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2021-07-31-accounts

London Mathematical Society Report for the Trustees for the period 1 August 2020 – 31 July 2021

INTRODUCTION

While the pandemic has continued to have a profound impact on the Society this year, it has also obliged us to find new and creative ways of pursuing the Society’s charitable objectives. We have, amongst many other things, launched new grants, run numerous online meetings and events, participated virtually in major international conferences and successfully developed an on-line A-level mathematics tutoring programme.

We are now, we hope, entering a period of rebuilding following the pandemic. But we also want to carry forward the lessons we have learnt about new ways of working. For example, we now know that online and hybrid online/in person meetings can be effective and make better use of everyone’s time. They are also cheaper, more inclusive and more environmentally friendly. This year, the Society adopted an environmental policy statement and the Society’s Council has made it clear that the Society should be a leader in the mathematics community in relation to sustainability.

We are also pleased that we have been able to launch new areas of activity during the pandemic. With the generous support of Dr Tony Hill, and in conjunction with Durham University and the University of Leicester, we have launched the Levelling Up tutoring programme for A-level mathematics students from under-represented backgrounds. We helped plan and deliver the first ‘Black Heroes of Mathematics’ conference in conjunction with the Institute of Mathematics and its Applications and the British Society for the History of Mathematics. This conference was held online and our aim is that this will be a regular event. We are delighted that another ‘Black Heroes of Mathematics’ conference is already scheduled for the coming year.

We have extended existing grant schemes, and developed new grant schemes, to help the mathematical community deal with the impact of the pandemic. This includes awarding extra Early Career Fellowships, offering additional funding to Research Groups for producing online lectures and creating our Research Reboot grants to allow individual researchers to focus again on their research. We’ve also tried to help the community in other practical ways, such as by extending the deadline for nominations for our prizes at the start of the year, and by developing a list of other non-LMS sources of funding on our website.

This year has seen a major programme of work to renew the Society’s contracts for publication of our

core journals and one of our partner journals. This work has confirmed that the academic publishing market is being transformed by the drive towards open access. As a result, the Society must now adapt to significant changes in our income from our publishing activities. While expenditure has also reduced during the pandemic, with fewer in person events and less travel, we are going to have to keep managing our finances closely going forwards. The pandemic has forced us to identify and focus on our priorities, which will help us greatly as we adjust to our new financial situation.

Over the course of its history, the Society has benefited from a number of very generous donations and we are delighted and grateful that this continues today. Among a number of significant gifts from donors this year, AEL Davies, a long time Member and supporter of the Society, has bequeathed to the Society her copy of the rare book of astronomical tables Urania Propitia by Maria Cunitz. Urania Propitia was published in 1650 and fewer than 25 physical copies are known to exist. The Society was also recognised this year by the Bank of England for its assistance in the development of the new £50 Alan Turing banknote, which went into circulation in June. The Bank of England presented the Society with one of the new banknotes from its first manufacturing run. The Society’s note has a low serial number of AA01 001936, referencing the year of publication in the Proceedings of the London Mathematical Society of Turing’s paper from which the mathematical formula and tables on the banknote were taken. We plan events in the coming year to celebrate the arrival of these treasures at the Society.

One thread that links many areas of the Society’s work is the importance of diversity and inclusion in mathematics. From grant schemes that aim to support those with caring responsibilities, to tutorial programmes for A-level students from underrepresented backgrounds, to celebrations of profound contributions to mathematical knowledge from across the mathematical community, the Society is committed to ensuring that mathematics is open to everyone.

It is of course only possible in this brief introduction to highlight a small number of the Society’s activities and achievements this year. A fuller description of the work of the Society in 2020–21 follows. Further information about the Society’s work can be found on its website.

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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 at a wide variety of different career stages and from around the world. In 2020–21, the Society signed two new Reciprocity Agreements: one with the Allahabad Mathematical Society and one with the Indonesian Mathematical Society. Such agreements allow full members of either Society to join the other Society at a reduced cost, provided that the members normally reside outside the country of the Society to which they pay reduced fees. Approximately 20% of the Society’s members are based outside the UK and the membership is drawn from over 60 different countries.

In 2021, the Society was delighted to elect Professor Ngô B ả o Châu, (University of Chicago, USA, and Vietnam Institute for Advanced Study in Mathematics), Professor Laure Saint-Raymond, (Institut des Hautes Études Scientifiques (IHES), France), Professor Peter Sarnak, (Institute of Advanced Study, Princeton, USA) and Professor Ya-xiang Yuan, (Chinese Academy of Sciences in Beijing, China) as Honorary Members.

(clockwise from top left) LMS Honorary Members Ngô B ả o Châu, Laure Saint-Raymond, Ya-xiang Yuan and Peter Sarnak.

developments are picked up and shared through the most appropriate communications channels.

Communication with its members and with other audiences including the wider mathematics and STEM community, policy makers and the public as a whole 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.

Communications and Engagement

This year, the Society agreed a Communications Strategy and Operational Plan and it appointed a Council member to lead on communications matters. As part of the Strategy, communications has become a standing item on the agendas of the Society’s key Committees, to ensure that newsworthy

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 made a number of public statements including on the proposed reduction in the size of the Pure Mathematics Group at the University

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of Leicester and on the conviction and violation of the human rights of Russian mathematician Azat Miftakhov. As a result of the changes at the University of Leicester, the Society collaborated in the foundation of the Protect Pure Maths campaign, one of the aims of which is to protect pure mathematics departments from further significant cuts.

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 65 LMS Representatives with whom the Society communicates via monthly emails and an annual LMS Reps Day at which the Society can engage with and obtain feedback from the Reps. The 2021 LMS Reps’ Day took place online. The discussions highlighted the need for the Society to support as many opportunities for networking face-to-face as possible, and to prioritise schemes that promote retention and that help early career researchers.

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 61 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.

In 2020–21, the Society began to publish in the LMS Newsletter a series of ‘Maximising Your Membership Benefits’ articles. These aim to highlight the benefits to LMS members so that they can make the most of their membership.

The LMS has three active Twitter accounts, @LondMathsoc, @womeninmaths and @DeMorganHouse. The combined number of followers for the past year has increased to over 35,700. The Society’s YouTube Channel subscriptions have risen to over 9,300. The Covid-19 pandemic afforded the Society the opportunity to record lectures online through video conferencing packages and to provide a more varied content stream for the Society’s YouTube Channel. Recent lectures include the Scheme 3 online lectures, 2021 Popular Lectures and the 2021 General Meeting Lecture presented by Professor Emily Riehl (Johns Hopkins University). 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 2020-21, the Newsletter has included mathematical feature articles on a diverse range of topics such as Pólya Urns, Penrose’s Incompleteness Theorem and Floating-Point Arithmetic. A new regular feature by Nick Trefethen, ‘Notes of a Numerical Analyst’, was introduced. The Editor-in-Chief, Eleanor Lingham, stepped down in July 2021 and was succeeded by Alina Vdovina.

2020 –21 highlights

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2021–22 plans

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SUPPORTING MATHEMATICS RESEARCH

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

The Society supports mathematical research by making grants, awarding prizes, maintaining and making available the Society’s Library and through its support and funding for computer science initiatives.

in Autumn 2020 and published on the Society’s YouTube Channel. These lectures were given by early career researchers who were part of Joint Research Groups but did not have permanent positions, and were aimed at new PhD students starting in September 2020.

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. The Society’s 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 2020–21 the Society’s Research Grants Committee awarded a total of £112.6k to 78 grants via its core grant schemes and supported 95% of the 82 applications received under these grant schemes. As part of the Society’s response to the pandemic, the Research Grants Committee enhanced 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 introduction of the Research Reboot Scheme. Two rounds of applications resulted in £13,989 being granted to support 29 researchers to reboot their research.

