i “NLMS_481” — 2019/2/13 — 11:04 — page 1 — #1 i i i NEWSLETTER Issue: 481 - March 2019 HILBERT’S FRACTALS CHANGING SIXTH AND A-LEVEL PROBLEM GEOMETRY STANDARDS i i i i i “NLMS_481” — 2019/2/13 — 11:04 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Iain Moatt (Royal Holloway, University of London) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or photog- Tomasz Brzezinski (Swansea University) rapher for the rights to reproduce. The LMS Lucia Di Vizio (CNRS) cannot accept responsibility for the accuracy of Jonathan Fraser (University of St Andrews) information in the Newsletter. Views expressed Jelena Grbic´ (University of Southampton) do not necessarily represent the views or policy Thomas Hudson (University of Warwick) of the Editorial Team or London Mathematical Stephen Huggett (University of Plymouth) Society. Adam Johansen (University of Warwick) Bill Lionheart (University of Manchester) ISSN: 2516-3841 (Print) Mark McCartney (Ulster University) ISSN: 2516-385X (Online) Kitty Meeks (University of Glasgow) DOI: 10.1112/NLMS Vicky Neale (University of Oxford) Susan Oakes (London Mathematical Society) David Singerman (University of Southampton) Andrew Wade (Durham University) NEWSLETTER WEBSITE The Newsletter is freely available electronically Early Career Content Editor: Vicky Neale at lms.ac.uk/publications/lms-newsletter. News Editor: Susan Oakes Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process. For membership details see lms.ac.uk/membership. LMS/EMS Correspondent: David Chillingworth Policy Roundup: John Johnston Production: Katherine Wright SUBMISSIONS Printing: Holbrooks Printers Ltd The Newsletter welcomes submissions of fea- ture content, including mathematical arti- EDITORIAL OFFICE cles, career related articles, and microtheses from members and non-members. Submis- London Mathematical Society sion guidelines and LaTeX templates can be De Morgan House found at lms.ac.uk/publications/submit-to-the- 57–58 Russell Square lms-newsletter. London, WC1B 4HS [email protected] Feature content should be submitted to the editor-in-chief at [email protected]. Charity registration number: 252660 News items should be sent to [email protected]. Notices of events should be prepared us- COVER IMAGE ing the template at lms.ac.uk/publications/lms- newsletter and sent to [email protected]. A fractal from conformal dynamics (see page 24). For advertising rates and guidelines see © avvlex — stock.adobe.com lms.ac.uk/publications/advertise-in-the-lms- newsletter. i i i i i “NLMS_481” — 2019/2/13 — 11:04 — page 3 — #3 i i i CONTENTS NEWS The latest from the LMS and elsewhere 4 LMS BUSINESS Reports from the LMS 9 FEATURES Hilbert’s Sixth Problem: the Path to Mathematical Rigour in Science 16 Measuring Changing Standards in Mathematics Exams 21 Fractal Geometry and Dynamics: One semester at Institut Mittag-Leer 24 The Singapore Mathematical Society 30 EARLY CAREER PWSAfrica 31 Microthesis: Dynamical Systems Methods for Waves in Fluids 33 REVIEWS From the bookshelf 35 OBITUARIES In memoriam 39 EVENTS Latest announcements 45 CALENDAR All upcoming events 50 i i i i i “NLMS_481” — 2019/2/13 — 11:04 — page 4 — #4 i i i 4 NEWS LMS NEWS Forthcoming LMS Events hold them to the highest standards. More details on the submission process and the link to submit can The following events will take place in the next two be found at tinyurl.com/y7cuaxbr. months: The current joint Editorial Board of the LMS jour- Christopher Zeeman Medal Presentation nals will continue to receive new submissions for and Lecture: 5 March, Royal Society, London the Bulletin, Journal and Transactions. Furthermore, (tinyurl.com/y84gvbyk) papers which were submitted to the Proceedings prior Hirst Lecture and Society Meeting: 21 March, De to 1 March 2019 will continue to be handled by the Morgan House, London (tinyurl.com/ybewfqz7) existing Board and decisions for acceptance will be held against the same criteria that were in place Mary Cartwright Lecture: 5 April, ICMS, Edinburgh at the time of submission. After 1 March, papers (tinyurl.com/ycv3ssfq) which would previously have been submitted to the LMS Meeting at the BMC: 10 April, Lancaster Proceedings will now be welcomed by the Journal. (tinyurl.com/yarpowdo) We ask the mathematical community to support this A full listing of forthcoming LMS events can be found exciting new chapter by considering submitting to on page 50. Proceedings any forthcoming papers that will help secure the uplift in quality for which we are striving. Changes to the Proceedings of the London Mathematical Society Tim Browning and Oscar Randal-Williams Managing Editors Founded in 1865, the VOLUME 121 PART 1 JULY 2020 Proceedings of the London Mathematical Society Proceedings is today seen by many as the agship journal of the LMS. With the support