Number 15 • Spring 2016

We hope that you will enjoy this annual newsletter. We are interested to receive Martin Bridson your comments, and also contributions for future newsletters. Please contact A note of welcome the editor, Robin Wilson, c/o [email protected]

On 1 October Prof. Martin Bridson, Whitehead Professor of Pure Mathematics and Fellow of Design & production by Baseline Arts Magdalen College, took over the reins as Head of the Mathematical Institute from Prof. Sam Howison. Martin writes:

We are at a moment in the history of Oxford Mathematics that is so self-evidently special that we cannot help but marvel at it. Two years after moving into our splendid new home, it is still thrilling to enter the Andrew Wiles Building and sense the intellectual excitement all around us. Students and visiting mathematicians are inspired by the statement that it makes: mathematics is important, and you are part of this great enterprise.

A different sense of recognition came with the results of the government’s 2014 Research Excellence assessments: Mathematical Sciences in Oxford was ranked first across the UK in all categories. Oxford’s reputation as a world centre for mathematics has never been stronger. ‘What then?’ sang Plato’s ghost, ‘What then?’.

Sam Howison’s tenure as Head of Department Martin Bridson In 2001 we had 54 permanent faculty members; ended in September 2015. At a small reception, today we have 100, as well as many postdocs and Sam spoke graciously about those who had over 1000 students. We treasure our informality supported him, and passed me the baton. and the unique sense of community that grows Immediately after finishing my champagne I Oxford’s from our shared passion for mathematics and its received a sharp reminder of the constant need reputation propagation. But we’re a big family and we have for renewal in mathematics. Half a dozen of our to organise ourselves well if we are to maximise Statutory Professors are about to retire in quick as a world our contribution to mathematics and society. succession. This loss is daunting, but it presents us with an opportunity to reflect: what are the most centre for Conscious of this, the Department is prioritising exciting trends in world mathematics, and where mathematics its efforts to raise philanthropic funds for DPhil should we be providing leadership? With our studentships that are open to students of all emeriti remaining active, this process of renewal has never nationalities working in all areas of mathematics. can lift us to new heights. been This is central to our plans for the future, and I hope that many of you will see it as an In the 1960s the Mathematical Institute was stronger. opportunity to support the life of the Institute. headed by a Curator, and then for a long time we had a Chairman. The University now prefers the It has been a pleasure to see so many alumni and title Head of Department, and perhaps this is a friends at our recent public events. I hope to see hint about the challenges that come with growth. many more of you here during my time as Curator. n

OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2016 . ISSUE 15 / 1 Anniversaries

Somerville. Although her mathematical Later in life Ada continued to pursue her pursuits were put on hold following her mathematical interests. Although she did marriage and the birth of three children, no further work on Babbage’s engines, she later went back to mathematics she and Babbage remained friends and and studied with the prominent British appear to have pursued recreational mathematician Augustus De Morgan. mathematics together: on one charming In a two-year correspondence course, document, for instance, we find an preserved in the Bodleian, we see her exploration of the problem concerning working through much of the same the Bridges of Königsberg. material as De Morgan’s students at UCL – limits, series, functions, differential The Oxford Ada Lovelace Symposium, equations, and the like. which took place on 9–10 December, saw a great variety of talks on subjects connected This background stood Ada in good with Ada, ranging from her contributions stead when she came to translate and to computing, to the literary influence on extend Menabrea’s article. Babbage’s her scientific thought, to a new (mixed) Analytical Engine was, in modern terms, a assessment of her mathematical abilities. general-purpose computer, programmed with punched cards, similar to those Thanks are due for the generosity of used at the time to control Jacquard the Clay Mathematics Institute and Ada Lovelace, aged 17 looms. In principle, it could calculate any the descendants of Ada Lovelace. The function. Ada’s paper presents it, not in presentations from the symposium may terms of ironmongery, but as what we be watched online at http://podcasts. Celebrating would now call an ‘abstract machine’, ox.ac.uk/series/ada-lovelace-symposium- describing the functions of memory, CPU, celebrating-200-years-computer-visionary. registers, loops, and so on. What is truly Images and transcriptions of Ada’s Ada Lovelace remarkable to the modern computer mathematical writings will be released Christopher Hollings and Ursula scientist reading the paper is Ada’s online at www.claymath.org in 2016. n Martin high-level view, and how her speculation on the capabilities and potential of the The Ada Lovelace Symposium at the 10 December 2015 was the 200th machine mirrors present-day concerns. Mathematical Institute. anniversary of the birth of the computing pioneer Ada Lovelace. Various events took place in Oxford to mark this anniversary, including a two-day symposium at the Mathematical Institute and an exhibition at the Bodleian Library.