Meanwhile, the recordings for the online lecture series — supported by grants in 2019–20 — were received

Formerly known as the LMS–Durham Symposia, the first LMS–Bath Mathematical Symposium was held online in August 2020 on the subject of Mathematics and Machine Learning , and the symposium programme will continue until 2025. The Symposia are an established and recognised series of international research meetings, since their foundation in 1974, that 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 symposia is that they will be complemented by a summer school, to prepare young researchers such as PhD students, or a “research incubator”, 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. Due to the Covid-19 pandemic, the associated workshops have been postponed.

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 organisotion’ to the IMU, through the International Affairs Committee and its secretariat. The

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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).

In 2020–21, the Society and the AUB ran a second 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 2021–22 to support visits by Maciej Dunajski (Cambridge) to the Center for Advanced Mathematical Sciences at the AUB and to Notre Dame University-Louaize. 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 and a visit by Ahmad Sabra of the AUB to the University of Sussex.

Through its Scheme with AMMSI, the Society normally supports postgraduate student attendance at mathematical conferences held in Africa. However, social distancing and lockdown measures across the continent due to Covid-19 resulted in fewer conferences and no applications to the scheme in 2020–21.

In 2020–21, 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. Three awards are made each year.

Four partnerships were awarded grants under the Mentoring African Research in Mathematics (MARM) programme in 2019-20, and the grant periods for these partnerships began in December 2020. 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 ECM Travel Grant schemes to support early career researchers and established researchers, the Society awarded 13 grants to support attendance by UK-based mathematicians at the 8ECM in June 2021, which was held as a hybrid event, having been postponed from 2020 due to the Covid-19 pandemic.

Prizes

The Society awarded a number of LMS Prizes this year, as well as working in partnership with the Institute of Mathematics and its Applications (IMA) to award the IMA-LMS David Crighton Medal. The Pólya Prize, the highest LMS prize given this year and which is in recognition of outstanding creativity in, imaginative exposition of, or distinguished contribution to mathematics in the UK, was awarded to Professor Ehud Hrushovski for his profound insights which transformed very abstract model-theoretic ideas into powerful methods in well-established classical areas of geometry and algebra. The Crighton Medal was awarded to Caroline Series in recognition of her fundamental and beautiful results connecting geometry and dynamical systems, and her outstanding service to the mathematical community. The Society also awarded the Hirst Prize and Lectureship to Professor Karine Chemla, in recognition of her outstanding work in the history of mathematics. This is now awarded as a joint prize with the British Society for the History of Mathematics. 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 UCL to review the Society’s 96 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 AEL Davies of a copy of Urania Propitia and the gift of a low serial number Turing £50 bank note from the Bank of England (see Introduction). The Society also received two donations to the Hardy Collection from the late Peter Neumann: Jordan’s Traité des Substitutions and Cayley’s Memoir on Quantics .

The low serial number Turing £50 bank note donated by the Bank of England

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Computer Science

The 2020 Computer Science Colloquium was held on 19 November 2020 with the topic Algorithms, Complexity and Logic. The event was held online, via Zoom. Speakers were Anupam Das, Nobuko Yoshida, Kitty Meeks and Igor Carboni Oliveira. The event, aimed at PhD students and post-docs, was very successful, with over 100 attendees.

The LMS/BCS–FACS (British Computer SocietyFormal Aspects of Computing Science) Evening Seminar, held in collaboration with the FACS Specialist Group, would have taken place in November 2020, but was postponed to the following year owing to Covid-19. The Society also normally supports the British Colloquium for Theoretical Computer Science (BCTCS) by funding the costs of an overseas speaker. However, as the event took place online, there were no speaker costs and the grant was withdrawn.

The LMS Computer Science Committee has this year continued its work on Impact Acceleration Papers. This is an initiative coordinated jointly by the Industrial Mathematics Knowledge Transfer Network (IM-KTN) and the Society. The committee commissioned two Impact Acceleration Papers in 2019–20, with the current expectation that they will be published in late 2021–22. Impact Acceleration Papers address areas where mathematics and computing have come together to provide significant new capability that is on the cusp of mainstream industrial uptake.

The Computer Science Committee awarded five Scheme 7 grants to facilitate collaborations in research at the interface of mathematics and computer science, to a total of £4,930.

2020 –21 highlights

2021–22 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 LMS Research Policy Committee has continued to seek robust evidence to inform its policy contributions. In 2020-21 the LMS ‘Evidence Bank’ was published on the LMS website and the Committee is currently consulting with other societies and HoDoMS regarding additional data to be included in it. The guidance document on Care for PhD Students was completed and the document will be distributed in autumn 2021. The Committee is working with the Women and Diversity in Mathematics Committee to request updated benchmarking data from HESA, which will include statistics relating to ethnicity as well as gender. Finally, the Committee continues to cultivate its relationship with 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 eighth 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, Technology, Engineering and Mathematics) disciplines and Members of Parliament. The event is normally held at the House of Commons, but this year was held very successfully online.

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. 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.

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 CMS represents the mathematical sciences to government, in particular to the Department for Business, Energy and Industrial Strategy (BEIS). It meets regularly with the EPSRC and aims to have similar interaction with UK Research and Innovation (UKRI). The key focus of these meetings this year has been the additional government funding for the mathematical sciences announced in 2020, and how CMS members can help ensure its effective use. 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), currently chaired by Sir Martin Taylor FRS. The four ‘contact groups’, based within the Royal Society governance structure and reporting directly to ACME, continue to work well. In addition, The Mathematical Futures Programme, launched in February 2020 and overseen by ACME, continues and aims to deliver a range of outputs between Autumn 2021 and Spring 2022.

The CMS Chair, Professor Sir Ian Diamond, who was appointed as National Statistician in October 2019, continued to promote the fundamental value of the mathematical sciences to government and its funding agencies, despite significant calls on his time due to the Covid-19 pandemic. A Big Mathematics Initiative (BMI) virtual event entitled An Academy for Mathematical

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Sciences was held, which brought together over 250 members of the mathematical community to discuss the role and mission of an Academy. A small working group is taking this work forward with the aim of producing a green paper by autumn 2021 for consultation and feedback.

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 Contact Groups.

The Society and the IMA have continued their collaborations throughout the year, including a joint LMS–IMA meeting on Topological Methods in Data Science held online, hosted by ICMS, in October 2020 and the award of the LMS–IMA Crighton Medal in 2021. The award ceremonies for the 2019 Crighton Medal winner, Professor Ken Brown, and the 2020 LMS–IMA Zeeman Medal winner, Matt Parker, are currently postponed until they can be held in person.

Development Activities

In 2020–21, the Society received a number of notable donations. Dr Tony Hill has continued with his generous donation enabling the establishment of the Levelling Up pilot scheme which went live in March 2021 (further details can be found under ‘Education’ on page 18) and the Heilbronn Institute for Mathematical Research (HIMR) contributed £20,000 towards the Early Career Fellowships (Round 2). Five members and friends of the Society have each donated at least £1,865 through De Morgan Donation scheme: Professor M. Bridson & Dr J.L. Bridson, Dr. C. Houghton, Professor Sir J.F. Kingman FRS, Professor Dame F.C. Kirwan FRS and Dr K. Mori.

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.

2020 –21 highlights

2021–22 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 currently publishes 12 peerreviewed journals, seven of which are in collaboration with other learned societies and institutions, as well as two book series and individual book titles.

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 highquality journals and books serve our authors through transparent, timely and professionally managed editorial and production processes, and serve our readers by providing content of wide interest and high quality. The Society seeks to maintain sustainable and ethical pricing for its publications, including the offer of free online access to LMS members and institutions in developing countries.

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

In October 2020, the LMS signed new contracts with the Russian Academy of Sciences and Institute of Physics Publishing for the continued publication of the translated Russian journals Sbornik: Mathematics, Izvestiya: Mathematics and Russian Mathematical Surveys until the end of 2025.

A Memorandum of Understanding was signed with Wiley in December 2020 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

will become electronic only. In addition, the move towards more content being published Open Access, which produces lower income per article, and greater access to free content will reduce the Society’s income from its publications in the future. The Society has taken steps to respond to these changes (see ‘Managing the Society Effectively’ below).

A Letter of Intent from Cambridge University Press for the continued publication of Compositio Mathematica during 2022–26 was received and countersigned by the LMS in May 2021.

