
 1,009,799 1,254,230
Governance and Other general
 Total
2021 Committee related
support		 2021
£ £ £
Staff costs 178,303 872,901 1,051,204
Office and Premises costs 27,740 121,559 149,299
IT costs 14,292 74,969 89,261
Depreciation 12,834 47,949 60,783
Irrecoverable VAT 3,204 11,459 14,663
Professional services 16,863 - 16,863
Costs of meetings 125 - 125
Elections of Trustees 3,677
 -
 3,677
Total 2021 257,038
 1,128,837 1,385,875

11. Analysis of general support and governance costs

56

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

12. Allocation of support and governance costs by activity

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
2021
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 2021		 Direct
Staff
£
25,779
8,593
8,593
42,965
97,076
80,822
187,335
33,346
166,020
564,599
607,564

Direct
Staff
£
25,140
24,770
16,227
66,137
113,716
76,832
197,509
23,565
155,261
566,883
633,020		 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



General
Office
General
Management
and Finance
Governance
and
Committee
£
£
£
47,030
11,214
461
39,003
1,834
461
3,293
1,536
461



89,326
14,584
1,383



57,436
53,332
51,131
28,139
39,431
51,131
53,833
56,493
51,131
5,830
19,088
51,131
38,926
39,399
51,131



184,164
207,743
255,655



273,490
222,327
257,038

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.

57

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

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		 2022
2021
£
£
711,962
782,856
18,360
20,827
82,595
87,819
(4,000)
-
142,724
152,379
951,641
1,043,881

The total employment costs (Salaries/NIC /Pension) for the Executive Management Team amounted to £399,502 (2021: £393,595). 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:

2022 2021
No. No.
£60,000 - £70,000 2 2
£70,000 - £80,000 1 1
£90,000 - £100,000 - 1
£100,000 - £110,000 1 -

The pension payments for the above members of staff amounted to £63,958 (2021: £61,611). 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		 2021/2022
Total
FTE
12.8
10.5
2.8
2.8


15.6
13.3

 2020/2021
Total
FTE
14.8
12.4
3.0
3.0


17.8
15.4

58

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

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 profit and loss account 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 profit and loss account.

The total movement to the profit & loss account is a loss of £227,987 (2021: loss of £38,952) as shown in note19.

The latest available complete actuarial valuation of the Retirement Income Builder is as at 31 March 2020 (the valuation date), and was carried out using the projected unit method.

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.

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
current life expectancies on retirement at age 65 are:
2022 2021
Males currently aged 65 (years) 23.9 24.6
Females currently aged 65 (years) 25.5 26.1
Males currently aged 45 (years) 25.9 26.6
Females currently aged 45 (years) 27.3 27.9

The current life expectancies on retirement at age 65 are:

A new deficit recovery plan was put in place as part of the 2018 valuation, which requires payment of 2% of salaries over the period 1 October 2019 to 30 September 2021 at which point the rate will increase to 6%. The 2021 deficit recovery liability reflects this plan. The liability figures have been produced using the following assumptions:


umptions:
2022 2021
Discount rate 2.59% 2.59%
Pensionable salary growth 1% 1%

59

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

15. Fixed Asset Investments

ixed Asset Investments
2022 2021
£ £ £ £
a) Quoted investments
Investment Investment Total Total
Assets Assets
in the UK outside the
UK
Total Market value at 31st July 2022 1,535,619
 12,230,551
13,766,170		 12,153,444
In the prior year, £2,309,154 of investment assets were in the UK with the remaining £9,844,290 being outside the UK.
Reconciliation of opening & closing market values: £ £
Market value at 1stAugust 2021 12,153,444 10,878,904
Additions at cost 2,096,909 89,612
Unrealised (losses)/gains (note 16a) (324,946) 1,329,834
Movement in cash (159,237) (144,906)
Total Market value at 31st July 2021 13,766,170
 12,153,444
Analysis by Fund:
Restricted Funds 249,467 255,230
Unrestricted Funds 13,516,703 11,898,214
The investments are entirely invested in the Schroder/Cazenove [68% in ordinary Charities Multi-Asset
Fund (CMAF) and 32% in Responsible Multi-Asset Fund (RMAF)] [Prior year: 100% in CMAF)
b) Residential Property investments 2022
 2021
£
 £
Market value at 31st July 2022 3,713,950 3,688,950
Reconciliation of opening and closing market values:
Market value at 1st August 2021 3,688,950 3,596,900
Unrealised gains (note 16b) 25,000
 92,050
Total Market value at 31st July 2022 3,713,950 3,688,950