Famous in her day as the daughter of the Romantic poet Lord Byron, Ada is noted amongst mathematicians and computer scientists for a paper published in 1843, which translated and extended a review (by an Italian engineer, Luigi Menabrea) of Charles Babbage’s ideas for a steam- powered computer, his unbuilt ‘Analytical Engine’. Ada’s substantial appendices contain an account of the principles of the machine, and a table displaying how it might compute Bernoulli numbers, often Unlucky 13 described as ‘the first computer program’. It has been pointed out to us that there was no issue Number 13 of this Newsletter; From an early age Ada showed both last year’s issue was Number 14. Was this due to superstition on the part of the Editor, interest and ability in mathematics or perhaps his inability to count? He justifies it on the grounds that issue Number 12 and science, and received tuition from was a double issue featuring the new building. a number of people, including Mary

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Wallis’s formula for 4/π

his favour was the esteem in which he of events in Europe was in part being was held in government circles for his decided by an Oxford mathematician codebreaking abilities. A more far-sighted labouring in his scarce free time in his mathematical appointment on false lodgings in New College Lane. grounds is difficult to imagine. Wallis’s appointment to the Savilian Chair, which Although Wallis was often conservative he held until his death fifty-four years in his use of mathematical notation he later, marked the beginning of an intense introduced two new symbols that we still period of activity which established use today, for ‘infinity’ and for ‘greater Oxford as the mathematical powerhouse than or equal to’. of the nation. Wallis’s last great mathematical work, A John Wallis’s Arithmetica Infinitorum Treatise of Algebra, Both Historical and (‘Arithmetick of Infinites’) appeared Practical, was published in 1685, in his John Wallis, by Sir Godfrey Kneller, Bt at a critical time for the development seventieth year. Of his vast output, it was of mathematics. Approaches using this work that was most widely read over geometrical indivisibles had previously the next hundred years, and was the first Celebrating been used to find areas under curves, substantial history of mathematics in the and were successful for any curve of the English language. form y = xn , where n is a positive integer, John Wallis but Wallis associated numerical values to Although Wallis’s main contribution Philip Beeley and Raymond Flood the indivisibles, allowing him to extend to learning was undoubtedly through the result to the case when n is fractional. his innovative and important work in 2016 marks the 400th anniversary the broad sphere of mathematics, he of the birth of John Wallis, who held The word ‘interpolation’ (in its excelled in other fields, too, including the Savilian Chair of Geometry for mathematical sense) was introduced classical scholarship and studies on 54 years. Oxford’s Wallis Chair of by Wallis in this work, and he would language. He also served for nearly half Mathematics is named after him. always be associated with supplanting a century as keeper of the archives, geometrical techniques to ‘quadratures’ one of the highest ranked officers in The introduction of John Wallis into with more rigorous arithmetical ones. It the University at that time, assiduously the University of Oxford was caused by was also here that Wallis produced his defending the institution’s ancient rights politics. During the early part of the Civil celebrated formula for what we would and privileges. Wars the University had been the Royalist call 4/π (and which he presented as headquarters, and in the subsequent pictured at the top of this page). Some measure of the impression that reckoning most college heads and fellows Wallis left on contemporaries may be were deposed. The Savilian professors Wallis’s fundamental engine of discovery seen in the remarkable full-length portrait were expelled in 1648 for Royalist was the exploration and recognition of him at the age of 86, by the court sympathies, and the Parliamentary of pattern. His career had been set in painter Sir Godfrey Kneller. This painting Commissioners replaced them by John motion by his cryptographical skills – in which the aged Wallis, swathed in Wallis as Professor of Geometry and Seth during the Civil Wars, and they seem to scarlet like some Renaissance prince- Ward as Professor of Astronomy. Wallis have characterised his mathematical prelate, stares out at the viewer with had been a moderate supporter of the style as well. Wallis deciphered unmistakable pride – was commissioned revolutionary cause during the Civil Wars. throughout his professional career, right by his friend Samuel Pepys for up to the final days before his death; he presentation to the University of Oxford. Prior to taking up the Savilian Chair John was justly regarded as Europe’s greatest Wallis had little mathematical experience codebreaker, working mainly on complex John Wallis’s life and work will be and enjoyed no public reputation as French numerical substitution ciphers. celebrated at a one-day meeting in the a mathematician. What counted in It is humbling to think how the course Mathematical Institute on 9 June 2016. n