More broadly, other developments included:

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 2020–21, for the first time all Society Meetings were held online, with support from the host

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institutions and the ICMS. Meetings during 2020–21 were the Joint IMA/LMS Meeting, the Black Heroes of Mathematics Conference (in conjunction with the IMA and the BSHM), the LMS Spitalfields History of Mathematics Meeting, the LMS Mary Cartwright Lecture, the LMS Midlands Regional Meeting (University of Lincoln), the Society General Meeting and Society Meetings as part of the Joint Mathematics Meeting 2021, the British Mathematical Colloquium/British Applied Mathematics Colloquium 2021 and the 8th European Congress of Mathematics.

Lockdown restrictions continued into 2021 and as mentioned above all meetings were moved online. Several meetings postponed from 2020 were able to take place making full use of the new online functionality which had been developed over the previous year. The Society Meeting at the British Mathematical Colloquium (BMC)/British Applied Mathematics Colloquium was hosted by ICMS on behalf of the University of Glasgow and the Mary Cartwright Lecture was able to go ahead in May 2021. In June 2021, both the Society General Meeting and Lecture and the Graduate Student Meeting took place online, hosted by the Society. Professor Emily Riehl (Johns Hopkins) presented the lecture at the General Meeting to over 80 members and guests, and Professor Markus Land (Copenhagen) gave the Graduate Student Meeting lecture to around 40 members and guests.

Lecture series

The Society’s funding for visiting international lecturers helps enable UK-based mathematicians to engage in

2022 Invited Lecturers Gitta Kutyniok (left) and Olga Kharlampovich

dialogue with current mathematical thinking from across the world. However, travel restrictions introduced during the Covid-19 pandemic meant that neither the Invited Lectures Series nor the postponed Hardy Lecture Tour could take place in person. Instead, there are plans in 2022 for a Hardy Lecture Tour by Peter Sarnak (IAS, Princeton) and an Aitken Lecture Tour by Lisa Orloff-Clark (Victoria University of Wellington). There will also be two Invited Lecture Series as follows:

2020 –21 highlights

2021–22 plans

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SUSTAINING THE MATHEMATICAL COMMUNITY

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

Ensuring that as much mathematical talent as possible is discovered and developed regardless of background is critical both in the interests of fairness and in the interests of academia, industry and society as a whole. This objective guides the Society’s work in this area, 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 eighth year) and Undergraduate Summer Schools.

With support from HIMR, the Society awarded over £48k in total funding to support 54 Undergraduate Research Bursaries from 83 applications in 2020– 21.

The 2020 Summer School, due to be held at the University of Swansea in July 2020, was postponed due to the Covid-19 pandemic and ran in July 2021 instead. The Summer School was held as an online event with 121 students attending lectures with Q&A sessions over two weeks.

For final year undergraduates and masters’ students considering a PhD in mathematics, the Society supports the Prospects in Mathematics Meeting which in 2020 was hosted online by Bath University and was attended by 200 students.

For postgraduates, there are LMS Research Schools, Cecil King Travel Scholarships to fund study or research abroad and Postgraduate Conference Grants. In 2020–21:

Nottingham ( Adaptive Methods & mOdel Reduction ) and one LMS Research School in Knowledge Exchange was due to take place in Lancaster ( Rigidity, Flexibility and Applications ). Together with the Research Schools that were postponed from 2020 ( Graph Packing organised by LSE, Methods of Random Matrix Theory and its Applications organised by Reading and Point Configurations: Deformations and Rigidity organised by UCL), all Research Schools have been postponed until 2022.

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LMS Early Career Fellowships

In 2020–21, there was one application round which attracted 31 applications and resulted in 15 awards. Some awards were partially supported by HIMR.

Women 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 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 mathematical community. The Chair of the Committee for Women and Diversity in Mathematics represents the Society on the Athena Forum. As a result of amendments to the Society’s By-Laws in July, the new Council role of Member-at-Large (Women and Diversity) was created. From the annual elections to Council in autumn 2021 onwards, the holder of this role will also Chair 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 June 2021 the Society held an online workshop focusing on academic progression in these challenging times.

During 2020–21 the Society:

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Dr Constanze Roitzheim (University of Kent) and Dr Jennifer Tweedy (working at the University of Bath).

from 2020 due to the pandemic. One Girls in Maths event was held over from 2020 with over 400 participants taking part in the event at Queens University Belfast.

2020 –21 highlights

2021–22 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 engage with and appreciate mathematics and recognise its contributions to society. It operates a number of initiatives which aim to achieve this.

Education

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

Over the past year the Society has been working on the pilot of 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. The LMS has worked initially with Durham University and the University of Leicester to develop and launch online tutorials to help increase aspirations and improve grades, with the goal of enabling more students from under-represented groups to study for a STEM degree. The first cohort of students began tutorials in March 2021 with a total of 55 students participating in a programme of online tutorials delivered by undergraduate maths students. The pilot scheme has been widely well received and the ambition is to expand the scheme to involve more university partners in future.

This year the Society’s Mathematics Teacher Continuing Professional Development (CPD) grants scheme made 14 awards, totalling £7,575, supporting the professional development of mathematics teachers and the improvement of mathematics teaching. The CPD scheme now includes grants for Teaching and Learning in HE, which offer partial funding for one-day workshops disseminating good practice in teaching mathematics. In addition, 24 awards, totalling £12,766, 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 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).

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 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. A code of practice for UK mathematics departments relating to promoting maths teaching was created this year and will be distributed in autumn 2021. In addition to signing up to the code of practice, mathematics departments will provide the name of a person who will act as a point of contact in their university for the TeMaC scheme. The sub-committee plans to hold its first event, which will include TeMaC contacts and other interested parties, in February 2022.

The Education Committee held the first Mathematics Communication Workshops in April and May 2021. The aim of these was to address the paucity of communications training specifically for mathematicians, and allow the LMS to take the lead in increasing the quantity and quality of mathematics communication and outreach in the UK. Two workshops, run by Ben Stokes and Katie Steckles, were held, at a beginners’ and an advanced level; both received much positive feedback.

Popularisation

The Society was delighted to be able to hold once again both the Popular Lectures and the Joint LMS/Gresham College Lecture after these events were postponed in 2020 due to the pandemic. Around 100 participants attended the first ever online Popular Lectures, which were presented by Aoife Hunt (Movement Strategies) and James Maynard (University of Oxford). A third Popular Lecture was held at Maths Week Scotland, hosted by Glasgow University; the speaker was Diana Davis (Phillips Exeter Academy, USA). The Joint LMS/Gresham College Lecture was presented by Professor Julia Gog.

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2020 –21 highlights

2021–22 plans

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MANAGING THE SOCIETY EFFECTIVELY

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

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

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

The Society is governed by a Council of Member Trustees, elected by the membership from the mathematical community (Annex 1). Day-to-day operations are undertaken by a full-time equivalent (FTE) staff of 14 at the time of writing (Annex 4). Council has chosen to delegate decision making on a number of matters to 18 standing committees and has also set up a number of temporary ad-hoc committees to deal with specific items of business (Annex 2). Council also maintains and reviews annually a Risk Register with respect to all activities undertaken by the Society.

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

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 (EMS), which has agreed to act as the Society’s EU GDPR Representative, to help the Society comply with these new 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 Membersat-Large, including one ‘Member-at-Large (Librarian)’.

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 Anti-Bribery 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 2020-21: in October and November 2020 and in January, April and July 2021. The Finance & General Purposes Committee met four times: in September 2020 and in January, March and June 2021. The Society holds an Annual General Meeting and a midyear General Meeting each year. In 2020-21 these were held in November 2020 and July 2021, respectively.

Following a review of the Society’s Royal Charter, Statutes and By-Laws – known collectively as the Standing Orders – and a vote by members in favour of amending them, a formal submission to change the documents was made to the Privy Council in February 2020. As a result of the pandemic, however, the changes to the Standing Orders were only approved in December 2020. These amendments to the Standing Orders have now been implemented.

