Professor Martin R Bridson FRS has been appointed President of the Clay Mathematics Institute from October 1, 2018. He is the Whitehead Professor of Pure Mathematics at the University of Oxford and a Fellow of Magdalen College. Until earlier this summer, he was Head of the Mathematical Institute at Oxford.
He studied mathematics as an undergraduate at Hertford College, Oxford, before moving to Cornell in 1986 for his graduate work. He completed his PhD there in 1991, under the supervision of Karen Vogtmann, with a thesis on Geodesics and Curvature in Metric Simplicial Complexes. After appointments at Princeton and at the University of Geneva, he returned to Oxford in 1993 as a Tutorial Fellow of Pembroke College. In 2002, he moved to Imperial College London as Professor of Mathematics and returned again to Oxford in 2007 as Whitehead Professor. He is a Fellow of the American Mathematical Society (2015) and a Fellow of the Royal Society (2016), to which he was elected "for his leading role in establishing geometric group theory as a major field of mathematics".
Professor Bridson has been recognised for his ground-breaking work on geometry, topology, and group theory in awards from the London Mathematical Society (Whitehead Prize 1999, Forder Lectureship 2005) and from the Royal Society (Wolfson Research Merit Award 2002), and by invitations to speak at the International Congress of Mathematicians in 2006 and to give the Abel Prize Lecture in Oslo in 2009.
Martin succeeds Professor Nick Woodhouse who has been President since 2012.
As someone who was drawn to mathematics and music from an early age, the connections between the two have always fascinated me. At a fundamental level the elements of music are governed by mathematics. For example, certain combinations of notes sound 'harmonious' because of the mathematical relationship between the frequencies of the notes. Musical harmony, the subdivision of music into bars and beats, the different permutations and combinations of rhythms, and so on, all give music an inherent mathematical structure. In fact just like mathematics, there is even a special notation used to describe that abstract structure. However, I think there are other, perhaps less obvious, connections. In a sense both mathematics and music are constrained, abstract, logical structures, but within these rigid constraints there is enormous freedom for creativity, with an important role played by both symmetry and beauty.
Mathematicians studying the foundations of mathematics are really studying structure, and the relationships between abstract structures. An equation $A=B$ is of course a statement of a relationship, saying that $A$ and $B$ are equivalent, in whatever sense is intended. It is straightforward enough to start writing down true equations, but this isn't what mathematicians do. Mathematicians seek interesting, elegant, or beautiful equations and structures. There is a strong aesthetic input. The way that mathematicians work, especially in the early stages of an idea, is often non-linear and intuitive, with more linear and methodical reasoning coming later. In music a composer often works in exactly the same way, but they do so for similar reasons: in both cases one is simultaneously trying to create and discover interesting and beautiful structures within a constrained system. Once you start to create, the constraints immediately lead to many consequences - sometimes wonderful consequences, but more often not what you are looking for - and one needs to use intuition to guide this simultaneous process of creation and exploration.
For some mathematicians, the connections between mathematical and musical creative processes extend further still. This was particularly true for Albert Einstein. Remarkably, he said the following about Relativity, his geometrical description of space, time and gravity: "The theory of relativity occurred to me by intuition, and music is the driving force behind this intuition. My parents had me study the violin from the time I was six. My new discovery is the result of musical perception.'' I would love to have been able to ask him more about what he meant by this! His wife Elsa once remarked: "Music helps him when he is thinking about his theories. He goes to his study, comes back, strikes a few chords on the piano, jots something down,returns to his study.'' I do the same when I'm working at home and have always regarded it as mere procrastination, but perhaps there's something deeper going on. The aesthetics one is seeking in mathematics and theoretical physics are common also in music. I think Einstein was looking for simplicity, harmony and beauty in his work, and music was for him an inspiration for this.
The notion of beauty in mathematics is hard to make precise, but for me one aspect of it has something to do with finding simplicity and complexity at the same time. By 'simple' here of course we don't mean trivial, but rather something natural and elegant; and the complexity is often initially hidden, to be uncovered by the mathematician. For example, take group theory, which is the study of symmetry in mathematics. The axioms of group theory are extremely simple, but it took hundreds of mathematicians more than a century to understand and classify the basic building blocks of these structures, which include extraordinarily complicated mathematical objects. To paraphrase the mathematician Richard Borcherds, there is no obvious hint that anything like this level of complexity exists, hidden in the initial definition. This is the sort of thing that mathematicians find beautiful. Of course, symmetries and patterns play a central role in both mathematics and music, and this is perhaps another reason why so many people are attracted to both.