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Transcendental numbers Jonathan Pila FRS

Transcendental numbers, like π number 7 on Hilbert’s famous 1900 list. (= 3.14159…) and e (= 2.71828…), have It was affirmed by Gelfond and Schneider long fascinated mathematicians. in the 1930s and generalised by Alan There are obstinate problems (is π + e Baker in the 1960s. transcendental, or even irrational?), fruitful connections, and an How might one prove such results? Proofs overarching conjectural picture. depend on the interaction between the analytic and arithmetic properties of A number that satisfies a polynomial the exponential function – in particular, equation with integer coefficients is the fact that it has a power series with called algebraic – for example, √2, 3√2, rational coefficients. We assume, for a and √2 + √3 are all algebraic, satisfying contradiction, that there is an algebraic the equations x2 = 2, x3 = 2, and x4 − 10x2 relationship, and then construct a + 1 = 0, respectively. If there’s no such quantity that (for analytic reasons) lies non-zero polynomial, the number is between 0 and 1, but is also an integer. transcendental. This contradiction proves the result.

The ancient Greek geometers tried We might expect numbers and their CJ Mozzochi (Princeton, NJ) © unsuccessfully to ‘square the circle’ – exponentials to be as ‘algebraically that is, to use a ruler and compasses to independent’ as they can be, subject to Jonathan Pila construct a square whose area equals the constraints imposed by the identity that of a given circle. They also tried to exp(x + y) = exp(x).exp(y). generalised by Grothendieck and ‘double the cube’. It turned out that only a A comprehensive conjecture was others to a bigger picture including zeta rather special kind of algebraic number is formulated by Stephen Schanuel in the function values, such as constructible using ruler and compasses 1960s: (one using the usual rules of arithmetic, together with the taking of square roots). Schanuel’s conjecture: If x1, . . . , xn Doubling the cube is impossible because are complex numbers that are linearly 3√2 is algebraic, but is not constructible. independent over the rationals, then which was proved irrational by This was proved in the 1830s with the at least n of the numbers x1, . . . , xn, Apéry (1979) and is thought to be development of algebra – but algebraic exp(x1), . . . , exp(xn) are algebraically transcendental (but this is unknown): methods cannot deal with π. independent over the rationals. work of Oxford’s Francis Brown is connected with these ideas. Second, The transcendence of π was proved in Schanuel’s conjecture implies all known various analogues of the conjecture can 1882 by Ferdinand Lindemann, who had transcendence results and conjectures be proved: in particular, it was proved discussed the matter with Oxford’s Henry about the exponential function. for functions by Ax (1971). Third, the Smith in 1876. His proof generalised For example, its truth would imply the conjecture serves as a paradigm in the methods of Charles Hermite, who unproved algebraic independence of model theory, guiding and inspiring proved the transcendence of e a few e, exp(e), exp(exp(e)), … (and similarly much work, including new diophantine years earlier: in fact Lindemann proved for π). For n = 1, Schanuel’s conjecture conjectures of Oxford’s Boris Zilber (2001) that if x is algebraic but non-zero then reduces to the Hermite–Lindemann which give a far-reaching extension of exp(x) is transcendental. It follows from theorem, but it is not known in general a famous 1922 conjecture of Mordell this that π is transcendental, because for n = 2. On the positive side, Nesterenko (proved by Gerd Faltings in 1983) about exp(2πi) = 1 is algebraic. Likewise, the proved in 1986 that π and exp(π) are rational points on curves. logarithm of a non-zero algebraic number algebraically independent, using the is transcendental. analytic and arithmetic properties of Thus, Schanuel’s conjecture guides certain modular functions studied by much current work, including much Leonhard Euler speculated that, if Ramanujan. of my own in Oxford, which revolves a and b are algebraic with a ≠ 0 or 1 around generalisations of Ax’s functional and b irrational, then ab should be While progress towards Schanuel’s versions of Schanuel’s conjecture transcendental: this includes 2√2, conjecture has been slow, it has been and applications to the diophantine (i)i, and exp(π) = (−1)−i: proving this was fruitful. First, the conjecture has been conjectures of Zilber and others. n

