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Home , Charles Coulson, Christopher Wren, Frances Kirwan, John Wallis, Mary Cartwright, Philip Maini

Maths News 2014 [f]_Maths newsletter 1 10/04/2014 10:41 Page 2

Oxford Mathematical Institute Spring 2014, 12 Newsletter

We hope that you enjoy this annual Newsletter. A Dame and We are interested to receive your comments, and also contributions for future Newsletters. Four Knights Please contact the editor, Robin Wilson, c/o We were delighted to learn that Professor FRS was [email protected] appointed a Dame Commander of the British Empire (DBE) in the 2014 New Year Honours list for services to . This is a wonderful Design & production by Baseline Arts recognition of her stature in the mathematics community, of her many contributions in research, and of her leadership of the Mathematical Society and the UK Mathematics Trust. She joins ’s four mathematical knights: Sir John Ball, Sir , Sir Martin Taylor and Sir .

Frances Kirwan studied in Oxford for her D. Phil. Dame Mary), who studied at St Hugh’s and became in algebraic and symplectic under the an Oxford graduate student of G. H. Hardy. supervision of Prof. . Since 1986 she has been a Fellow in Mathematics at Balliol Frances is also Chair of the UK Mathematics College, and in 1996 became an Oxford Trust, which every year has more than half a University Professor of Mathematics. million young people from over 4000 secondary schools involved in its events and competitions In 2001 she was elected to a Fellowship of the (see the feature article in Newsletter 10). Royal Society, and from 2004 to 2005 was Dame Frances with the President of the London Mathematical Society Her comment on the appointment was: I am of four knights: Sir John Ball, (LMS), the second-youngest in the Society’s course very pleased, but if anyone I know Sir Martin Taylor, Sir Roger Penrose and history and only the second woman to hold that addresses me as Dame Frances I will assume Sir Andrew Wiles. position – the first was (later that they are seriously annoyed with me ... n

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History

THE FIRST SAVILIAN CHAIRS History of In 1619, Sir Henry Savile, Warden of Merton, deploring the terrible state of Oxford Mathematics Oxford mathematics, founded the Savilian Professorships of Geometry and Robin Wilson and Raymond Flood . The first geometry professor was Henry Briggs, who improved The opening of the Andrew Wiles of the time, who wrote: Napier’s newly invented logarithms, Building is but the latest event in Mathematics reveals every genuine calculating by hand extensive tables of eight centuries of mathematical truth, for it knows every hidden secret. base-10 logs to fourteen decimal activity in Oxford. Here we outline He became Archbishop of Canterbury in places. The Sedleian Chair of Natural the eventful story. 1349, but died of the Black Death soon Philosophy was founded in 1621. after. EARLY DAYS After the Civil War, the mathematical In 1214 Oxford University elected its first An unexpected name that arises here is scene moved to Wadham College. In Chancellor, Bishop Robert Grosseteste, Geoffrey Chaucer, who wrote on 1648 Warden gathered a founder of the tradition of scientific mathematical instruments. His 1393 of brilliant men, the ‘Oxford thought in medieval Oxford. Particularly Treatise on the Astrolabe was one of Philosophical Society’, to discuss interested in geometry, he wrote: the earliest science books in English. ‘philosophicall experiments’. Wilkins’s The usefulness of considering lines, group included (Savilian angles and figures is the greatest, Oxford’s students arrived in their early Professor of Geometry for 54 years), because it is impossible to understand teens and were assigned tutors who , and natural philosophy without them. By were responsible for their moral (Savilian Professor of the power of geometry, the careful behaviour. The curriculum comprised the Astronomy). Members of this group observer of natural things can give seven liberal arts: the trivium, a 4-year founded the Royal Society in London. the causes of all natural effects. course on grammar, rhetoric and logic , followed by the 3-year quadrivium, the Wallis’s successor as Savilian Professor Grosseteste’s most famous admirer was Greek mathematical arts of arithmetic, of Geometry was . While Roger Bacon, whose Folly Bridge music, astronomy and geometry. still an undergraduate he sailed to St observatory became a place of Helena to catalogue the Southern stars. pilgrimage for scientists. Centuries later, Following the invention of printing, a Among his achievements were cajoling wrote: press was set up, which eventually Newton to write Principia Mathematica, So to Friar Bacon’s study: I up and became the . The becoming Astronomer Royal, and saw it, and gave the man a shilling. first mathematical book was the 1520 predicting the return of the comet that Oxford mighty fine place. Compotus Manualis, which showed how now bears his name. to calculate the date of Easter on one’s fingers. Other notable books by Oxford THE 18TH AND 19TH CENTURIES authors appeared around this time. Throughout the 18th century Newtonian Cuthbert Tonstall’s De Arte Supputandi philosophy flourished in the Old was the first major arithmetic text to be Ashmolean Building, now the of published in , while Robert the History of Science, in Broad Street. Recorde’s 1557 algebra text The The first public museum in England, it Whetstone of Witte, contained the first also contained the first science teaching appearance of our equals sign – two rooms and teaching laboratory. Many parallel lines ‘bicause noe. 2. thynges, scientific lectures were given there by Roger Bacon’s observatory. can be moare equalle’. the Savilian professors, one of whom, , was responsible for By the early 14th century, scholars were the , then Europe’s organising themselves into colleges. best-equipped astronomical observatory Merton College soon became pre-eminent and now part of Green Templeton College. in scientific studies, and the Merton Following another decline in the School became famous throughout University’s fortunes, changes came in Europe, as its members tried to quantify In 1570 Henry Billingsley, a former the 19th century, when science degrees natural phenomena, such as heat, light Oxford student who became Lord Mayor were introduced, examinations included and colour. Most important was Thomas of London, published the first English written papers, and the University Bradwardine, the greatest English edition of Euclid’s Elements. Museum was built.