Following a recommendation by Council, at the General Meeting held in July 2021 members approved amendments to the Society’s By-Laws to create the Council role of Member-at-Large (Women and Diversity). This role will be contested as part of the annual elections to Council in autumn 2021.

Council has established several standing committees which advise Council and to which it has delegated some

decision making. A list of all committees and committee membership is given in Annex 2.

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

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

Public benefit

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

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

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

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Financial Review

In the period 2020–21 income (excluding gains on investment assets) exceeded expenditure by £785k, against an expected budget forecast of £83k deficit. This was mainly due to underspend in Society’s activities against budget due to the Covid-19 pandemic and the associated government restrictions, some of the Society’s activities (grants and events) have had to stop for the time being. Fewer activities have meant less expenditure for the Society, but the Society deeply regrets that this is because it has provided less support to the mathematics community than it had planned.

Despite the surplus, the pandemic has undoubtedly had an impact on the Society’s income as well, with the conference business in De Morgan House coming to a halt.

discussions were therefore held to decide how the Society should respond to the income reduction it faces. Council reviewed all the Society’s activities in order to identify savings and decided on reductions in its budget for the 2021–22 financial year accordingly.

The Society remains in a strong position financially and has significant reserves readily available to fund future activities. 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.

The sources of income (see Figure 1) were:

The gain on Investments was £1.42m.

During the year, the value of the Society’s assets rose from £17.4m to £19.6m.

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 the pandemic on the Society’s income. The Society also continues to work on developing new sources of funding.

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

In spite of the considerable uncertainty over the future of academic publishing, publications income has remained in a steady state. As noted earlier in this report, the Society is set to lose a significant part of its income from its publications activities soon. Although Council is actively exploring other sources of income, it is clear that these cannot generate the necessary replacement income in the short-to-medium term. During the first half of 2021, two dedicated Council

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

Risk management

Council and F&GPC annually review the Society’s Risk Register with the

Figure 1: sources of income 2020/21

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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.

Figure 2: expenditure in 2020/21 broken down by objective

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) have materialised, although it is anticipated that this is temporary. The impact of the virus has been reflected in changed risk ratings and commentaries against relevant risks. All Covid-19 adjustments to the Risk Register have been tagged so that these changes (i) are easier to see at a glance, and (ii) can be targeted for review — and removal — as and when the Covid-19 pandemic recedes and the related restrictions are eased.

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 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, as part of its response to this risk, the Society initiated a formal tendering process for partnering to publish the Bulletin, Journal, Proceedings, Transactions, the Journal of Topology and Mathematika from January 2022. Key terms have been agreed with partners for the extension of publishing arrangements beyond 2021, with detailed agreements expected to be signed in the autumn of 2021. As also noted elsewhere in this report, the Society has taken steps to manage the impact of such changes to its finances.

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 Activities (SoFA), therefore, recognise (within the year the grant is awarded) both liabilities and provisions for grant commitments. Normally grant commitments will be claimed by the end of the financial year, although the claim period may be extended by a further year where the start or end date of the grant so requires.

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

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

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Investments

The Society decided to invest up to 30% of its relevant assets in residential property, as valued at the time of purchase, with the remainder given over to the Society’s investment managers. Investment in such residential property 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 current quoted investment strategy for the portfolio, which is managed by investment managers Schroders (Cazenove), has been modelled to achieve RPI + 4% per annum nominal return over five years (a 4% return in real terms after allowing for average service sector wage inflation). Due to the change in the investment climate Council agreed to accept a lower than 4% return in order to reduce risks. Close attention is paid to our investment policy and to the performance of Schroders, with whom we have regular meetings.

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.

The majority of the Society’s reserves – both Restricted and Unrestricted – are invested and managed by the Society’s investment managers, Schroders (Cazenove). It is Society policy to review on a regular basis the performance of those professional bodies it employs. 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, on which its future capacity to maintain its activities depends. The primary long-term target is that the Society’s portfolio produces a total return of inflation (RPI) plus 4% pa. 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 a single investment in the Schroder Charity Multi-Asset Fund. A summary of the main categories of investments and the geographical split is provided in the notes to the financial statements in accordance with the Charities’ SORP. The Schroder Charity 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 Inconforms 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 were 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.

For most of 2020–21 the Conference Centre was closed due to Covid-19 restrictions and reopened in July 2021. Of the rooms available for commercial tenancies, one is unoccupied at the time of writing following a tenant vacating their office space in July 2021. The room is currently being advertised to find a new tenant.

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, it provides a home for the UK Mathematical Sciences Directory 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 2020–21, the Society undertook a major upgrade of the Drupal Content Management System and implemented a Society-wide review of the website content, to ensure that its website remains up-to-date and fit for purpose.

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Statement of Trustees’ Responsibilities

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

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

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

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

Professor Jonathan Keating (President)

15/10/2021

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

Date

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ANNEX 1: COUNCIL, EXECUTIVE TEAM AND PROFESSIONAL ADVISERS

Membership of Council during the period 1 August 2020 to 31 July 2021

President: Jon Keating Vice-Presidents: Iain Gordon Cathy Hobbs Treasurer: Robert Curtis (until November 2020) Simon Salamon (from November 2020) General Secretary: Stephen Huggett (until November 2020) Robb McDonald (from November 2020) Programme Secretary: Chris Parker Publications Secretary: John Hunton Education Secretary: Kevin Houston Members-at-Large: Mark McCartney (Librarian) Peter Ashwin (from November 2020) Alexandre Borovik (until November 2020) Tara Brendle (until November 2020) Elaine Crooks Andrew Dancer Anne-Christine Davies (from November 2020) David E. Evans (until November 2020) Tony Gardiner Minhyong Kim (from November 2020) Niall MacKay (from November 2020) Frank Neumann Brita Nucinkis Richard Pinch (until November 2020) Mariya Ptashnyk (until November 2020) Anne Taormina Amanda Turner (from November 2020) In attendance: Eugenie Hunsicker (Chair, Committee for Women and Diversity in Mathematics)

Executive Management Team during the period 1 August 2020 to 31 July 2021

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, Devonshire House, 60 Goswell Road, London, EC1M 7AD Investment Advisers: Cazenove/Schroder & Co. Limited, 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 2021)

Membership of Committees as at 31 July 2021

Computer Science Committee: P. Wong (Chair), P. Ashwin, A. Beckmann, M. Cryan, O. Dardha, J. Davenport (Institute of Mathematics and its Applications (IMA)), R. Heirons (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 Designate, G. Dales, A. Dancer. J. Rodrigo, C. Roney-Dougal.

Early Career Research Committee: C. Parker (Chair), J. Grbic, H. Johnston, D. Maclagan, R. Newton, M. Ptashnyk, S. Roy, I. Short, A. Thillaisundaram, S. Whitehouse.

Education Committee: Education Secretary (Chair), P. Glaister, Vice-President C. Hobbs, J. Anderson, 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, C. Budd (UK representative to International Commission on Mathematical Instruction), J. Fraser (Edinburgh Mathematical Society (EdMS)), G. Gibson (President of the EdMS), P. Glaister (IMA), M. Mathieu, B. Nucinkis, J. Parker, S. Schroll, N. Walkey (Royal Statistical Society).

Investment Sub-Committee: Treasurer (Chair), all other Members of Finance and General Purposes Committee, R. Bogni, J. Dodd, 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), Publications Secretary, LMS Archivist, I. Falconer, S. Hart, C. Hollings.

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

Nominating Committee: K. Falconer (Chair), I. D. Abrahams, C. Budd, M. Kim (Council), B. Pelloni, M. Rees, G. Stallard, E. Winstanley.

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

Taormina, N. MacKay.

Prizes Committee: President (Chair), J. Bennett, P. Cameron, C. Elliott, I. Gordon, S. Schroll, I. Smith, A. Taormina, B. Wingate, M. Wemyss.

Publications Committee: Publications Secretary (Chair), Vice-President C. Hobbs, Treasurer, M. Brown, E. Crooks, R. Kessar, A. Lazarev, I. Leary, N. MacKay, C. Parker, T. Sanders, S. Taylor, A. Turner.