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‘Diamond – Vert Veronese – Clebsch’ Art in the Andrew Wiles by Katrina Blannin building Sam Howison Objects was a fascinating addition to this tradition. The The relationship between mathematics and art has been debated for display cabinets were filled with centuries. Some of its aspects are straightforward, such as proportion, models and sculptures, alongside a perspective and projective geometry, but others are more allusive. The Andrew number of paintings and drawings, and Wiles Building has provided our Department with a venue in which to make our there was also a poetry event featuring own contribution. new work by a number of poets. It was a thought-provoking contribution to the The building itself does this. Many visitors On either side of the entrance bridge art–mathematics debate, and we hope have commented that the interior brings is Antoni Malinowski’s wall-based that it will be the first of many. to mind M. C. Escher’s work, especially his commission Spectral Flip, which probes impossible staircases: Roger Penrose’s the interplay of colour, surface textures For more details of all our art, see recent BBC programme on this artist and and illumination. www.maths.ox.ac.uk/about-us/art-and- his mathematical connections was partly oxford-mathematics n filmed there. We followed it up with an The ‘permanent collection’ has been Escher symposium featuring a showing complemented with temporary of the film and talks about the underlying exhibitions in the Mezzanine public mathematics by Jon Chapman and Roger space. The most recent of these was himself; you can watch it on our website. Illegitimate Objects, a group show As well as the staircases, we have the two in which artists made new work in crystals and the wonderfully decorative response to the Department’s collection Penrose tiling; these all reinforce the of 19th-century models of geometric message that this is both a building for surfaces. These models, most likely mathematics and a work of art in its bought by J. J. Sylvester, Oxford’s own right. Savilian Professor of Geometry at the time, were once at the cutting edge of We have commissioned two major research and teaching. Changing tastes pieces for the building. Matt Chivers’ in mathematics relegated most of them sculpture Axiom, which greets visitors in to the store cupboard, but they turned the entrance lobby, shown in Newsletter up in the move to the new building, and © Peter Douglas Edwards, Bridgeman Images (www.peteredwards.net), and Hertford College 14, is based on a triangulation of a we now have a complete catalogue, with Sir Christopher Zeeman. shape generated by expanding bubbles; explanations of their purpose, which you it explores a number of mathematical can see on our website’s ‘History’ section. ideas, including the interesting interface Models of this kind have inspired many Sir Christopher between mathematical perfection and artists, including Man Ray, Henry Moore Zeeman the imperfections of the real world. and Barbara Hepworth, and Illegitimate Sir Christopher Zeeman FRS died in Malinowski with part of ‘Spectral Flip’. February, aged 91. Although most of his distinguished mathematical career was as Founding Professor of Mathematics at Warwick University, working in catastrophe theory and dynamical systems, he spent the years 1988 to 1996 in Oxford as Principal of Hertford College. He was also President of the London Mathematical Society and Vice- President of the Royal Society, but is best remembered in the wider world for his popularisation of mathematics, giving the Royal Institution Christmas lectures in 1978 and founding the Royal Institution