The combination of simplicity, complexity, symmetry and beauty in music reaches a pinnacle in the compositions of Johann Sebastian Bach. Much of Bach's music makes use of counterpoint, where independent melodies are woven together. He often builds large, complex musical works, with many such simultaneous melodies, starting from only a small fragment of a theme. Bach then systematically works through different combinations and permutations, much like a mathematician might, making repeated use of symmetry and patterns. Writing music like this involves a great deal of analytical skill, and is very similar to solving a mathematical problem. Starting with a small, simple idea, and creating/discovering a large structure from it is very appealing to mathematicians - it is elegant. It perhaps also inspired Einstein, who was a great admirer of Bach's music. Bach's genius meant that he was able to use this approach to create beautiful music that also has a more abstract mathematical beauty. For me, it's this combination that makes his music so special.
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James Sparks and City of London Sinfonia - Bach and the Cosmos
9th October, 7.30pm-9.15pm, Mathematical Institute, Oxford, OX2 6GG
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James Sparks - Bach and the Cosmos (30 minutes)
City of London Sinfonia - J S Bach arr. Sitkovetsky, Goldberg Variations (70 minutes)
Oxford Mathematics of Consciousness and Applications Network (OMCAN) is a new network with a focus on bringing mathematics to bear on one of sciences' greatest challenges.
Over the last few decades scientists from various disciplines have started searching for the general theoretical bases of consciousness and answers to related questions such as how can consciousness be unified with physics, what medical, ethical and commercial benefits might theoretical progress bring, and is there a type of mathematical structure with the property of consciousness. This has resulted in several new mathematically formulated theories (or partial theories) of consciousness, many of which are complementary to each other. Whilst these theories are preliminary, advances in computer science are rapidly being made involving ever more parallel systems, often inspired by biological architectures, which highlights the pressing need for a step change in the level of research being undertaken to establish the general theoretical bases of consciousness.
Oxford Mathematics of Consciousness and Applications Network (OMCAN) provides researchers from across the University of Oxford with the opportunity to share their knowledge in this area, participate in relevant seminars and discussions, and find funding in support of collaborative research. Supported by the Mathematical Physical and Life Sciences Division in Oxford, it will be based at the Mathematical Institute.
OMCAN is holding its networking launch event on 19th September and you can attend and give a short introduction about yourself and your relevant interests. Please RSVP by 31 August to @email and include up to three slides in pdf format about your relevant research interests.
Prof. Steve Furber (University of Manchester) is giving the OMCAN Inaugural Lecture on 7th November titled 'Biologically-Inspired Massively-Parallel Computation on SpiNNaker (Spiking Neural Network Architecture).
Oxford University is committed to encouraging as wide a range of applicants as possible. Oxford Mathematics is part of that commitment. But what does that mean in practice? Well over the Summer months it means UNIQ, Oxford’s way of breaking down barriers and building bridges. A kind of construction work for the mind.
Over the last two weeks, ninety students from schools around the country have visited us in the Mathematical Institute on the UNIQ Summer Schools. These summer schools offer an impression of what it’s actually like to study Maths at Oxford. Places are given to students who are doing well at school, who are from areas of the country with low progression to university, or from low socio-economic status backgrounds. So far, so good, but what do they actually do?
Well, the week consists of taster lectures and tutorials, and, crucially, plenty of opportunities to talk about maths, both with each other and with our team of student ambassadors. Lots of the students say that meeting other people who are interested in maths is the best part of the summer school; for some of them, no-one else at their school or sixth form is as keen on maths as they are, (a refrain that persists well beyond school of course).
During the week the students have had a fascinating series of talks on topics including Benford’s Law, the Twin Paradox and the game theory of the TV show The Chase. But they have also been working together on group presentations on their favourite topics in mathematics and they’ve been working together modelling projects - open-ended problems which they’re free to approach with a variety of methods which give them an insight in to how maths actually works and enables them to spend time trying out different ideas, a luxury they may not get at school.
For example, groups have been comparing strategies to tackle malaria, investigating refraction, and optimising a bridge network. We use these projects to give the students an impression of what tutorials are like; each group has a half-hour tutorial on their project with a member of our faculty. By giving the students a first-hand experience of studying at Oxford, we can break down some of the myths, and make the whole system more transparent.
As well as giving the students a taste of the mathematics that they might study, the UNIQ summer schools also give the students a chance to experience life in Oxford. They’ve been staying in St. Anne’s College and New College, where they’ve had a quiz night, a scavenger hunt and a ghost tour, before a party on the last evening. Life in Oxford is not so different to anywhere else.
Throughout the week, the students have been helped and guided by a fantastic team of ambassadors, who are all current students or recent graduates of Oxford. One of the signs of success of the UNIQ summer schools is the high application rate to study at Oxford from UNIQ students on the summer school, and some of the ambassadors were themselves previously on UNIQ summer schools as students.