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Head of Department’s letter Head of Department’s letter Sam Howison

I am not going to say much about the large debts, it is more crucial than ever first this did not work – two discerning Andrew Wiles building this year: you that we can support them. I think our pairs nested on the window sills of the have already had to put up with too alumni can make a real difference here, Whitehead Professor of Mathematics and much from me on this topic in the past. by combining to fund Alumni Graduate the Savilian Professor of Geometry – but Let me simply say that it is wonderful, Scholarships. A number of you have last week Nobby was seen near fabulous, transformative – and you must already contributed generously, and if Somerville breakfasting on something come to see it. But now that the move others would like to join in, there is a grey and fluffy ... is over, we’re looking at the challenges dedicated page on our website. Please to come. think hard about making a regular Finally, let me quote from recent student contribution, however modest. feedback forms concerning two of our High among these is the issue of star lecturers, Peter Neumann and funding for doctoral students. Some of Turning now to lighter matters, pigeons Richard Earl: ‘Dr Neumann is such a the brightest young in have also been on our minds. Our window babe [from a student young enough to the world want to do their D.Phil. here ledges are tempting nesting sites, so last be his grandchild] – this guy has swag!’ but we can only fund a small proportion summer we engaged the services of and ‘Dr Earl is a lad! I used to think I of them. And now that UK students (as Nobby the Harris hawk to fly around could learn it all from books. Boy was I well as others) finish their studies with regularly and deter the interlopers. At wrong!’ Says it all, really. n

and the new Waynflete Chair in Pure mathematicians, Michael Atiyah, Simon Mathematics. Donaldson and Daniel Quillen, were awarded Fields Medals, the mathematical A major boost to Oxford’s mathematics equivalent of the Nobel Prize. was G. H. Hardy’s appointment to the geometry chair. Mainly remembered as a Sir Roger Penrose is a major Cambridge man, he spent eleven fruitful international figure in and years in Oxford, publishing over 100 astrophysics, while Sir Andrew Wiles, papers and establishing a world-famous who proved ‘Fermat’s last theorem’, was