© David Fleming Masterclasses for schoolchildren. n

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Appointments... Naylor prize and Lectureship in Applied Iain Smears has shared the 2015 Leslie Fox Prize Mathematics: to Jon Chapman, Professor in Numerical Analysis (named after Oxford’s first We are delighted to welcome the following of Mathematics and its Applications, for his professor of Numerical Analysis and founder of new Faculty members. contributions to modelling and methods the Oxford University Computing Laboratory) by Alvaro Cartea (UCL): development in applied mathematics. the Institute of Mathematics and its Applications; Lecturer in Mathematical a second prize was awarded to Patrick Farrell. Pólya Prize: to Boris Zilber, Professor of Finance. Research Mathematical Logic, for his contributions to interests: algorithmic and Oxford awards model theory and its applications. high-frequency trading, Vicky Neale, Whitehead Lecturer, has won an commodities and energy Whitehead prizes: to Peter Keevash, Oxford University Student Union Teaching Award finance, mathematical Professor of Mathematics, for his work in in the Most Acclaimed Lecturer category. finance and financial economics. combinatorics, in particular his proof of the Jan Obloj has been appointed the title of existence of combinatorial designs for all Christopher Hollings Professor in the University’s annual Recognition appropriate parameters; to James Maynard, (Oxford): Lecturer in of Distinction exercise. Research Fellow, for his results on gaps between Mathematics and its prime numbers, in particular answering a Catherine Wilkins has won a Mathematical, History, and Senior major unsolved conjecture of Paul Erdős; to Physical and Life Sciences Division award for Research Fellow at the Mason Porter, Professor of Nonlinear and teaching excellence. Queen’s College. Research Complex Systems, for his interdisciplinary interests: development of Thomas Woolley and William Binzi were contributions, and in particular to the emerging modern algebra, Soviet mathematics, scientific awarded runner-up prizes in the OxTALENT field of network science; and to Dominic Vella, communication during the Cold War. competition for their work in creating a video Associate Professor of Applied Mathematics, for series of A Mathemagician’s Holiday. Harald Oberhauser (UCL): his contributions to the modelling of instability Associate Professor in and interfacial phenomena in fluids and solids. Fellows of the Royal Society Probability and Tutorial The following have been elected Fellows of Fellow at St Hugh’s College. the Royal Society: Research interests: systems that evolve under the Alison Etheridge, Professor of Probability, influence of randomness, and has made significant contributions in the their applications. theory and applications of probability and in the links between them. Her particular areas Damian Rössler (Toulouse): of research have been in measure-valued Professor of Mathematics processes (especially super processes and and Tutorial Fellow at their generalisations), in theoretical population Pembroke College. Research genetics and in mathematical ecology. interests: algebraic geometry Recently she has created a flexible framework in positive characteristic, for modelling biological populations which, for number theory, Arkelov the first time, combines ecology and genetics in theory. Oxford’s Terry Lyons, LMS President, presenting the award to Dominic Vella a tractable way, while introducing a novel and Ricardo Ruiz Baier mathematically interesting class of stochastic (Lausanne): Lecturer in Other awards processes. Numerical Analysis. Research Marcus du Sautoy OBE has been awarded an Philip Maini, Professor of Mathematical interests: numerical methods Honorary Doctorate of Science by the University Biology, is renowned for his mathematical and for PDEs, finite elements, of South Wales. computational modelling of spatiotemporal hybrid finite volume Patrick Farrell and his collaborators have processes in biology and medicine, which has discretizations, adaptive won the 2015 Wilkinson prize, recognising their led to significant scientific advances in both. schemes, error estimation. work in developing dolphin-adjoint, a package He has, for instance, developed multiscale Melanie Rupflin (Leipzig): that automatically derives and solves adjoint models for wound healing and for vascular Associate Professor in and tangent linear equations from high-level tumour growth, and thereby elucidated the the Analysis of Nonlinear mathematical specifications of finite element underlying mechanisms by which particular PDEs, and Tutorial Fellow discretisations of PDEs. growth factors reduce scar formation and at Trinity College. Research provided detailed insight into the design of James Maynard has been awarded a Clay interests: geometric analysis, combination cancer therapy. Research Fellowship by the Clay Mathematics in particular the study of Institute. Jonathan Pila, Reader in Mathematical Logic, has geometric flows, harmonic analysis and minimal pioneered the study of the distribution of rational surfaces. Peter Neumann OBE was President of the points on sets defined by real analytic conditions, Mathematical Association for 2015–16. In leading (with collaborators) to a powerful theorem addition, he has been awarded an Honorary Recognition... in the setting of o-minimal structures, a part of This has been another good year for awards. Doctorate of Science by the University of Hull. model theory. This theorem has found significant London Mathematical Society prizes Ebrahim Patel won the 2015 Early Career applications to central problems in diophantine Six prizes were awarded to Oxford Mathematician Catherine Richards Prize, geometry and has opened up a rich new mathematicians by the London Mathematical awarded by the IMA, for a co-authored article connection between diophantine geometry and Society: entitled ‘Mixing motions’. mathematical logic. n