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

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)

2021
Unrestricted
funds

£
a. Unrealised gains in market value ofQuoted investments
1,303,759
b. Unrealised gains in market value ofResidential Properties
92,050

Total gains
1,395,809
 Restricted
funds
£
(8,133)
-

(8,133)
Restricted
funds
£
26,075
-

26,075		 Total
£
(324,946)
25,000

(299,946)
Total
£
1,329,834
92,050

1,421,884

60

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

17. Tangible Fixed Assets Leasehold Fixtures Total
Property Fittings and
Equipment
£ £ £
Cost
Brought forward at 1st August 2021 2,175,353 191,560 2,366,913
Additions - 17,504 17,504
Disposal Adjustment -
 (40,069)
 (40,069)
Carried forward at 31st July 2022 2,175,353
 168,995
 2,344,348
Depreciation
Brought forward at 1stAugust 2021 1,010,101 153,928 1,164,029
Charge for the year 44,817 18,122 62,939
Disposal Adjustment -
 (40,069)
 (40,069)
Carried forward at 31st July 2022 1,054,918
 131,981
 1,186,899
Net book value
At 31st July 2022 1,120,435
 37,014 1,157,449
At 31stJuly 2021 1,165,252
 37,632 1,202,884
• Part of the leasehold property is let out and the rental derived is shown on the SOFA under ‘Activities for Generating Funds’.
18. Debtors 2022 2021
£ £
Publications 135,535 219,165
Conference facilities 10,356 980
Other debtors 55,918 54,989
Gift-aid receivable - 500
Prepayments and accrued interest 39,566
 36,813
241,375
 312,447
19. Creditors and Deferred Income 2022 2021
£ £
Creditors: amounts falling due within one year
Accruals 38,650 37,861
Grant creditors 341,389 540,934
Taxation and other Social Security creditors 66,118 82,305
Other creditors 357,490
 300,983
803,647
 962,083
Deferred income:
Unexpired publications’ subscriptions:
Balance brought forward 107,349 138,382
Amount released in year (107,349) (138,382)
Income deferred to future years 47,887
 107,349
Balance carried forward 47,887
 107,349
Creditors: amounts falling due after more than one year
Brought Forward Pension Provision 209,682 170,730
Movement 227,987
 38,952
Carried Forward Pension Provision 437,669
 209,682

61

NOTES TO THE FINANCIAL STATEMENTS

For the year ended 31st July 2022

20. Restricted Funds

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
•
The transfer of £1,500 from the General Fund to Restricte
•
The transfer of £10,238 from General Fund to Grants and
2021
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
HIMR Fund
Total Funds		 Balance
at
1.08.21
Other &
Investment
Income
Expenditure
Investment
loss
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

d Funds is to cover a shortfall in income for the Whitehead prizes.
Contracts represent LMS’s contribution for MARM grant.
Balance
at
1.08.20
Other &
Investment
Income
Expenditure
Investment
gain
Transfers
£
£
£
£
£
32,407
49
-
-
-
30,559
46
-
-
-
18,716
681
(1,500)
2,193
-
46,521
1,692
-
5,450
-
18,472
672
-
2,164
-
-
-
(10,500)
-
10,500
13,835
503
-
1,621
-
35,893
1,305
-
4,205
-
89,124
3,241
-
10,442
-
221
-
-
-
-
32,542
3,249
(6,000)
-
-
-
-
-
-
-
-
6,000
(6,000)
-
-
-
25,000
(22,855)
-
(2,145)
-
65,000
(23,684)
-
-
-
40,000
(13,240)
-
-
-
74,834
(74,834)
-
-





318,290
222,272 (158,613)
26,075
8,355		 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
Balance
at
31.07.21
£
32,456
30,605
20,090
53,663
21,308
-
15,959
41,403
102,807
221
29,791
-
-
-
41,316
26,760
-

416,379

62

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

21. Unrestricted Funds

d. The transfer of £100,182 from the
e. The transfer of £24,918 from COVID
2021
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
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		 Compositio Fund to General Fund represents the management fee and the LMS’s profit share relating
-19 Emergency Fund to General Fund represents the closure of COVID-19 Emergency Fund
Balance
at
01.08.20
Income
Expenditure Gain/(loss)
on
investments
Actuarial
gains
(losses) on
pension
scheme
Transfer
£
£
£
£
£
£
13,156,123 2,597,821 (1,889,837) 1,395,809
(38,952)
302,565







600,000
-
-
-
-
-
3,000,000
-
-
-
-
-
226,000
-
(7,000)
-
-
(198,000)
-
328,998
(216,078)
-
-
(112,920)