The University Museum, 1860. school in analysis and number theory. a former Merton undergraduate who has Another important influence was returned to Oxford after many years in There were three notable Savilian Waynflete professor Henry Whitehead, the USA (see page 7). Professors of Geometry at this time: whose school of topology attracted n Baden Powell wrote texts on scholars from around the world; a keen pig Recent expansion in Oxford’s mathematical geometry and and was a farmer, he claimed to derive mathematical activity has been spectacular. Syllabuses populariser of science – one of his inspiration by scratching his pigs’ backs for have continually changed and joint sons later founded the Boy Scout an hour every afternoon. A third popular degrees were introduced with philosophy, movement figure was Charles Coulson, who at statistics and computer science. With n Henry Smith made major various times held professorships in three centres for mathematical biology, contributions to algebra and number universities in three subjects (mathematics, financial mathematics, industrial applied theory, but died relatively young and ). A well-known lay mathematics and much else besides, n had been preacher, Coulson was involved with the Oxford mathematics has gone from unable to secure an Oxbridge post, founding of in 1942. strength to strength, with great promise being a Jew, but after the rules changed for the future in our exciting new building. in 1871 was appointed at age 69. Hardy, Whitehead and Coulson were all Charles Dodgson (Lewis Carroll) was energetic advocates for a Mathematical Reference also teaching mathematics in Oxford Institute, and after occupying various John Fauvel, Raymond Flood, and Robin around this time. buildings, the Mathematics Faculty Wilson (eds.), Oxford Figures: Eight acquired its own home in St Giles in 1966. Centuries of the Mathematical Sciences THE 20TH CENTURY (2nd edition), OUP, 2013. n In 1900 there were three mathematics Meanwhile, Oxford continued to attract This note first appeared in Oxford Today and chairs — in geometry, natural philosophy many distinguished figures. Three Oxford is republished here with kind permission.

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The building opens Construction and opening of

Work begins – pictured are Nick Woodhouse (former Head of Department), Sam Howison (Head of The reception following the official opening Department), Lavinia Clay (benefactor), Andrew Wiles, and Ewan McKendrick (University Registrar). 5 of the building. 5

Members of the department attend the topping-out party in August 2012. 1

(Above right) David Willetts, Minister of Education and Science, at the Opening Ceremony.

Prof. Ingrid Daubechies lecturing at the official Opening meeting of the building on 3 October 2013. 3

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The building opens the Andrew Wiles building

Head of Department Sam Howison with Andrew Wiles and Ingrid Daubechies who presented lectures on Opening day. 5

Frances Kirwan with the plaque announcing the Opening of the building by Sir Michael Atiyah, OM. 5

View from one of the crystals to the cafeteria below. 5

Our main benefactors, Landon and Lavinia Clay. 5 The building in use: the Christmas lunch for graduate students and staff 5

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The Andrew Wiles building

The entrance leading into the spacious The staircases of the building are modelled on the ‘impossible staircase’ designs of the Dutch reception . 1 artist Maurits Escher, a friend of Oxford’s Sir Roger Penrose. 5

The ‘Penrose tiling’ outside the building – Roger Penrose’s non-periodic tiling is formed from two basic shapes (the light and dark rhombuses). 5

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The Andrew Wiles building

The staff and graduate common room with its magnificent view of the Radcliffe Observatory in Green Templeton College. 1

One of the two ‘crystals’, representing the frequencies of a drum whose skin is stretched across the opening – the other crystal represents Pascal’s ‘mystic hexagon’ theorem in geometry. 7

PROFILE

Sir Andrew Wiles KBE, FRS

Oxford University’s Mathematical Institute is named the Andrew Wiles Building, in line with the wish expressed by the principal benefactors at the time of their original gift in 2005, and in celebration of one of Oxford’s most distinguished mathematicians.

Andrew Wiles read mathematics at Merton College, coming up in 1971. He took his PhD degree under John Coates at Cambridge before moving to Princeton, USA – first to the Institute for Advanced Study and then as professor at . He visited Oxford The inscription (supposedly above Plato’s as a Royal Society Research Professor from 1988 to 1990, and Academy), ‘Let no-one destitute of geometry returned again in 2011 to a Royal Society 2010 Anniversary Chair. enter here’ appears at the entrance to the building. 5 Andrew Wiles has made huge contributions to number theory, starting with his work on the arithmetic of elliptic curves with John Coates and on Iwasawa theory over the rational with Barry Mazur. He is best known for his proof of Fermat’s Last Theorem, published in 1995.

In 1999 he was awarded an honorary degree from Oxford, when the Public Orator described him as: temporum nostrorum Archimeden, numerorum magistrum singularem, theorematis ultimi enodatorem incomparibilem [the of our times, the outstanding master of numbers, the incomparable unriddler of the Last Theorem].

He was knighted in 2000, and an asteroid has been named in his honour. n

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Educational projects

different values of words: any word has Words and their the same value as 1, a, aa or aaa. Then we spend a few minutes investigating wonderful ways what happens if 4 is replaced by another number, such as 12. To get to this point Peter M. Neumann usually takes about 50 minutes.