6 / OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2016 . ISSUE 15 Outreach

them, please fill in the form on www. We now look forward to the return of External relations alumniweb.ox.ac.uk/secure/maths_email. PROMYS Europe next summer, with a Dyrol Lumbard select group of older teenagers from across We’ve also launched a new Oxford Europe immersing themselves in number External relations may seem a one-way Mathematics Alphabet on our Life in theory for six weeks. We’re delighted that street – we tell the world what we do Oxford Mathematics webpage, which we can share our building with over 3000 to promote Oxford Mathematics – but features an area of our research for each school students a year, as we spread the we’d rather characterise it as a mutual letter of the alphabet – beginning with word about the wonder of mathematics exchange: we tell you what we do, and Aperiodic tiles (by Sir Roger Penrose) and and Oxford’s place in its study. n you in turn tell us what you’re doing and Bayesian inference (Robin Evans). n what you’d like to hear about. Women in Maths With that in mind we’ve developed our Alumni Stories feature where alumni meeting give us a Q & A version of their lives Frances Kirwan since leaving Oxford. Please have a look at the stories so far and let us know In 2015, the London Mathematical yours (www.maths.ox.ac.uk/about-us/ Society’s annual ‘Women in Maths engagement/alumni-stories). day’ was expanded to four days and hosted in Oxford as part of the LMS Equally, several of you have told us 150th anniversary celebrations, with that you want more on our latest two days for school students and two research, so that is both a feature of this days for university mathematicians and annual Newsletter and of the electronic mathematical scientists. newsletters that we send throughout the year. If you’re not currently receiving The meeting was a great success, with about 430 participants for the first two days, and 250 for the last two. As the LMS President wrote, ‘the event, which Public lectures Working with is being talked about far and wide, has been one of the highlights of the Our Oxford Mathematics Public Lectures schoolchildren Society’s 150th Anniversary year so far, series, aimed at sixth-formers and above, Rebecca Cotton-Barratt and as a result of its success the Women is now well established and plays to in Mathematics Committee is hoping to packed audiences. Amongst others over The Andrew Wiles Building is proving to be able to further develop its work with the past year we’ve had Martin Bridson be an inspiring place for mathematical school students and undergraduates’. talking on symmetry and undecidability, events for schoolchildren. We’ve hosted Roger Penrose on Escher, Étienne Ghys Royal Institution Masterclasses on A short video of the meeting, produced on the dancing skills of vortices, and Saturdays for local teenagers who are by Mareli Augustyn, can be viewed on Marcus du Sautoy on the logistical and so keen that they keep coming back www.maths.ox.ac.uk/events/conferences/ mathematical challenges that Santa year after year, events for the Further past-events/women-maths, together with Claus faces every Christmas Eve. If you Mathematics Support Programme photographs by Jennifer Balakrishnan, want an enjoyable late afternoon out, giving more students access to Further a photo collage created by participants please come along – and if you can’t Maths at A Level, and events for the UK to show the present and future of UK make it, these lectures are all online on Mathematics Trust ranging from team women in mathematics, and a link to the our events pages. n maths challenges for 13-year-olds from programme. n Oxfordshire and nearby to summer schools for 16-year-olds invited from across the country. In addition we hold the Maths and Maths & Stats UNIQ summer schools as part of Oxford’s work on widening participation. Our days to promote mathematics to schoolgirls last April (see following article) proved so popular that we ran them again in January for several hundred more students.