Research Grants Committee: A. Dancer (Chair), J. Brodski, G. Derks, A. Lazarev, F. Neumann, B. Nucinkis, N. Peyerimhoff,

M. Ptashnyk, A. Turner, A. Vdovina, J. Zimmer (Bath Symposia Representative).

Research Policy Committee: Vice-President I. Gordon (Chair), P. Ashwin, K. Brown, S. Gutierrez, A. Caraiani, J. van

den Heuvel (HoDoMS), S. Howison, O. Jensen, T. Liverpool, H. Krieger.

Society Lectures and Meetings Committee: B. Nucinkis (Chair), M. Kambites, K. Leschke, N. Petrovskaya, M. Todd, V.

Styles, A. Vdovina.

Committee for Women and Diversity in Mathematics: E. Hunsicker (Chair), Vice-President I. Gordon, H. Herrera (Operational Research Society, ORS), A. Lecuona (Edinburgh Mathematical Society, EdMS), A. Davis, S. Lombardo, D. Maclagan, S. Pumpluen, L. Rodgers (Royal Statistical Society, RSS), C. Smith, M. Sommacal.

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Sub-Groups, Ad-hoc Committees and LMS appointments as at 31 July 2021

Publications Nominating Group: Publications Secretary (Chair), G. Brown, M. Gross, J. Maynard, A. Lazarev, M. Pollicott, U. Tillmann, C. Tretter.

Covid Working Group: Vice-President I. Gordon (Chair), Treasurer, B. Nucinkis (Chair, Society Lectures and Meetings Committee), A. Dancer (Chair, Research Grants Committee), C. Parker (Chair, Early Career Research Committee), A. Turner, Executive Secretary.

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

Good Practice Scheme Steering Group: A. Davis (Chair), P. Davies, E. Hunsicker (Chair, Women in Mathematics Committee), S. Lombardo, N. Mazza, C. Smith, A. Taormina, J. van den Heuvel (HoDoMS), J. Walker.

LMS–IMA Crighton Medal Committee 2020 (LMS Members): President, K. Brown, G. Stallard.

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: B. Nucinkis, E. Crooks.

Council Webmaster: R. McDonald.

LMS/EMS Newsletter Correspondent: D. Chillingworth.

Election Scrutineers: C. Goldie and C. Lance.

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ANNEX 3: EXTERNAL REPRESENTATIVES (as at July 2021)

Representatives on external committees and boards as at 31 July 2021

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

British Science Association Mathematics Section: Education Secretary.

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

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

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

European Mathematical Society (EMS) Council: President, Programme Secretary, M. Mathieu, C. Roney-Dougal.

Heads of Departments of Mathematical Sciences Committee: J. Parker.

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

International Commission on Mathematical Instruction (ICMI) UK representative: C. Budd.

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

Isaac Newton Institute (INI) Correspondent: B. Pelloni.

Joint Mathematical Council (JMC): Education Secretary.

Parliamentary and Scienti ic 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

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ANNEX 4: STAFF

Staff in post in the period 1 August 2020 to 31 July 2021

Executive Secretary’s Office

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

Caroline Wallace Clare Ralphs Ephrem Abate Valeriya Kolesnykova Susan Oakes

Publications

Publications Development Manager: Editorial Manager: Publications Assistant:

Suzanne Abbott Ola Törnkvist Georgina Gale

Society Business

Head of Society Business: Membership and Grants Manager: Society Communications Officer: Society Governance Officer: Society & Research Officer: Grants and Membership Administrator: Projects, Events & Membership Administrator/CMS Assistant

Lindsay Walsh Elizabeth Fisher John Johnston James Taylor Katherine Wright

Lucy Covington

Tammy Tran (until April 2021)

Conferences and Building Group

Head of Conferences and Buildings: Events Administrator: Receptionist:

Andrew Dorward Abul Rashed (until January 2021) Valeriya Kolesnykova (acting as Membership Assistant due to the closure of De Morgan House during the Covid-19 pandemic) Angela Waidson (until January 2021)

33

ANNEX 5: GRANT SCHEMES

General policy on grant-making

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

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

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

34

Summary of main grants and training schemes

Conference Grants (Scheme 1)

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

Visitors to the UK (Scheme 2)

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

Support of Joint Research Groups (Scheme 3)

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

Online Lecture Series (Scheme 3)

The Scheme is to provide support for the early career researchers in the Joint Research (Scheme 3) Groups who do not have permanent positions. The Groups are required to produce online lectures aimed at new PhD students in September 2020. This will enable current early career researchers to enhance their skills and experience in planning and delivering online lectures.

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.

35

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 Educational 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 Teacher Continuing Professional Development (CPD) Grants

The Scheme is to provide opportunities for mathematics teachers to attend training which is specifically mathematical. Any application for a grant under this scheme must be made by a teacher of mathematics or Initial Teacher Education provider based in the UK. The grants are open to teachers of mathematics from primary school to A-Level or equivalent.

The grants are to support teacher attendance at one or two day conferences/events organised by professional mathematical organisations. The grants are also to assist providers of professional development to run conferences and courses that allow participants to further their professional development. The grants can also cover the costs of external trainers in schools or educational institutions.

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.

36

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

Undergraduate Research Bursaries in Mathematics

The Scheme aims to give training in research to undergraduates with research potential to encourage them to consider a career in scientific research. Grants are awarded for a six-to-eight week summer research project undertaken with the guidance of a research supervisor.

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.

37

Celebrating New Appointments (Scheme 9)

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

Travel Grants for Early Career Researchers

The Travel Grant Scheme provides partial support for UK-based early career researchers to attend conferences or undertake research visits either in the UK or overseas. Grant holders are early career researchers in mathematics, based in the UK, defined as a 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.

38

ANNEX 6: 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 inflation + 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. At present Residential Properties are making a return of 4% through rent, and more than keeping pace with inflation.

The Society normally maintains £600k free reserve (operating reserve) cash at bank to ensure that there is enough working capital to stabilise the Society’s finances by providing contingency against unexpected events, as well as to handle losses in income and large unbudgeted expenses.

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.

General Fund £15,523,529

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

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

39

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 £21,000
Covid-19 Emergency Fund
This fund is set aside to help mitigate the impact of the Covid-19 pandemic on mathematical
research,includingthe ‘peoplepipeline’ of earlycareer researchers		 £27,251

Restricted Funds

Restricted Funds
Prizes Fund(for Berwick/De Morgan/Lord Rayleigh’s/Fröhlich/Shephardsprizes) £215,484
A.J. Cunningham Research Fund(forpublication of work on the factorisation of large numbers £102,807
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		 £29,791
Levelling Up Scheme Fund (for tutorial of A-level maths students from under-represented
backgrounds)		 £41,316
Campaign for Pure Mathematics Fund (for campaigning to protect and promote pure
mathematics)		 £26,760
£416,379

40

ANNEX 7: AUDITOR’S REPORT

Opinion

We have audited the financial statements of The London Mathematical Society for the year ended 31 July 2021 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.

