Roger Penrose on Stephen Hawking
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The Oxford Mathematics Newsletter • Spring 2018 Roger Penrose on Stephen Hawking Women tutors in the 1940s and 1950s Mathematical biology Oxford Admissions in Mathematics Head of Contents Departmental News Department’s letter Departmental News 3 Experiences with Stephen Hawking 4 Martin Bridson FRS Women tutors in the 1940s and 1950s 6 Mathematical biology 7 Appointments and achievements 8 There is much to celebrate this year in the continued Oxford Admissions in Mathematics 9 Frances Kirwan elected Andrew Wiles awarded John Ball awarded development of Oxford Mathematics, but I want to Public Lectures 10 Savilian Professor Copley Medal King Faisal Prize concentrate on a single new term in our lexicon – OMMS, More research Frances Kirwan FRS has been elected Oxford mathematician Sir Andrew Wiles Oxford’s Sedleian Professor of Natural the Oxford Masters in Mathematical Sciences. to Oxford University’s Savilian Chair of FRS has been awarded the Copley Medal, Philosophy, Sir John Ball FRS, has been Leslie Fox plaque Geometry (founded in 1619). She will be the Royal Society’s oldest and most awarded the King Faisal Prize for Science. The dictionary on my desk records OMS as the plural of a “mantra used in the 20th occupant of this position, and is prestigious award. This medal is given Launched by the King Faisal Foundation contemplation of ultimate reality”. OMMS offers more specific pathways Alumni Garden Party and tours 11 the first woman to hold a historic Oxford annually for outstanding achievements in and granted for the first time in 1979, the Mathematics Chair: previous Savilian research in any branch of science. Previous King Faisal Prize recognises the outstanding to enlightenment. Outreach professors have included Henry Briggs, winners have included Gauss, Darwin works of individuals and institutions in five John Wallis, Edmond Halley and G. H. Hardy. and Einstein, and Oxford mathematicians major categories, one of which is Science. Working with our colleagues in Statistics and Computer Science, we will Oxford Mathematical Alphabet Michael Atiyah and Roger Penrose. bring fifty of the most talented students from across the globe to Oxford Frances has received many honours. She John Ball is Director of the Oxford Centre each year to study on this new one-year MSc degree. Students will Obituaries was elected a Fellow of the Royal Society Since 2011 Andrew has been a Royal for Nonlinear Partial Differential Equations in 2001 and President of the London Society Anniversary Professor at Oxford, and Fellow of The Queen’s College. His choose from a broad array of courses, ranging from the core of Some 2017 highlights and 2018 Mathematical Society from 2003 to 2005. and in 2016 he won the Abel Prize. An main research areas lie in the calculus of fundamental mathematics to new frontiers of application in genomics resolutions from Institute members She was created a Dame Commander of active member of Oxford’s eminent variations, nonlinear partial differential and data science. OMMS will equip students for careers in research and the British Empire (DBE) in 2014. Her number theory research group, he is equations, infinite-dimensional dynamical innovation across academia and beyond. Roger Bacon will smile on them Writing for the public 12 research interests lie in algebraic and currently developing new ideas for the systems and their applications to nonlinear across the centuries: symplectic geometry – notably moduli Langlands Program, a set of far-reaching mechanics. Our favourite shop spaces in algebraic geometry, geometric conjectures connecting number theory invariant theory, and their connections with to algebraic geometry and the theory of “He who knows not mathematics cannot know the other sciences nor moment maps in symplectic geometry. automorphic forms. the things of this world… A knowledge of this science prepares the mind and raises it up to a well-authenticated knowledge of all things.” Our ability to deliver OMMS is rooted in the fact that our permanent Landon Clay 1926–2017 faculty has doubled in size over the last twenty years: it now stands at just over one hundred. This enables us to offer advanced courses With the death of Landon T. Clay last by world-leading researchers across the full spectrum of mathematics. July, Oxford Mathematics lost a treasured Our advanced undergraduates already benefit enormously from this friend whose committed support and generosity were key factors in the recent rich offering, and now we are able to extend the same opportunities development of the Mathematical Institute. to the best masters-level students from elsewhere. The support of Landon and his wife Lavinia was the indispensable mainstay of the New Professor of The introduction of OMMS is a landmark in the history of the project to create the magnificent new home Mathematical Institute. The fee income from this programme will enable for Oxford Mathematics: the Andrew Wiles Mathematical Finance Building symbolises the enduring legacy us to provide