SPRING 2016 . ISSUE 15 / 7 Epsilons and deltas

Alumni events Fellows of the Royal Andrew Wiles

Last year’s Mathematical Institute Society portrait Garden Party was held in the Andrew Alison Etheridge’s election to a A recently commissioned portrait by Wiles Building during the University’s Fellowship of the Royal Society (see Rupert Alexander of Sir Andrew Wiles Alumni weekend. The speaker was Ben page 6) brings to six the total number of FRS, has been unveiled at the National Green FRS, Waynflete Professor of Pure women mathematicians who have ever Portrait Gallery. It can be viewed at www. Mathematics, on ‘Problems about points been elected FRS. Three of the six are maths.ox.ac.uk/node/14675 and lines’. currently working in Oxford, the other two being Frances Kirwan (left) and This year’s Garden Party will take place Ulrike Tillmann (right). Two of the others, Undergraduate on 17 September in the Andrew Wiles Mary Cartwright and Mary Rees, were Building. You can book online at www. summer research formerly students at Oxford. maths.ox.ac.uk/about-us/alumni/alumni- projects garden-party. Professor Jon Chapman, Director of OCIAM, will give a lecture on In the summer vacation of 2015, over 25 ‘The mathematics of M. C. Escher’. undergraduates took part in summer research projects supervised by members of the Oxford Mathematical Institute. Some of the students described their work in posters currently on display in the Mezzanine of the Andrew Wiles Building. At the moment, we are helping students who want to do projects in 2016 to match with willing supervisors, and are seeking funding Frances Kirwan, Alison Etheridge and Ulrike to try to enable all those who want to Tillmann do a summer project to be able to get a taste of mathematical research, with the TV programmes aim of inspiring the next generation of Jon Chapman’s modern update on Escher’s research students. n ‘Print Gallery’. A number of recent television programmes have featured the Andrew Wiles Building. Ida Busbridge These include a BBC4 programme on the mathematical art of M. C. Escher by Cheers... A biography of Sir Roger Penrose FRS, and an hour-long Dr Ida Busbridge, BBC4 documentary on Algorithms by At a meeting in Edinburgh on The who taught Marcus du Sautoy. Most spectacularly, Science of Beauty at which all three mathematics in the Mathematical Institute was the scene were guest speakers, Sir Michael Atiyah Oxford from 1935 of a dramatic bomb blast that killed the (left) and Sir Roger Penrose (right) to 1970, has been professor of geometric topology in the enjoyed a relaxing drink with Sir David written by her final episode of ITV’s detective series Lewis. Attenborough. n former student E. Clare Friedman. A popular tutor and lecturer, ‘Buz’ was appointed Fellow of St Hugh’s College in 1946, the first woman to be appointed to a college fellowship in mathematics. In 1962 she was awarded a Doctor of Science degree for her work in integral equations and radiative transfer. Her booklet on Oxford Mathematics and Mathematicians can be accessed online at www.maths.ox.ac.uk/about-us/history/ Kevin Whately and Laurence Fox in the Andrew Photo by Gerardo Jaconelli; courtesy of the Royal Society of Edinburgh busbridge-lecture. Wiles Building

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