Thank you to everyone. There is much to be done, but in some not so small part of the mathematical world, progress is being made.
Each summer, a group of very enthusiastic teenage mathematicians come to spend six weeks in Oxford, working intensively on mathematics. They are participants in the PROMYS Europe programme, now in its fourth year and modelled on PROMYS in Boston, which was founded in 1989. One of the distinctive features of the PROMYS philosophy is that the students spend most of the programme discovering mathematical ideas and making connections for themselves, thereby getting a taste for life as a practising mathematician.
Mornings start with a number theory lecture followed by a problems sheet, which sounds very traditional. But at PROMYS Europe, the lectures are always at least three days later than the material comes up on the problems sheets! This allows the students to have their own mathematical adventures, exploring numerical data and seeking patterns, then proving their own conjectures before the ideas are discussed in a lecture. Another crucial part of PROMYS Europe is the community feel. This year there are 21 students participating for the first time, and six who have returned for a second experience. In addition, there are eight undergraduate counsellors, who mentor the students. Each counsellor gives daily individual feedback to their three or four students, allowing each student to progress at their own rate and to focus on their own particular interests. The counsellors are also working on their own mathematics - this year they are teaching themselves about p-adic analysis. The returning students are working in small groups on research projects, and this year are also exploring group theory. The PROMYS Europe faculty are also available to the students for much of the time, reinforcing the supportive and collaborative nature of the programme.
The occasional guest lectures give the participants glimpses of current research mathematics and of topics beyond the programme. So far, in the first two weeks of the 2018 programme students have learned about Catalan numbers and quivers from Konstanze Rietsch (King's College London), and Andrew Wiles (University of Oxford) spoke about using analysis to solve equations.
As Andrew said: "PROMYS has done very impressive work over many years in creating an environment in Boston in which young mathematicians from all over the United States can immerse themselves in serious mathematical problems over several weeks, without distraction. It is an exciting development that PROMYS and the Clay Institute have now opened up the same opportunity in Europe."
The programme is very intensive, and students spend a great deal of time grappling with challenging mathematical ideas through the daily problem sets. At the weekends, students have extra-long weekend problem sets, but also have time to explore Oxford and the surrounding area. So far this has included a tour of Oxford colleges, the chance to go punting, and a visit to Bletchley Park and the National Museum of Computing.
As in previous years, this year's group is very international, coming from 15 countries across Europe. Students have to demonstrate a sufficient command of English when they are applying, and the international language of mathematics soon transcends linguistic and cultural differences once participants arrive!
Students apply to attend PROMYS Europe, and are selected based on their mathematical potential, as displayed in their work on a number of very challenging problems. This year there were more than 200 applications for around 21 places: the students who are invited to participate have produced exceptional work on the application problems, and displayed significant commitment and mathematical maturity. The programme is dedicated to the principle that no student should be unable to attend PROMYS Europe due to financial need, and is able to provide partial and full financial aid to students who would otherwise be unable to participate.
Alumni of PROMYS in Boston have gone on to achieve at high levels in mathematics. More than 50% of PROMYS alumni go on to earn a doctorate, and 150 are currently professors, many at top universities in the US. PROMYS Europe alumni are also proving to be dedicated to pursuing mathematical studies, with several now studying at the University of Oxford. Of this year's eight counsellors, seven previously participated in PROMYS or PROMYS Europe as students, and four are Oxford undergraduates.
PROMYS Europe is a partnership of PROMYS, Wadham College and the Mathematical Institute at the University of Oxford, and the Clay Mathematics Institute. The programme is generously supported by its partners and by further financial support from alumni of the University of Oxford and Wadham College, as well as the Heilbronn Institute for Mathematical Research.
'To a physicist I am a mathematician; to a mathematician, a physicist'
7.00pm, 30 October 2018, Science Museum, London, SW7 2DD
Roger Penrose is the ultimate scientific all-rounder. He started out in algebraic geometry but within a few years had laid the foundations of the modern theory of black holes with his celebrated paper on gravitational collapse. His exploration of foundational questions in relativistic quantum field theory and quantum gravity, based on his twistor theory, had a huge impact on differential geometry. His work has influenced both scientists and artists, notably Dutch graphic artist M. C. Escher.
Roger Penrose is also one of the great ambassadors for science. In this lecture and in conversation with mathematician and broadcaster Hannah Fry he will talk about work and career.
This lecture is in partnership with the Science Museum in London where it will take place. Please email @email to register.
John Ball is retiring as Sedleian Professor of Natural Philosophy, Oxford oldest scientific chair. In this interview with Alain Goriely he charts the journey of the applied mathematician.as the subject has developed over the last 50 years.
