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Okay it's not so hard.

Welcome to our new undergraduate students, young mathematicians of diverse nationalities from Afghan to Kazakh, Syrian to Pakistani, Malaysian to Greek. And 70% of UK students from state schools. Welcome to Oxford Mathematics, all of you.

And watch out for a snippet or two from their lectures next week on our Twitter and Facebook pages. We hope it will inspire those of you who hope to join them in the future.

Amid all the debate about equipping ourselves for the 'technological' world of the future, one thing is for sure: the quality of research in the Mathematical and Life Sciences (and beyond) depends on the quality of its young researchers. In that spirit we are delighted to welcome our latest cohort of DPhil (PhD) students, 43 of them, all fully funded, from across the globe. 13 from the UK, 15 from the European Union and a further 15 from India, Kenya, Norway, Australia, Mexico, USA, China, Switzerland, Argentina, Israel and South Africa.  

We would also like to welcome our masters students and in particular our first cohort of Oxford Masters in Mathematical Sciences (OMMS) students, 36 in total, 26 men and 10 women from 17 different countries. This standalone course offers students the opportunity to join our current fourth year undergraduates and work with our internationally renowned faculty.

Welcome to everyone. We (and we don't just mean Oxford) need you all.

Roger Penrose's relationship with the artist M.C. Escher was not just one of mutual admiration. Roger's thinking was consistently influenced by Escher, from the famous Penrose tiling to his groundbreaking work in cosmology. The respect was mutual, as was clear when Roger dropped in to see Escher at his home...

Oxford Mathematics hosted this special event in its Public Lecture series during the conference to celebrate the 20th Anniversary of the foundation of the Clay Mathematics Institute. 

The Society for Mathematical Biology has announced its 2018 Awards for established biologists and among the winners are Oxford Mathematicians Helen Byrne and Francis Woodhouse.

Helen will be the recipient of the Leah Edelstein-Keshet Prize for her work focused on the development and analysis of mathematical and computational models that describe biomedical systems, with particular application to the growth and treatment of solid tumors, wound healing and tissue engineering. This award recognizes an established scientist with a demonstrated track record of exceptional scientific contributions to mathematical biology and/or has effectively developed mathematical models impacting biology. "Dr. Byrne has made outstanding scientific achievements coupled with her record of active leadership in mentoring scientific careers." The Edelstein-Keshet Prize consists of a cash prize of $500 and a certificate given to the recipient. The winner is expected to give a talk at the Annual Meeting of the Society for Mathematical Biology in Montreal in 2019.

Francis has won the H. D. Landahl Mathematical Biophysics Award. This award recognizes the scientific contributions made by a postdoctoral fellow who is making exceptional scientific contributions to mathematical biology. The award is acknowledged with a certificate, and a cash prize of USD $500.

Oxford Mathematics and the Clay Mathematics Institute Public Lectures

Roger Penrose - Eschermatics

Roger Penrose’s work has ranged across many aspects of mathematics and its applications from his influential work on gravitational collapse to his work on quantum gravity. However, Roger has long had an interest in and influence on the visual arts and their connections to mathematics, most notably in his collaboration with Dutch graphic artist M.C. Escher. In this lecture he will use Escher’s work to illustrate and explain important mathematical ideas.

You can watch live at:

https://www.facebook.com/OxfordMathematics/

OR

https://livestream.com/oxuni/Penrose

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

To whet your appetite here is Roger demonstrating the Impossible Triangle from his 2015 lecture.

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)

Alexandra Wood - Director/Violin

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Please email @email to register

Watch live:
https://www.facebook.com/OxfordMathematics
https://www.livestream.com/oxuni/Bach-Cosmos

The Oxford Mathematics Public Lectures are generously supported by XTX Markets

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.

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Photography by Ian Wallman

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.