Next we work with a two-letter alphabet In the past two years, under the chairmanship of Frances Kirwan, the UK {a, b}. This offers an interesting Mathematics trust has developed several new projects for the enrichment of the digression – what is a sensible way to list mathematical experience of schoolchildren. One of these, Mathematical , the words? Alphabetical order does not supported by the Department of Education, offers two-day master classes to work – the dictionary never reaches b. 30–40 Year-10 students (14–15-year-olds). My contributions use two sessions of After a short time a few participants offer 70–90 minutes for a class called ‘Words and their wonderful ways’, in which I what is called ‘length-lex’ ordering: order attempt to lead the children to an appreciation of a major research problem that is by length, and order words of the same still only partially solved after 112 years of effort. length lexicographically. So the dictionary looks like this: 1, a, b, aa, ab, ba, bb, aaa, aab, . . . , and gives rise to non- trivial homework exercises such as ‘what is the 2014th word in the list?’. For a two-letter alphabet we work with exponent 2 (not 4): expansion and contraction of a word w involve insertion and deletion of strings of the form uu. How many different words do we end up with? The first session usually ends here.

Next morning, most of the children suggest that the answer is 7: any word has the same value as 1, a, b, ab, ba, aba or bab. At one session a very bright girl seemed uneasy, believing that the answer should be smaller. With only very little help, she discovered, and was able to explain to the whole class, that ab = ba, so that the answer is 4 and any word has the same value as 1, a, b or ab. Then we spend a little time with the same rule A UKMT activity session (exponent 2) and a larger alphabet, followed by just enough time working We start with an alphabet {a, b, c, . . . }, u) anywhere between two letters of w or with a two-letter alphabet and exponent usually small. The ‘words’ are strings of at the beginning or the end of w. 3 (insertion or deletion of uuu) to letters, such as abbabbbaa. The length of Conversely, if in a word w we see a part discover that this problem is really hard. a string is the number of letters in it. of the form uuuu, then w may be The answer is 27, but that lies at Since the word of length 0 is invisible, contracted by deleting this part and advanced undergraduate level. we use the symbol 1 to indicate where it closing up any resulting gap. Words v, w is on the page. are then said to have the same value At this point, with about 20 minutes (written v = w) if v may be obtained from remaining, I move into lecture mode and The substance of the mathematics lies in w by some sequence of these tell the students about the Burnside transformation rules. We start with a transformations. Problem. For words in an alphabet with simple example. Our alphabet has only m letters and for exponent n (so that the one letter a, and we choose a number, Although some of the children are not transformation rules permit insertion or say 4 (later to be called the ‘exponent’). familiar with arithmetic modulo 4, it does deletion of un for any word u), is A word w may be expanded by insertion, not take long until everyone understands B(m, n), the list of different words, finite for any word u, of uuuu (four that, with a one-letter alphabet and or does it go on for ever? And if it is consecutive non-overlapping instances of these rules, we end up with just four finite, how large is it?

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Educational projects

The problem was B(m, 3) has size 3(m3 + 5m)/6; for exponent complete during his stay in Oxford in posed in 1902 (in 4 the list is finite and good estimates for 2012–13, that B(2, 11) is infinite. In different terms, as its size have been developed (here in this context, if correct, that is a problem in group Oxford), of the form 4r m for suitable real spectacular progress. theory) by William numbers r. For exponent 5 the problem Burnside, professor is wide open, though it is known that if What will be even more spectacular of mathematics at B(2, 5) is finite, then its size is 534. For will be a solution of the Burnside the Royal Naval exponent 6 we know that B(m, 6) is Problem for exponent 5: is B(2, 5), the College, . finite and we know its size precisely. For list of different words obtained from most exponents n > 100 it is known that words in the alphabet {a, b} by We now know a lot about it, but much B(m, n) is infinite. In the last few years insertion or deletion of strings uuuuu, remains unknown: for exponent 2, Samson Adeleke has been developing a finite or infinite? That way fame and B(m, 2) has size 2m; for exponent 3, proof, which he was working to fortune lie. n

