i i “NLMS_494” — 2021/4/19 — 10:44 — page 1 — #1 i i NEWSLETTER Issue: 494 - May 2021 THE POETRY FERMAT’S THE SHAPE OF GEORGE TWO SQUARES OF A MODULE BOOLE THEOREM CATEGORY i i i i i i “NLMS_494” — 2021/4/19 — 10:44 — page 2 — #2 i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Eleanor Lingham (Sheeld Hallam University) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when EDITORIAL BOARD reproducing whole articles. Contributions to the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or David Chillingworth (University of Southampton) photographer for the rights to reproduce. Jessica Enright (University of Glasgow) The LMS cannot accept responsibility for the Jonathan Fraser (University of St Andrews) accuracy of information in the Newsletter. Views Jelena Grbic´ (University of Southampton) expressed do not necessarily represent the Cathy Hobbs (UWE) views or policy of the Editorial Team or London Christopher Hollings (Oxford) Mathematical Society. Robb McDonald (University College London) Adam Johansen (University of Warwick) Susan Oakes (London Mathematical Society) ISSN: 2516-3841 (Print) Andrew Wade (Durham University) ISSN: 2516-385X (Online) Mike Whittaker (University of Glasgow) DOI: 10.1112/NLMS Andrew Wilson (University of Glasgow) Early Career Content Editor: Jelena Grbic´ NEWSLETTER WEBSITE News Editor: Susan Oakes Reviews Editor: Christopher Hollings The Newsletter is freely available electronically at lms.ac.uk/publications/lms-newsletter. CORRESPONDENTS AND STAFF LMS/EMS Correspondent: David Chillingworth MEMBERSHIP Policy Digest: John Johnston Joining the LMS is a straightforward process. For Production: Katherine Wright membership details see lms.ac.uk/membership. Printing: Holbrooks Printers Ltd EDITORIAL OFFICE SUBMISSIONS London Mathematical Society De Morgan House The Newsletter welcomes submissions of 57–58 Russell Square feature content, including mathematical articles, London WC1B 4HS career related articles, and microtheses from [email protected] members and non-members. Submission guidelines and LaTeX templates can be found at Charity registration number: 252660 lms.ac.uk/publications/submit-to-the-lms-newsletter. Feature content should be submitted to the COVER IMAGE editor-in-chief at [email protected]. The Coxeter projection of the E root system, a 8 News items should be sent to string art created by Tamás Görbe (University [email protected]. of Leeds). For more details and images, see tamasgorbe.com/symmetry. Notices of events should be prepared using the template at lms.ac.uk/publications/lms-newsletter Do you have an image of mathematical interest and sent to [email protected]. that may be included on the front cover of a future issue? Email [email protected] for For advertising rates and guidelines see details. lms.ac.uk/publications/advertise-in-the-lms-newsletter. i i i i i i “NLMS_494” — 2021/4/19 — 10:44 — page 3 — #3 i i CONTENTS NEWS The latest from the LMS and elsewhere 4 LMS BUSINESS Reports from the LMS 13 FEATURES Cover Image: Exceptionally Beautiful Symmetries 17 Notes of a Numerical Analyst 18 Mathematics News Flash 19 The Poetry of George Boole 20 Fermat’s Two Squares Theorem for a Prime p ≡ 1 ¹mod 4º 26 The Shape of a Module Category 32 Inside Out 37 EARLY CAREER Microthesis: Nonabelian Cohomology and Cohomotopy of Cosimplicial Groups 38 REVIEWS From the bookshelf 40 OBITUARIES In memoriam 45 EVENTS Latest announcements 49 CALENDAR All upcoming events 50 i i i i i i “NLMS_494” — 2021/4/19 — 10:44 — page 4 — #4 i i 4 NEWS LMS NEWS LMS President-Designate Mathematical Society in 2012 and a Member of the Appointed Next Director of INI German National Academy of Sciences Leopoldina in 2017. More information is available at tinyurl.com/2vskdjbo. The ‘Research Reboot’ Scheme In response to a proposal from its Covid Working Group, the Society’s Council has approved a new ‘Research Reboot’ grant scheme. This scheme aims to help mathematicians restart their research activities following the intense disruption and upheaval of the pandemic. Researchers may have found themselves with very little time for research due to illness, caring responsibilities, increased teaching or administrative loads, or other factors. This scheme offers funding for accommodation Professor Ulrike Tillman FRS, LMS President designate, and caring costs for applicants so that they can leave has been appointed the next Director of the their usual environment to focus entirely on research Isaac Newton Institute (INI). Professor Tillmann will for a period from two days to a week. The initial period become the seventh Director since the INI opened of the scheme will run from June to September 2021 and in 1992, following in the footsteps of Sir Michael could, for example, cover the costs of a hotel or holiday Atiyah, Professor Keith Moatt, Sir John Kingman, apartment. Sir