Annual Elections to LMS Council Proceedings of the of the LMS Publications London Committee, we took on The LMS Nominating Committee is responsible for Mathematical proposing slates of candidates for vacancies on Coun- Editorial Board the task of elevating the Society Nalini Anantharaman Timothy Browning Hélène Esnault cil and vacancies on its own membership. The Nomi- James McKernan position of the journal Oscar Randal-Williams Raphaël Rouquier nating Committee welcomes suggestions from the Scott Sheffield Anna Wienhard further and strength- Daniel T. Wise ening its position with membership. relation to other top-ight mathematics journals. Anyone who wishes to suggest someone for a The rst step in this endeavour has been to appoint position as an Ocer of the Society or as a Member- an Editorial Board of leading international experts, at-Large of Council (now or in the future) is invited to including Nalini Anantharaman, Hélène Ésnault, James send their suggestions to Professor Kenneth Falconer, McKernan, Bryna Kra, Manuel del Pino, Raphaël the current Chair of Nominating Committee (nomina- Rouquier, Scott Sheeld, Anna Wienhard and Daniel [email protected]). Please provide the name and insti- T. Wise. tution (if applicable) of the suggested nominee, their mathematical specialism(s), and a brief statement to The Editorial Board has been selected to attract explain what they could bring to Council/Nominating articles of the highest quality and signicance across Committee. a broad spectrum of mathematics, and the edito- rial procedures have been designed to help ensure It is to the benet of the Society that Council is submissions are dealt with in an ecient and timely balanced and represents the full breadth of the math- manner. ematics community; to this end, Nominating Commit- tee aims for a balance in subject area, geographical From 1 March 2019, this new Editorial Board will be- location and gender in its list of prospective nomi- gin handling submissions to the Proceedings, and will nees. i i i i i “NLMS_481” — 2019/2/13 — 11:04 — page 5 — #5 i i i NEWS 5 Nominations should be received by 19 April 2019 in such a result to subsets of the primes meeting cer- order to be considered by the Nominating Commit- tain equidistribution criteria, and with special atten- tee. tion to the uniformity in k. For example, the paper establishes that there are intervals of length log x In addition to the above, members may make that contain at least C log log x primes for( some) direct nominations for election to Council or Nom- positive C . Since a typical( ) interval of such length inating Committee. Direct nominations must be contains at( most) one prime, these intervals may be sent to the Executive Secretary’s oce (nomina- thought of as containing dense clusters of primes. [email protected]) before noon on 1 September 2019. Another striking example of the results in this paper: For details on making a direct nomination, see there are arbitrarily large intervals of length log x lms.ac.uk/about/council/lms-elections. containing m ≥ log log x consecutive primes all lying in the same reduced residue class a mod q . The slate as proposed by Nominating Committee, ( ) together with any direct nominations received up to Compositio Mathematica is published by the London that time, will be posted on the LMS website in early Mathematical Society on behalf of its owner, the August. Foundation Compositio Mathematica. Compositio Prize Gerard van der Geer President Foundation Compositio Mathematica Every three years, the Foundation Compositio Mathematica awards a Abel Prize Announcement prize for the best pa- per published in Com- The Norwegian Academy of Science and Letters positio Mathematica in a will announce the winner of the 2019 Abel Prize at preceding three-year pe- 11.00am (GMT) on Tuesday 19 March 2019. For the riod. The winner of the rst time, the announcement will be transmitted live Compositio Prize 2018 to an invited audience at the Science Gallery, King’s for the period 2014–2016 College London, in collaboration with the London is the paper by James Maynard, ‘Dense clusters of Mathematical Society. The transmission from Oslo primes in subsets’ (Compositio Mathematica 152 (2016) will be followed by a panel, to include LMS President no. 7, 1517–1554). Professor Caroline Series FRS, which will discuss the winner’s life and scientic work. Breakfast will be A celebrated earlier result of Maynard (and discov- available in the Gallery from 10.00am and the event ered independently by Tao) established that for will begin at 10.45am. All LMS members have been any natural number k one can nd innitely many invited to attend but registration is necessary. For intervals of bounded length C k containing at least more information about the event and to register, k primes.