41

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:

42

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

18 October 2021 Date .....................................................................

Devonshire House 60 Goswell Road London EC1M 7AD

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

43

ANNEX 8: STATEMENT OF FINANCIAL ACTIVITIES

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

44

STATEMENT OF FINANCIAL ACTIVITIES For the year ended 31st July 2021

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
-
-		 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		 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/(losses) on investment assets
16
Net Income/ (expenditure) 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
Fund balances carried forward
1		 5,523,529 3,648,251 416,379
19,588,159

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

45

BALANCE SHEET

as at 31st July 2021

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		 2021
2020
£
£
£
£
12,153,444
10,878,904
3,688,950
3,596,900
15,842,394
14,475,804
1,165,252
1,210,069
37,632
27,975
1,202,884
1,238,044
17,045,278
15,713,848
1,531
1,531
312,447
144,133
3,508,017
2,752,292
3,821,995
2,897,956
962,083
882,279
107,349
138,382
1,069,432
1,020,661
2,752,563
1,877,295
(209,682)
(170,730)
19,588,159
17,420,413
15,523,529
13,156,123
3,648,251
3,946,000
416,379
318,290
19,588,159
17,420,413

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

Approved by the trustees on 15[th] October 2021 and signed on their behalf by:

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

46

Cash Flow Statement

For the year ended 31 July 2021

2021
£
£
Cash flow from operating activities
Net movements in funds
2,167,746
Add / (Deduct) gains/(losses) on investments (note 16)
(1,421,884)
Add back re-invested gains (note 2)
89,612
Add back investment management fees (note 4)
53,063
Add back VAT on investment management fees
2,231
Deduct investment income (note 2)
(502,606)
Add back depreciation charge (note 17)
60,783
Decrease / (Increase) in debtors (note 18)
(168,314)
Decrease / (Increase) in medals in stock
-
(Decrease)/increase in creditors (note 19)
87,723
Net cash provided by operating activities
368,354
Cash flow from Investing activities
Purchase of tangible fixed assets (note 17)
(25,623)
Purchase of fixed asset investments (note 15)
(89,612)
Investment income (note 2)
502,606
Net cash provided by investing activities
387,371
Change in cash and cash equivalent in the year
755,725
Cash and cash equivalent at the beginning of the year
Cash in bank and deposit
2,752,292
Cash held in investments
100
2,752,392
Cash and cash equivalent at the end of the year
Cash in bank and deposit
3,508,017
Cash held in investments
100
3,508,117		 2020
£
£
(206,087)
464,453
74,297
52,596
2,218
(529,674)
57,724
97,728
-
219,224
232,479
(17,905)
(404,176)
529,674
107,593
340,072
2,412,290
30
2,412,320
2,752,292
100
2,752,392

47

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 Charites: 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 COVID-19 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, with restrictions preventing in-person events for a significant part of the 2020-2021 year and a lag in the return to in-person events after restrictions were lifted in July 2021. 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. The Society’s 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. The Society’s core operations have been able to continue throughout this period.

As noted earlier in this report, the Society is set to lose a significant part of its income from its publications activities soon. 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 the 2021-2022 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:

48

1. Accounting Policies (continued)

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.

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.

g) Investments

The Society may 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 will be directly managed by the Society rather than by 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

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 portfolio is invested in a range of equity, cash and fixed-interest investments in both UK and overseas markets. The key objective of the Society’s portfolio is to produce a real return (capital growth) of at least 4% pa, and to provide an investment income determined by ‘total return policy’ of 3.5% pa (based on Yale model).

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

As a safeguard against possible poor 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. 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.

49

1. Accounting Policies (continued)

h) Publications

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

i) Joint Ventures

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

j ) Grants and Contracts

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

k) Recognition of grant liabilities

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

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

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

l) Grants payable

m) Taxation

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

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

50

1. Accounting Policies (continued)

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

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

r) Restricted Funds

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

51

1. Accounting Policies (continued)

s) Support and governance costs

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

t) Employee benefits

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

u) Heritage assets

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

2. Investment Income

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

2020
Unrestricted Designated Restricted
£
£
£
a) Investment income receivable:
Total returns/ Unit Trust Distribution
(Bond interest, Equities dividends, etc.)
449,173
-
7,608
Re-invested total returns
(74,297)
-
-



Net investment income receivable
374,876
-
7,608
b) Residential property rental income
131,844
-
-
c) Interest receivable (Treasury Reserve and Bank deposits)
14,871
162
313



Total investment income 2020
521,591
162
7,921
 Total
2021
£
454,732
(89,612)

365,120
135,976
1,510

502,606

Total
2020
£
456,781
(74,297)

382,484
131,844
15,346

529,674

52

3.
Income from other trading activities

a) DMH Conference facilities
b) DMH Rental income
c) Advertising in Newsletter
Total		 2021

£
7,288
112,484
4,645

124,417		 2020
£
146,296
110,301
4,630

261,227
4.
Costs of raising funds
2021
£
£
a)
Conference facilities
General expenditure
11,030
Apportioned support and governance costs
83,845

94,875
b)
Service for tenants
69,831
c)
Investment Management fees
53,063
d)
Residential Investment Property costs
58,098

Total
275,867
5.
Charitable activities: Advancing the interests of Mathematics
2021
£
£
Members’ services:
LMS Newsletter
23,978
Other costs
3,222
Unrecoverable subscriptions
4,599

31,799
Activities to support Women in Mathematics
150
Activities to support Maths -Computer Sciences
-
Library, binding and archives
6,450
EMS, IMU, ICIAM subscriptions & ICM costs
13,935
Prizes
18,122
Apportioned support and governance costs (note 12)
275,615

Total
346,071
2020
£
£
22,935
113,611

136,546
65,138
52,596
60,017

314,297
2020
£
£
22,812
7,414
1,413

31,639
1,195
2,465
9,024
14,050
18,061
279,155

355,589

53

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

2021
Grant Schemes
£
£
Research Grants (Schemes 1 – 5)
108,102
Research Workshop Grants
4,410
Support for Mathematics in Africa
-
Early Career Support (Schemes 8 and 9/ECR travel grants)
9,951
Research School Grants(incl. £27k HIMR Fund)
45,000
Prospects in Mathematics Grants
3,500
Early Career Fellowship Grants(incl. £13k HIMR Fund)
123,800
Undergraduate Bursaries(incl. £15k HIMR Fund)
48,107
Computer Science Grants
4,930
Teachers CPD Grants
7,575
Small Educational Grants
17,767
Women in Mathematics Grants (Event/Childcare/Diversity)
10,732
Atiyah UK-Lebanon Fellowships
3,000
ECM/ICM travel Grants
4,829

391,703
Less: cancellation and refunds
(65,623)


326,080
Covid response Fund(Restricted) (Incl. £19,834 HIMR fund)
112,583
Mentoring African Research in Mathematics (MARM)(Restricted)
-
Cecil King Grants (Restricted)
6,000
Emmy Noether Fellowship (Restricted)
22,855
INI/ICMS/ACME Grants (Designated)
7,000
Ad hoc Grants to Mathematical Bodies (UK & International)
12,133
Charitable giving of LMS rooms
-
Apportioned support and governance costs (note 12)
195,533

Total
682,184
2021
ANALYSIS OF GRANT AWARDS
£
a) Grants: contractual commitments
University of Cambridge (INI grant)
-
Heriot- Watt University (ICMS grant)
-
Royal Society (ACME grant)
7,000

7,000
b) Other grant awards to institutions
304,620
c) Other grant awards to individuals
247,654

Total grant awards
552,274
_ Grant awards to each institution can be up to a maximum of £30k_
2021
GRANT REFUNDS AND CANCELLATION
£
Grant refunds
10,288
Grants not taken up (out of date)
55,335

Total grant refunds and cancellation
(65,623)
2021
MOVEMENT IN OBLIGATION GRANT COMMITMENTS
£
Grant recognised at the start of the year
473,406
New grants charged to the SoFA in year
552,274
Grants paid during the year
(429,411)
Grants not taken up (‘out of date’)
(55,335)

Amount of grant recognised at the end of the year
540,934**		 2020
£
£
367,211
15,750
2,000
60,203
45,000
7,000
72,000
33,366
7,296
9,206
18,241
14,009
11,000
-

662,282
(73,699)

588,583
-
16,000
5,000
21,791
73,000
13,084
24,709
230,505

972,672
2020
£
45,000
21,000
7,000

73,000
737,922
53,235

791,157
2020
£
32,282
41,417

(73,699)
2020
£
238,989
791,157
(515,323)
(41,417)

473,406

54

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		 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
 2020
£
£
1,423,206
(500)
-
(23,991)

(24,491)

1,398,715
(407,617)

991,098
157,870
51,320
21,030
15,535

245,755
107,923
(10)

107,913
35,873

1,380,639

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		 2021
£

328,998
(43,596)
(172,482)

(216,078)

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

-
 2020
£
313,702
(44,959)
(160,820)

(205,779)

107,923
(39,000)
(68,923)