David Wallace, Professor John Toland and current Director Professor David Abrahams. Her ve-year Applicants should be mathematicians based in the UK, appointment begins on 1 October 2021. the Isle of Man or the Channel Islands and may be at any career stage. We will prioritise applications from Professor Tillmann is known for her leading those who, as a result of the pandemic, faced increased contributions to algebraic topology and for her caring responsibilities such as homeschooling. However, many contributions to the LMS and the broader applications from those with additional professional mathematical community. Her research interests demands such as teaching and administration are also include Riemann surfaces and the homology of welcome. their moduli spaces. Her work on the moduli spaces of Riemann surfaces and manifolds of There will be an optional online support network for higher dimensions has been inspired by problems successful applicants. Applicants who are not able to in quantum physics and string theory. More recently commit to a period of time away from home can still her work has broadened into areas of data science. apply to join the support network. She has supported the wider mathematical Research Reboot Scheme 2021 community both nationally and internationally. This Application deadline: 15 May 2021 includes as a Fellow of the Alan Turing Institute and also serving on the scientic boards of several The value of the award will be a maximum of £100 international insititutions, including the Oberwolfach per day for accommodation, subsistence, and other Mathematical Research Institute (MFO). Professor necessary expenses to enable the research project. Tillmann was also a member of Council of the Royal An additional £100 per day may be applied for to Society until the end of 2020 and served as an cover Caring Costs for those who have dependents. interim Vice-President in 2018. For more information and the application form visit lms.ac.uk/grants/research-pairs-scheme-4. Professor Tillmann has received several prestigious Prospective applicants are advised to consult the honours including the LMS Whitehead Prize in guidance available at tinyurl.com/63tmtc. Contact 2004. She was elected a Fellow of the American [email protected] if you have any queries. i i i i i i “NLMS_494” — 2021/4/19 — 10:44 — page 5 — #5 i i NEWS 5 News for US Taxpayers The LMS is always grateful for donations small or large. There are about 175 LMS members living in the United States and we are hopeful that many of We are delighted to announce that it has recently them may take this new and exciting opportunity to become possible for US taxpayers to make donate to the LMS. tax-deductible donations to the LMS. Until now this has not been possible and we are aware that it has been an issue for people wishing to make donations Forthcoming LMS Events in the past. The following events will take place in forthcoming The scheme works as follows. The LMS has recently months: been approved as an institutional member of the LMS Spitalelds History of Mathematics American non-prot organisation the British Schools Meeting: 14 May, online (tinyurl.com/y3kpv6ye) and Universities Foundation (BSUF, bsuf.org). The sole purpose of BSUF is to allow tax-deductible donations Mary Cartwright Lecture 2021: 24 May, online from US donors to be made to British educational and cultural institutions. Anyone wishing to make LMS Good Practice Scheme Workshop: 26 May, a donation to the LMS through this means donates online (tinyurl.com/3ednhb82) the money to BSUF, designating the LMS as their Midlands Regional Meeting and Workshop: preferred institution. BSUF will then forward the full 2–4 June, Lincoln (tinyurl.com/y5vtaytx) amount of the donation to the LMS. Donor advised funds may also be used for this purpose. LMS Meeting at the 8ECM: 22 June, online (tinyurl.com/pk4zy6nw) Donations can be made electronically via the ‘Donate’ button on the BSUF website; alternatively, cheques Summer Graduate Student Meeting: 24 June, can be sent to the New York oce of BSUF. For online (tinyurl.com/rt8xwn8) full details see the Donate section of the LMS website lms.ac.uk/content/donations. Professor Tim Summer General Society Meeting: 2 July, London, Riley of Cornell University has taken on the role online (tinyurl.com/rt8xwn8) of the LMS’s US representative for this purpose Northern Regional Meeting: 6–10 September, and donations by cheque may also be sent to him; University of Manchester (tinyurl.com/yamy8uvq) please check with him in advance. Queries can be addressed to [email protected] or to Tim Riley A full listing of upcoming LMS events can be found at [email protected]. on page 50. OTHER NEWS International Mathematics one teacher as Team Leader; individual students Competition for University Students without Team Leaders are welcome.