Sharing the beauty of networks Mason A. Porter

During the past couple of years, with my Oxford students and some other collaborators and friends, I have invited several school students to Oxford and visited schools across the UK to teach pupils of ages 13–16 about ‘network science’, the study of connectivity, closely in’ to the study and beauty of The group organisers related to graph theory. mathematics. The students experience networks all the time in their everyday The mathematics of networks appeals lives (via Facebook, transportation naturally to teenagers and others who networks, and more), so it is easy to Magic Sudoku do not pursue mathematics or other connect with their experiences, thereby Fill in the empty cells in the square sciences as a vocation, and is an making mathematics more tangible and below, so that each row, each column, effective medium to try to ‘suck people less rote than what they are used to and each 3 × 3 block contains all the seeing in their school curricula. numbers from 1 to 9, and so that the rows and columns in each 3 × 3 block We have developed teaching materials, add up to the same number (that is, which we have published in the journal each block is a semi-magic square). Network Science, along with a description of our outreach efforts. Our modules focus mostly on the applied side of network mathematics, but our introduction to graph theory has been our most successful module. In this module, we consider a special ‘two-colour problem’ as an introduction to the four-colour problem on the colouring of maps. We also occasionally discuss Hall’s ‘marriage theorem’. In other modules, we explore topics such as small-world networks, biological and social epidemics on A graphs/networks picture networks, and the PageRank . n A hint, and the solution, are on page 12.

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Departmental news

Appointments... Luc Nguyen (Princeton, n a to Tom Sanders for his USA): University Lecturer spectacular results in additive combinatorics We are delighted to welcome the in the Analysis of and related following new Faculty members of the Nonlinear Partial Oxford mathematicians at ICM 2014: Ben Mathematical Institute. Differential Equations and Green FRS and have been Tutorial Fellow at St Konstantin Ardakov invited to give plenary lectures at the 2014 Edmund Hall. Research (Queen Mary, London): International Congress of Mathematicians in interests: partial differential equations University Lecturer in Pure Seoul, Korea. Konstantin Ardakov, David and geometry. Mathematics and Tutorial Conlon, Terry Lyons FRS and Tom Sanders Fellow at Brasenose will give invited section lectures. Steve Shkoller College. Research (California, Davis, USA): David Acheson was interests: applying non- Professor of Mathematics awarded an honorary DSc commutative algebra to the representation of and Fellow at Trinity degree by the University p-adic Lie groups and arithmetic algebraic College. Research of East Anglia in geometry. interests: analysis of PDE recognition of his work on free-boundary problems, the public understanding Coralia Cartis finite-time singularity formation and multi- of mathematics. (Edinburgh): University dimensional hyperbolic equations. Lecturer in Numerical In the University’s 2013 Divisional Teaching Optimization and Tutorial Awards exercise, Luis Fernando Alday and John Wettlaufer (Yale, Fellow at Balliol College. Philip Maini received two of the four Individual USA): Professor of Research interests: Awards for their outstanding contributions to Applicable Mathematics numerical for undergraduate and graduate teaching, and Senior Research optimisation problems, non-convex problems, respectively. Greg Gyurko won the Special Fellow at Jesus College. analysis, compressed sensing and Category Award for Support Staff for his Research interests: climate modelling. contributions to teaching (especially for the phase transitions, moving MSc in Mathematical and Computational boundaries, crystal growth, colloidal Ben Green (Cambridge): Finance). suspensions, fluid , and Waynflete Professor of experimental applied mathematics with Marcus du Sautoy OBE, Simonyi Professor for Pure Mathematics. applications in astro/bio/geophysics. the Public Understanding of Science, was Research interests: awarded an honorary DSc degree by the discrete mathematics, Retirements and departures University of in recognition of his number theory, analysis, making mathematical sciences accessible to a and ‘Retirement’ is a hazy concept. Academics have wider audience. combinatorial geometry. never taken it very seriously, regarding it more as an asymptotic state, but while the formal Terry Lyons FRS has commenced his two-year Peter Grindrod stage exists we mark it, and this year we saw term as President of the London Mathematical (Reading): Professor of the ‘retirement’ of a long- Society (see Newsletter 11), in succession to Mathematics. Research standing member of the Graeme Segal FRS (also from Oxford). interests: dynamical department, Janet Dyson, Tom Sanders won the prestigious European networks, modelling, and Tutorial Fellow of Prize in Combinatorics, awarded to a young probability within social Mansfield College. A European researcher for excellent contributions networks, demand/ month later she became to this subject. consumption, modelling our Faculty Teaching cognition within human brains. Adviser. Steve Shkoller and John Wettlaufer were Photo by Keiko Ikeuchi awarded Royal Society Wolfson Research Merit Andras Juhasz (Imperial, Awards – Steve for his analysis of moving free- London): Royal Society Achievements boundary problems in fluid dynamics, and John Research Fellow and for his work on applicable physical mathematics This has been another excellent year for Tutorial Fellow at Keble at the interface. awards and achievements. College. Research Jackie Stedall won the interests: low-dimensional The London Mathematical Society has 2013 Neumann Prize and differential topology, awarded: (named after Dr Peter Heegaard–Floer homology n the to Frances Neumann OBE), awarded and its applications. Kirwan FRS for her work on geometric every other year by the invariant theory and the geometry and British Society for the Peter Keevash (Queen topology of moduli spaces History of Mathematics for Mary, London): Professor n the Naylor Prize and Lectureship in Applied a non-specialist mathematics book containing of Mathematics and Mathematics to Nick Trefethen FRS for his historical material; her prizewinning book was Fellow of Mansfield exceptional contributions to numerical OUP’s The History of Mathematics: A Very College. Research analysis and his ability to communicate his Short Introduction. interests: extremal subject to a wider audience combinatorics, graphs and n a Whitehead Prize to Luis Fernando Alday Balázs Szendrői was awarded a Royal Society hypergraphs, random for his work on properties of supersymmetric Leverhulme Trust Senior Research Fellowship, structures, combinatorial optimisation and gauge theory and its connections with enabling him to pursue his research into combinatorial number theory. conformal field theory and string theory cohomological Donaldson–Thomas theory.