-

55

8. Charitable activities: Disseminating Mathematical Knowledge

– Conference and meeting programmes

Society meetings and regional workshops
Invited Lectures
Apportioned support and governance costs (note 12)
Total
9.
Charitable activities: Promoting Mathematical Research &
Policy
CMS
Communication and External Relations
Annual dinner
Subscriptions to UK organisations
Education and young people, public engagement
Holgate Lecturers
Popular Lectures
Other educational activities
Levelling Up Scheme
Promoting Women in Mathematics activities
Campaign for Pure Mathematics
Apportioned support and governance costs (note 12)
Total		 2021
£
£
4,130
-

4,130
99,614

103,744

its benefits
2021
£
£
15,257
8,479
-
2,136

25,872
1,800
905
4,000

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

354,218
 2020
£
£
21,307
4,411

25,718
119,020

144,738

2020
£
£
9,126
29,247
9,359
2,116

49,848
3,150
-
542

3,692
-
431
-
326,313

380,284

56

10. Governance and other committees’ costs

2021 2020
£
 £
£
 £
Professional services
Solicitors fees 2,504 4,950
Audit and accountancy fees 13,550 12,650
Audit and accountancy fee over/(under) - accrual 774 (64)
Other professional fees 35
 35
16,863 17,571
Costs of meetings (Catering/Accommodation/Travel/Subsistence)
Governance(Council/F&GPC/Nomination, etc.) 94 24,273
Other Committees 31
 15,917
125 40,190
Election of Trustees 3,677 6,634
General office and staff costs (apportioned)(note 11_)_ 236,373
 246,658
Total 257,038 311,053
nalysis of general support and governance costs
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
Governance and Other general
 Total
2020 Committee related
support		 2020
£ £ £
Staff costs 173,924 927,950 1,101,874
Office and Premises costs 34,074 149,530 183,604
IT costs 21,541 110,777 132,318
Depreciation 12,330 45,394 57,724
Irrecoverable VAT 4,789 13,699 18,488
Professional services 17,571 - 17,571
Costs of meetings 40,190 - 40,190
Elections of Trustees 6,634
 -
 6,634
Total 2020 311,053
 1,247,350 1,558,403

11. Analysis of general support and governance costs

57

12. Allocation of support and governance costs by activity

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
2020
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 2020		 Direct
Staff
£
25,140
24,770
16,227
66,137
113,716
76,832
197,509
23,565
155,261
566,883
633,020

Direct
Staff
£
42,541
15,407
12,148
70,096
90,764
84,113
202,978
22,185
161,485
561,525
631,621		 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



General
Office
General
Management
and Finance
Governance
and
Committee
£
£
£
58,181
12,333
556
47,292
1,784
556
2,866
1,573
556

108,339
15,690
1,668

54,725
71,789
61,877
38,837
45,678
61,877
67,490
75,272
61,877
7,051
27,907
61,877
46,079
56,872
61,877

214,182
277,518
309,385

322,521
293,208
311,053

Basis of apportionment

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

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

58

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
Employer’s Pension Contributions
Total*

 2021
2020
£
£
782,856
804,755
20,827
-
87,819
89,341
152,379
150,202

1,043,881
1,044,298

A government furlough grant of £16,849 was received. The grant is credited under ‘Other income’ and shown on the SoFA.

The total employment costs (Salaries/NIC /Pension) for the Executive Management Team amounted to £393,595 (2020: £415,444). 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:

2021 2020
No. No.
£60,000 - £70,000 2 2
£70,000 - £80,000 1 -
£80,000 - £90,000 - 1
£90,000 - £100,000 1 -

The pension payments for the above members of staff amounted to £61,611 (2020: £46,185). 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		 2020/2021
Total
FTE
14.8
12.4
3.0
3.0


17.8
15.4

 2019/2020
Total
FTE
16.0
12.9
3.0
3.0


19.0
15.9

59

14. Pension costs

The Society participates in Universities Superannuation Scheme. 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 £38,952 (2020: loss of £11,719) as shown in note18.

The latest available complete actuarial valuation of the Retirement Income Builder is at 31 March 2018 (the valuation date), which was carried out using the projected unit method. A valuation as at 31 March 2020 is underway but not yet complete.

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 2018 valuation was the fifth valuation for the scheme under the scheme-specific funding regime introduced by the Pensions Act 2004, which requires schemes to adopt a statutory funding objective, which is to have sufficient and appropriate assets to cover their technical provisions. At the valuation date, the value of the assets of the scheme was £63.7 billion and the value of the scheme’s technical provisions was £67.3 billion indicating a shortfall of £3.6 billion and a funding ratio of 95%.

The key financial assumptions used in the 2018 valuation are described below. More detail is set out in the Statement of Funding Principles.

Pension increases (CPI) Term dependent rates in line with the difference between the Fixed Interest
and Index Linked yield curves, less 1.3% p.a.
Discount rate (f/wd rates) • Years 1-10: CPI + 0.14% reducing linearly to CPI – 0.73%
• Years 11-20: CPI + 2.52% reducing linearly to CPI + 1.55% by year 21
• Years 21 +: CPI + 1.55%

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 2018 actuarial valuation. The mortality assumptions used in these figures are as follows:

2018 valuation
Mortality base table Pre-retirement:
• 71% of AMC00 (duration 0) for males and
• 112% of AFC00 (duration 0) for females
Post-retirement:
• 97.6% of SAPS S1NMA “light” for males and
• 102.7% of RFV00 for females
Future improvements to mortality CMI_2017 with a smoothing parameter of 8.5 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:
2021 2020
Males currently aged 65 (years) 24.6 24.4
Females currently aged 65 (years) 26.1 25.9
Males currently aged 45 (years) 26.6 26.3
Females currently aged 45 (years) 27.9 27.7

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:
2021 2020
Discount rate 2.59% 2.59%
Pensionable salary growth 1% 4.2%

60

15. Fixed Asset Investments

ixed Asset Investments
2021 2020
£ £ £ £
a) Quoted investments
Investment Investment Total Total
Assets Assets
in the UK outside the
UK
Total Market value at 31st July 2021 2,309,154
9,844,290
 12,153,444
10,878,904
In the prior year, £2,719,726 of investment assets were in the UK with the remaining £8,159,178 being outside the UK.
Reconciliation of opening and closing market £ £
values:
Market value at 1stAugust 2020 10,878,904
11,398,171
Additions at cost 89,612
74,226
Unrealised gains/(losses) (note 16a) 1,329,834
(464,453)
Movement in cash (144,906)
(129,040)
Total Market value at 31st July 2021 12,153,444
10,878,904
Analysis by Fund:
Restricted Funds 255,230
222,560
Unrestricted Funds 11,898,214
10,656,344
The investments are entirely invested in the Schroder Charities Multi-Asset Fund.
b) Residential Property investments 2021 2020
£
 £
Market value at 31st July 2021 3,688,950
3,596,900
Reconciliation of opening and closing market values:
Market value at 1st August 2020 3,596,900
3,266,950
Additions at cost -
329,950
Unrealised gains (note 16b) 92,050
-
Total Market value at 31st July 2021 3,688,950
3,596,900

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

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
2020
Unrestricted
funds

£
a. Unrealised losses in market value ofQuoted investments
(453,978)
b. Unrealised gains/(losses) in market value ofResidential Properties
-

Total losses
(453,978)		 Restricted
funds
£
26,075
-

26,075
Restricted
funds
£
(10,475)
-

(10,475)		 Total
£
1,329,834
92,050

1,421,884
Total
£
(464,453)
-

(464,453)