Describing his struggles with exams and his time at Cambridge, Sussex and Heriot-Watt before coming to Oxford in 1996, John reflects on how his interests have developed, what he prizes in his students, as well as describing walking round St Petersburg with Grigori Perelman, his work as an ambassador for his subject and the vital importance of family (and football).
Oxford Mathematician Ian Griffiths has won a Vice Chancellor's Innovation Award for his work on mitigation of arsenic poisoning. This work is in collaboration with his postdoctoral research associates Sourav Mondal and Raka Mondal, and collaborators Professor Sirshendu De and Krishnasri Venkata at the Indian Institute of Technology, Kharagpur.
As part of this award a short video was produced explaining the problem and its possible mathematical solution.
Oxford Mathematician Heather Harrington has been awarded a Whitehead Prize by the London Mathematical Society (LMS) for her outstanding contributions to mathematical biology which have generated new biological insights using novel applications of topological and algebraic techniques.
In the words of the citation Heather "has made significant advances through the application of ideas originating in pure mathematics to biological problems for which the techniques of traditional applied mathematics are inadequate. This has involved in particular the development of methods in algebraic statistics which allow one to characterize the qualitative behaviour of dynamical systems and networks, adapting approaches from algebraic geometry to test whether a given mathematical model is commensurate with a given set of experimental observations."
Oxford mathematician Sir Andrew Wiles, renowned for his proof of Fermat’s Last Theorem, has been appointed by Her Majesty the Queen to be Oxford’s first Regius Professor of Mathematics.
The Regius Professorship – a rare, sovereign-granted title – was granted to Oxford’s Mathematical Institute as part of the Queen’s 90th birthday celebrations. It is the first Regius Professorship awarded to Oxford since 1842.
Sir Andrew is the world’s most celebrated mathematician. In 2016 he was awarded the highest honour in mathematics, the Abel Prize, for his stunning proof of Fermat’s Last Theorem, a conundrum that had stumped mankind for 350 years. In recognition of this transformative work, he was also awarded the Copley medal, the Royal Society’s oldest and most prestigious award.
Professor Louise Richardson, Vice-Chancellor of Oxford University, said: ‘I know my colleagues join me in offering our warmest congratulations to Sir Andrew on being named Oxford’s newest Regius Professor. It is a fitting recognition of his outstanding contribution to the field of mathematics.’
Professor Martin Bridson, Head of Oxford’s Mathematical Institute, said: ‘The award of the Regius Professorship to Oxford recognised both our pre-eminence in fundamental research and the enormous benefits that flow to society from mathematics.
‘It is entirely fitting that the first holder of this Professorship should be Sir Andrew Wiles. Nobody exemplifies the relentless pursuit of mathematical understanding in the service of mankind better than him. His dedication to solving problems that have defied mankind for centuries, and the stunning beauty of his solutions to these problems, provide a beacon to inspire and sustain everyone who wrestles with the fundamental challenges of mathematics and the world around us. We are immensely proud to have Andrew as a colleague at the Mathematical Institute in Oxford.’
Sir Andrew, who will remain the Royal Society Research Professor of Mathematics at Oxford and a Fellow of Merton College, dedicated much of his early career to solving Fermat’s Last Theorem. First formulated by the French mathematician Pierre de Fermat in 1637, the theorem states:
There are no whole number solutions to the equation $x^n + y^n = z^n$ when n is greater than 2, unless xyz=0
Fermat himself claimed to have found a proof for the theorem but said that the margin of the text he was making notes on was not wide enough to contain it. Sir Andrew first became fascinated with the problem as a boy, and after years of intense private study at Princeton University, he announced he had found a proof in 1993, combining three complex mathematical fields – modular forms, elliptic curves and Galois representations.
The Norwegian Academy of Science and Letters, which presents the Abel Prize, said in its citation that ‘few results have as rich a mathematical history and as dramatic a proof as Fermat’s Last Theorem’. The proof has subsequently opened up new fields of inquiry and approaches to mathematics, and Sir Andrew himself continues to pursue his fascination with the subject. In his current research he is developing new ideas in the context of the Langlands Program, a set of far-reaching and influential conjectures connecting number theory to algebraic geometry and the theory of automorphic forms.
The new Regius Professorship in mathematics was one of a dozen announced by the government to celebrate the increasingly important role of academic research in driving growth and improving productivity during Queen Elizabeth II’s reign. The creation of Regius Professorships falls under the Royal Prerogative, and each appointment is approved by the monarch on ministerial advice.
Sir Andrew’s father, Maurice Wiles, was Regius Professor of Divinity at Oxford from 1970 to 1991.
You can watch Sir Andrew's Oxford Mathematics London Public Lecture and interview with Hannah Fry here.