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Departmental news

Student achievements Peter Keevash proves Brain workshop William Perry of Keble College won the Best the existence illustrates the Mathematics Student Award at the 2013 SET (Science, Engineering & Technology) Awards conjecture for convergence of ceremony for a project on Spin two- dimensional local field theories. There were combinatorial designs scientific disciplines over 500 entries from a hundred universities.

Laura Kimpton has been awarded the prestigious Lighthill–Thwaites Prize by the Institute of Mathematics and its Applications Obituaries CHRISTOPHER J. BRADLEY (1938–2013) Christopher Bradley was a popular and effective Picture of curvature analysis for polymicrogyria, Fellow and Tutor in courtesy of Waney Squier and Alain Goriely Mathematics at Jesus College from 1964 to 1977, after which he entered schoolteaching, notably at Clifton Oxford’s Peter Keevash has proved a The convergence of scientific disciplines College, near . As Deputy Leader of long-standing conjecture for has gathered pace in recent years, and the British Mathematical Olympiad team and combinatorial designs, answering a nowhere was this more visible than in for many years Secretary of the British question of Jakob Steiner from 1853. the 2014 Oxford Brain Mechanics Mathematical Olympiad Committee, he was A Steiner triple systemon a set X is a Workshop held in Oxford in January. known for his elegant Olympiad problems. He was also involved with the UK Maths Trust co llection T of 3-element subsets of X Understanding the brain, its pathology, and the . for which each pair of elements of X is injury and healing, is no longer just a contained in exactly one triple in T. An priority for clinicians, but is a field While in Oxford he co-authored a major study of the mathematical theory of symmetry in example of Julius Plücker in 1835 is the where data analysis and mathematical solids, and later wrote introductory texts for above affine plane of order 3, consisting modelling can work with clinical practice the UK Maths Trust and a book on of 12 triples on a set of 9 po ints. Plücker to further our understanding of the Challenges in geometry: for mathematical observed that a Steiner triple on most complex of human organs. Olympians past and present. a set with n elements can exist only if n The following problems are taken from one is congruent to 1 or 3 (mod 6), and Fourteen speakers represented a range of Christopher Bradley’s books: Thomas Kirkman showed in 1846 that of disciplines from medical sciences, Prove that one member of a Pythagorean this necessary condition is also sufficient. neuroscience, and biology to triple is always divisible by 5, and that the area of any right-angled triangle engineering, physics and mathematics. with integer sides is divisible by 6. In 1853 Steiner posed a natural Areas of focus included the modelling extension of this: given integers q and r, of brain tissue, normal and abnormal MARY KEARSLEY for which n can we choose a co llection brain development, and the impact of (1931–2013) Q of q-element subsets of an n-element traumatic brain injury. Over seventy Mary Kearsley studied set X so that any r elements of X are delegates attended, sharing ideas and at Somerville and then at Manchester University contained in exactly one set in Q? Some beginning the critical process of before coming to St natural necessary divisibility conditions collaboration. Anne’s in 1958 as Tutor generalise the above necessary condition in Mathematics. Her research area was for Steiner triple . Th e existence The workshop was organised by the theoretical physics and she published on conjecture states that, for all but finitely newly founded International Brain potential theory and Newtonian gravitation. Her devotion to her students and the many n, these divisibility conditions are Mechanics and Trauma Laboratory amount of time that she was willing to also sufficient for the existence of (IBMTL) with the support of the Oxford expend on them were legendary, and many general Steiner systems (and for more Centre for Collaborative Applied successful generations of St Anne’s general situations). Mathematics (OCCAM). IBMTL is an mathematicians were proportionately devoted international collaboration based in to her. She retired in 1998 after nearly 40 Peter has recently proved the existence Oxford, on projects related to brain years as a Fellow. conjecture, and shown more generally mechanics and trauma. This A brilliant linguist, she was a translator from that the natural divisibility conditions are multidisciplinary team is motivated by Russian of Landau and Lifshitz’s classic Electrodynamics of continuous media. Her sufficient for clique decompositions of the need to study brain cell and tissue linguistic skills led also to an interest in simplicial complexes that satisfy a certain mechanics and its relation with brain Japanese culture. n pseudo- condition. n functions, diseases or trauma. n