61

17. Tangible Fixed Assets Leasehold Fixtures Total
Property Fittings and
Equipment
£ £ £
Cost
Brought forward at 1st August 2020 2,175,353 165,937 2,341,290
Additions -
 25,623
 25,623
Carried forward at 31st July 2021 2,175,353
 191,560
 2,366,913
Depreciation
Brought forward at 1stAugust 2020 965,284 137,962 1,103,246
Charge for the year 44,817
 15,966
 60,783
Carried forward at 31st July 2021 1,010,101
 153,928
 1,164,029
Net book value
At 31st July 2021 1,165,252
 37,632 1,202,884
At 31stJuly 2020 1,210,069
 27,975 1,238,044
• Part of the leasehold property is let out and the rental derived is shown on the SOFA under ‘Activities for Generating Funds’.
18. Debtors 2021 2020
£ £
Publications 219,165 51,320
Conference facilities 980 -
Other debtors 54,989 52,594
Gift-aid receivable 500 2,389
Prepayments and accrued interest 36,813
37,830
312,447 144,133
19. Creditors and Deferred Income 2021 2020
£ £
Creditors: amounts falling due within one year
Accruals 37,861 32,501
Grant creditors 540,934 473,405
Taxation and other Social Security creditors 82,305 56,471
Other creditors 300,983
319,902
962,083 882,279
Deferred income:
Unexpired publications’ subscriptions:
Balance brought forward 138,382 120,262
Amount released in year (138,382) (120,262)
Income deferred to future years 107,349
138,382
Balance carried forward 107,349 138,382
Creditors: amounts falling due after more than one year
Brought Forward Pension Provision 170,730 159,011
Movement 38,952
11,719
Carried Forward Pension Provision 209,682 170,730

62

20. Restricted Funds

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
1.08.20
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
31.07.21
£
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
2020
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
Total Funds		 Balance
at
1.08.19
Other &
Investment
Income
Expenditure
Investment
loss
Transfers
£
£
£
£
£
32,246
161
-
-
-
30,407
152
-
-
-
20,471
678
(1,500)
(933)
-
47,109
1,558
-
(2,146)
-
18,705
619
-
(852)
-
-
-
(9,000)
-
9,000
15,529
514
(1,500)
(707)
-
37,865
1,253
(1,500)
(1,725)
-
90,249
2,986
-
(4,111)
-
221
-
-
-
-
-
-
-
-
32,542
-
6,000
(16,000)
-
10,000
-
5,000
(5,000)
-
-
-
25,000
(21,791)
-
(3,209)





292,802
43,921
(56,291)
(10,475)
48,333		 Balance
at
31.07.20
£
32,407
30,559
18,716
46,521
18,472
-
13,835
35,893
89,124
221
32,542
-
-
-

318,290

63

21. Unrestricted Funds

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
 Balance
at
01.08.20
£
13,156,123


600,000
3,000,000
226,000
-

120,000

3,946,000

17,102,123		 Income
Expenditure Gain/(loss)
on
investments

£
£
£
2,597,821 (1,889,837) 1,395,809



-
-
-
-
-
-
-
(7,000)
-
328,998
(216,078)
-
-
(92,749)
-



328,998
(315,827)
-



2,926,819 (2,205,664) 1,395,809		 Actuarial
gains
(losses) on
pension
scheme
Transfer
Balance
at
31.07.21
£
£
£
(38,952)
302,565 15,523,529


-
-
600,000
-
-
3,000,000
-
(198,000)
21,000
-
(112,920)
-
-
-
27,251


-
(310,920)
3,648,251


(38,952)
(8,355)
19,171,780

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.

d) The transfer of £112,920 from the Compositio Fund to General Fund represents the management fee and the LMS’s profit share relating to the journal.

2020
General Fund:
(see note1(p))

Designated Funds:
a) Building & Development
Reserve Fund
b) Printing& Publication
Reserve Fund
c) Grants Payable
Reserve Fund
d) Special Activities
Reserve Fund
e) Compositio Fund
f) COVID-19 Emergency
Fund
 Balance
at
01.08.19
Income
Expenditure Gain/(loss)
on
investments
Actuarial
gains
(losses) on
pension
scheme
Transfer
Balance
at
31.07.20
£
£
£
£
£
£
£
13,402,318 2,717,777 (2,470,407) (453,978)
(11,719)
(27,868) 13,156,123







600,000
-
-
-
-
-
600,000

3,000,000
-
-
-
-
-
3,000,000
299,000
-
(73,000)
-
-
-
226,000
32,380
162
-
-
-
(32,542)
-
-
313,702
(205,779)
-
- (107,923)
-

-
-
-
-
-
120,000
120,000






3,931,380
313,864
(278,779)
-
-
(20,465)
3,946,000






17,333,698
3,031,641 (2,772,477) (453,978)
(11,719)
(48,333)
17,102,123

d)The transfer of £32,542 from the Designated Fund represent that Frank Gerrish Fund as Restricted Fund

e) The transfer of £107,923 from the Compositio Fund to General Fund represents the management fee and the LMS’s profit share relating to the journal. f) The transfer of £120,000 from General Fund is in respect of the COVID-19 Emergency Fund.

64

22. Analysis of net assets between funds

nalysis of net assets between funds

2021
Fund balances are represented by
Tangible fixed assets
Investments
Current assets
Current liabilities
Long-term liabilities
Total net assets

2020
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/BMI
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
£
£
1,202,884
-
11,966,164
3,621,000
3,633,595
27,251
(1,069,432)
-
(209,682)
-


15,523,529
3,648,251


Unrestricted funds
General
Designated
£
£
1,238,044
-
10,307,244
3,946,000
2,802,226
-
(1,020,661)
-
(170,730)
-


13,156,123
3,946,000


2021
£
£
47,415
(83,001)

(35,586)
-
-

-		 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
Restricted
Total
Funds
Funds
£
£
-
1,238,044
222,560
14,475,804
95,730
2,897,956
-
(1,020,661)
-
(170,730)


318,290
17,420,413
2020
£
£
56,408
(101,378)

(44,970)
6,000
(16,000)

(10,000)

23. Grants and Contracts Management account

24. Transactions with Trustees and connected persons

Trustees receive reimbursement only for expenses actually incurred in attending meetings. No remuneration is paid to trustees except as disclosed below. The gross amount that has been reimbursed in respect of attendance of meetings in the period amounted to £7 for 1 Trustee (2020: £12,689 for 19 Trustees).

During the year £450 (2020: £450) was paid to Dr A. Gardiner for delivering Holgate lectures. As this work falls outside of his duties as a trustee, a written agreement was produced between the Society and Dr Gardiner.

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

65

25. Comparison figures of each fund (2019/20 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
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
£
£
£
16,778
-
25,000



144,947
-
-
1,423,206
-
-

281,628
313,702
-
61,137
-
11,000



1,910,918
313,702
11,000
261,227
-
-
521,591
162
7,921
7,263
-
-


 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
16,778
-
25,000



144,947
-
-
1,423,206
-
-

281,628
313,702
-
61,137
-
11,000



1,910,918
313,702
11,000
261,227
-
-
521,591
162
7,921
7,263
-
-


 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
16,778
-
25,000



144,947
-
-
1,423,206
-
-

281,628
313,702
-
61,137
-
11,000



1,910,918
313,702
11,000
261,227
-
-
521,591
162
7,921
7,263
-
-


 Unrestricted
General
Funds
Designated
Funds
Restricted
Funds
£
£
£
16,778
-
25,000



144,947
-
-
1,423,206
-
-

281,628
313,702
-
61,137
-
11,000



1,910,918
313,702
11,000
261,227
-
-
521,591
162
7,921
7,263
-
-
Total Income 2,717,777 313,864 43,921
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
 314,297

342,089
856,881
432,118
144,738
380,284

2,156,110
 -

-
73,000
205,779
-
-

278,779
 -

13,500
42,791
-
-
-

56,291
Total expenditure 2,470,407 278,779 56,291

Net income/(expenditure) before
gains and losses on investment
Net losses on investment assets
16
Net (expenditure)/ Income for the year
Transfers between funds
20,21
Actuarial losses on defined benefit pension schemes 14,19

247,370
(453,978)

(206,608)
(27,868)
(11,719)
35,085
-

35,085
(20,465)
-

(12,370)
(10,475)

(22,845)
48,333
-
Net movement in funds for the year (246,195) 14,620 25,488


Reconciliation of funds:
Total funds brought forward
13,402,318 3,931,380
Fund balances carried forward
13,156,123
3,946,000

66