stable funding for more doctoral students – a priority of their insightful and incisive support for Rama Cont has been appointed to the that I wrote to you about last year. It will also fund research fellowships, Get in touch mathematics and science. Oxford Professorship of Mathematical providing postdoctoral opportunities that bring the best early career Finance. Currently Professor of researchers to Oxford and sustain the pipeline of talent into mathematics. We hope that you will enjoy this annual In 1998 Landon Clay founded the Clay Mathematics and Chair in Mathematical newsletter. We are interested to receive your Mathematics Institute, whose scientific Finance at Imperial College London, he comments, and also contributions for future arrangements are now run from Oxford: has held teaching and research positions Thus OMMS will bolster our research while enabling us to share the newsletters. Please contact the editor, Robin this has had a profoundly beneficial effect on in Paris and New York. His research excitement of modern mathematics with new cohorts of talented Wilson, c/o [email protected] the progress and appreciation of research into interests focus on stochastic analysis, young people. fundamental mathematics. He may be best stochastic processes, and mathematical @OxUniMaths remembered for his inspired creation of the modelling in finance. He will take up the facebook.com/OxfordMathematics Millennium Mathematics Prizes, which drew post in July 2018. Welcome, OMMS! www.maths.ox.ac.uk the public’s attention to the fundamental importance of the prize problems themselves, Design: William Joseph rather than to the prizewinners. Landon Clay and Andrew Wiles Round up • Oxford Mathematics • Spring 2018 3 Because I like to think of things geometrically, I began Stephen was I think that our disagreements on this issue reflect the to consider them in terms of space-time geometry, difference in our views about the overarching nature to see whether they might be generic or something the most of current quantum mechanics. For me, quantum that happened only under special circumstances. determined mechanics will need to be modified in a gravitational I’d been thinking about such matters in a different context. Stephen’s different view required that unitarity context where topological issues were important, person I have must be preserved at all costs. This divergence of and had developed techniques from differential ever met, as he opinions is probably responsible for our taking different topology rather than trying to solve Einstein’s routes in our subsequent work in theoretical physics. equations in any detailed way. continued to do his original Stephen and I were once at a conference in Brussels I later realised that I could characterize where the and a local resident had offered to drive us to the predicted collapse reached a point of no return (a research airport. This was generous and we both agreed, but ‘trapped surface’) and that my earlier techniques against the the poor chap had no idea of how to get there and could be used to demonstrate that a gravitational we took numerous wrong turnings. It soon became so collapse which had passed this point must result in greatest late that we thought we would surely miss the plane. a singularity. With these techniques there was no physical But he eventually discovered the right route and we requirement for Oppenheimer and Snyder’s spherical arrived at the airport with very little time to spare. I symmetry, or for the collapsing material to be dust. obstructions. remember rushing Stephen’s wheelchair up and down Developing these ideas I showed, under some other various ramps at great speed, and being nervous that natural assumptions (such as Einstein’s general he’d be scared about this violent activity – but the theory of relativity holding true), that such a expression on his face showed how he was really rather singularity must develop. enjoying the whole thing. Perhaps this is representative of his obvious enjoyment of situations that many of us In 1965 I lectured on my findings in Cambridge would find too nervous to undergo, such as when he to an audience that included the young Stephen experienced weightlessness in an aeroplane in freefall. Hawking who was beginning research at Cambridge. After my talk I described the general techniques to Stephen was the most determined person I have ever Stephen, and to George Ellis, whose work required met, as he continued to do his original research against some symmetry assumptions that would not hold the greatest physical obstructions. So let me end by in general. Stephen latched onto these ideas very saluting this remarkable man, with his enormous skills quickly and showed how to use my result for a in mathematics and physics, with his great enjoyment local gravitational collapse, but in the context of of life (despite so many appalling difficulties), and with cosmology, where my ‘trapped-surface’ condition his profound statements on his worries about where the could be applied at infinity when the universe was human race may be heading.