120,000
-
(92,749)
-
-
-






3,946,000
328,998
(315,827)
-
-
(310,920)






17,102,123
2,926,819 (2,205,664) 1,395,809
(38,952)
(8,355)






Balance
at
01.08.21
Income
Expenditure Loss/(gain)
on
investments
Actuarial
gains
(losses) on
pension
scheme
Transfer
£
£
£
£
£
£
15,523,529 2,322,183 (1,799,773) (291,813)
(227,987) 115,972







600,000
-
-
-
-
-
3,000,000
-
-
-
-
-
21,000
-
(7,000)
-
-
-
-
285,865
(185,683)
-
-
(100,182)

27,251
-
(2,333)
-
-
(24,918)






3,648,251
285,865
(195,016)
-
-
(125,100)






19,171,780 2,608,048 (1,994,789) (291,813)
(227,987)(11,738)

to the journal.
Balance
at
31.07.21
£
15,523,529

600,000
3,000,000
21,000
-
27,251

3,648,251

19,171,780

Balance
at
31.07.22
£
15,639,501

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

3,614,000

19,253,501

c) The transfer of £198,000 from Grant Payable Fund to General Fund represent that LMS is no longer providing grant for INI/ICMS reflecting that INI/ICMS are receiving other source of funding available for them. The Society and INI/ICMS will continue collaborate an activity for Mathematics community.

63

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

22. Analysis of net assets between funds

23.


2022
Fund balances are represented by
Tangible fixed assets
Investments
Current assets
Current liabilities
Long-term liabilities
Total net assets

2021
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
£
£
1,157,449
-
13,616,653
3,614,000
2,154,602
-
(851,534)
-
(437,669)
-


15,639,501
3,614,000

Unrestricted funds
General
Designated
£
£
1,202,884
-
11,966,164
3,621,000
3,633,595
27,251
(1,069,432)
-
(209,682)
-


15,523,529
3,648,251

2022
£
£
54,419
(87,874)

(33,455)
5,762
(16,000)

(10,238)		 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
Restricted
Total
Funds
Funds
£
£
-
1,202,884
255,230
15,842,394
161,149
3,821,995
-
(1,069,432)
-
(209,682)


416,379
19,588,159
2021
£
£
47,415
(83,001)

(35,586)
-
-

-

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 £4,800 for 12 Trustees (2021: £7 for 1 Trustee).

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

64

NOTES TO THE FINANCIAL STATEMENTS For the year ended 31st July 2022

25. Comparison figures of each fund (2020/21 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
£
£
£
14,236
-
130,000


146,062
-
-
1,421,064
-
3,200
320,090
328,998
-
52,615
-
80,834


1,939,831
328,998
84,034
124,417
-
-
494,368
-
8,238
24,969
-
-

 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
14,236
-
130,000


146,062
-
-
1,421,064
-
3,200
320,090
328,998
-
52,615
-
80,834


1,939,831
328,998
84,034
124,417
-
-
494,368
-
8,238
24,969
-
-

 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
14,236
-
130,000


146,062
-
-
1,421,064
-
3,200
320,090
328,998
-
52,615
-
80,834


1,939,831
328,998
84,034
124,417
-
-
494,368
-
8,238
24,969
-
-

 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
14,236
-
130,000


146,062
-
-
1,421,064
-
3,200
320,090
328,998
-
52,615
-
80,834


1,939,831
328,998
84,034
124,417
-
-
494,368
-
8,238
24,969
-
-

 2021
Total
Funds
£
144,236

146,062
1,424,264
649,088
133,449

2,352,863
124,417
502,606
24,969
Total Income 2,597,821 328,998
 222,272 3,149,091
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
275,867

334,071
478,746
380,115
103,744
317,294

1,613,970
 -
-
99,749

216,078
-
-
315,827
-

12,000
103,689
6,000
-
36,924

158,613
275,867

346,071
682,184
602,193
103,744
354,218

2,088,410
Total expenditure 1,889,837 315,827
 158,613 2,364,277
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
707,984
1,395,809

2,103,793
302,565
(38,952)
 13,171
-
13,171
(310,920)
-
63,659
26,075

89,734
8,355
-
784,814
1,421,884

2,206,698
-
(38,952)
Net movement in funds for the year
2		 ,367,406 (297,749) 98,089 2,167,746

Reconciliation of funds:
Total funds brought forward
1
3,156,123
 3,946,000

318,290 17,420,413
Fund balances carried forward
1		 5,523,529 3,648,251
 416,379
19,588,159

65