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Epsilons and deltas

Professor Daubechies is a leading Oxford Figures: authority on the theory of wavelets (the Eight Centuries of basis of jpeg compression), and in 1987 the Mathematical she constructed an important class of these that vanish outside a finite interval; Sciences these are now among the most common Edited by John Fauvel, Raymond Flood type of wavelets used in applications. and Robin Wilson. Second edition, Hardback, ISBN 978-0-19-968197-6 In October she was one of the distinguished speakers at the official Institute Garden An updated and opening meeting of the Andrew Wiles expanded edition Parties building (see page 4). n of Oxford Figures Last year’s Mathematical Institute Garden was published by Party was held in our new Andrew Wiles Oxford University building. Prof. Marcus du Sautoy lectured Press in time for on The Secret Mathematicians, and there the opening of was an opportunity to tour the building. the Andrew Wiles building. Covering 800 years of Oxford This year’s event will take place on mathematics, this new edition features 20 September in the Andrew Wiles some two hundred pictures and includes From left to right: Sir John Ball FRS, Lady Wiles, building, with Sir Roger Penrose as the new chapters by Peter Neumann OBE on Sir Andrew Wiles FRS, Professor Daubechies, lecturer. For more details visit our website the major expansion in Oxford’s Professor Terry Lyons FRS, Lady Ball. www.maths.ox.ac.uk. We note with mathematical activities in recent years, pleasure that the University’s Alumni and Robin Wilson on the mathematical Weekend will be held in the Andrew Wiles activities of Oxford don Charles Dodgson Solution to Magic Sudoku building on the same weekend. n (Lewis Carroll). n (page 9) The key to the solution is to note that Marcus and Yoko Exclusive 30% Discount: was £39.99, the only ways of splitting the numbers Now £27.99 1–9 into three triples, each summing to In June 2013 Yoko Ono curated the Readers of this Newsletter can order the 15, are 1–5–9 / 2–6–7 / 3–4–8 and Meltdown Festival on London’s South book directly from OUP at a reduced 1–6–8 / 2–4–9 / 3–5–7. Bank, featuring the dazzling talents of price. To claim your discount visit Iggy Pop, Patti Smith and (to add www.oup.com/uk, add the book to your mathematical rigour) Marcus Du Sautoy shopping basket, and use the code who explained why numbers, codes and AAFLY6 at the checkout. pattern searching are among the best tools for looking into the future. The Professor Ingrid event took place in the Purcell Room at the Queen Elizabeth Hall. London. n Daubechies awarded Oxford honorary The One Show doctorate In November, BBC TV’s The One Show It is a rarely that mathematicians are was broadcast live from outside Balliol awarded honorary degrees from Oxford Solution to last year’s puzzle: College as part of a Children in Need University: in recent years Izrail Gelfand special. The programme welcomed a (1983) and Andrew Wiles (1999) are team of five teenage rickshaw riders among the few to be so recognised. who had cycled 700 miles across Britain Last June Ingrid Daubechies, President over eight days. To celebrate their of the International Mathematical Union achievement the show gathered a group (in succession to Oxford’s Sir John Ball), of Oxford academics including Jon Chair of the Committee and Chapman, Professor of Mathematics and Professor of Mathematics at Duke its Applications, to answer challenging University, USA, received an honorary questions about travelling by rickshaw D.Phil. degree at Oxford University’s and the meaning of life. n annual Encaenia ceremony.

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