A message from James Sparks, Head of the Mathematical Institute

On 1 September I took over from Professor Mike Giles as Head of the Mathematical Institute. Although only 6 weeks into the job, I've already come to appreciate just how varied and interesting a role this is. It's also an enormous privilege.

Earlier in the summer, on 5 July, a group of us gathered together at 8am in Lecture Theatre 1 of the Mathematical Institute. Given the early hour, and the fact that the majority of people only knew we were there to watch the awards ceremony of the International Congress of Mathematicians in Helsinki, the number of people present was surprisingly large. Some might have been there for the free breakfast. I suspect, though, that a number of others had an inkling of what was about to happen, despite the sworn secrecy that surrounded this event.

The Fields Medal is universally regarded as the highest honour any young mathematician can receive, and is often considered the top prize in mathematics, period, even though only those under forty are eligible to win (that's me out). They are also only awarded every four years. A very small number of us knew that Oxford Mathematician Professor James Maynard was one of the four recipients this year, a few weeks in advance of the medal ceremony. There was a huge buzz of excitement in L1 as James' name was announced that morning. He was not at all a surprise winner, though - James is widely regarded as one of the leading number theorists in the world. He has made spectacular advances in the theory of prime numbers, most of which can quite easily be explained to a general audience. For example, James showed that there are infinitely many primes with no "7" in their decimal expansion (nothing special about 7 here - insert your favourite digit!). While simple to state, the proof was a tour de force of technical reasoning, running to nearly 100 pages. New results about primes are enormously significant, not least since new insights are rare; James has produced several. We hope to properly celebrate his exceptional accomplishment in the New Year with a colloquium and party, after James returns from visiting the Institute for Advanced Study in Princeton this autumn.

James began his research career in Oxford as a DPhil student under the supervision of Professor Roger Heath-Brown. Roger's research achievements were also further recognised this summer with him being awarded the Royal Society's Sylvester Medal. Research success is everywhere in the Mathematical Institute, with groundbreaking work ranging from foundational results in prime number theory and mathematical logic, to applications such as the early prediction of sepsis from clinical data, and mathematical models of filtration leading to more effective water filters used in developing countries.

To me, all these successes only further emphasise the importance of continued funding and support for the next generation of mathematics DPhil students. The mathematical sciences are not only central to mathematical and scientific progress - they are also fundamental to UK industry and the economy as a whole. Back in 2020 when I was Director of Graduate Studies, the UK government had promised to invest an additional £300 million in advanced maths research in the UK, over five years. A large part of this had been funding mathematics DPhil students, but unfortunately quite late in the graduate admissions round this year we learned that this funding wasn't to be delivered. Fortunately last year we had launched an appeal for the Oxford Mathematical Institute Fund (OMIF) - an expendable endowment that currently supports a number of our talented graduate research students. We are enormously grateful to those of you who have supported this. As incoming Head of Department, trying to secure additional funding is high on my list of priorities. This includes scholarships for MSc students, particularly for students from disadvantaged backgrounds, and for whom family income is a barrier to postgraduate study. Again we're enormously grateful for recent support we've received on this, from both the Martingale Postgraduate Foundation and Optiver Foundation.

On a different note, the Mathematical Institute is delighted to be hosting the exciting new exhibition "Cascading Principles: Expansions within Geometry, Philosophy and Interference" by Conrad Shawcross. The exhibition brings together almost 40 sculptures by the artist, created over the last 17 years. Conrad draws inspiration from mathematics, physics and philosophy, with the tetrahedron forming a basic unit, or atom, for his work. The Mathematical Institute almost seems to have been purpose-built to house this remarkable collection, although of course that's in no small part due to input from Conrad and the expert curation of Fatos Ustek. The exhibition will run for a whole year, with various events taking place throughout that year, organized in partnership with Modern Art Oxford and the Ruskin School of Art (of which Conrad is an alumnus).

I think what's particularly interesting about this exhibit is that every mathematician will look at Conrad's work and see something different. To me, when looking at the three-dimensional polytopes, subdivided into tetrahedra, I see the seven-dimensional spaces I've been working on recently, where the three-dimensional polytope captures their "toric" geometry. In turn these spaces capture information about certain black holes, and the matter they interact with, in four spacetime dimensions. It's wonderful that this exhibition will bring many people to the Mathematical Institute who might otherwise never have come, fostering cross-fertilisation of thought and creativity by bringing different disciplines together. Please do come to visit us to see the exhibition at one of these events over the coming academic year, or indeed as part of visiting for one of our regular public lectures.

I will write more about what we're planning to do on other fronts in a future newsletter, especially with regard to teaching and assessment. One of my aims is to broaden the types of assessment we use in our undergraduate mathematics degrees. We had a department "away day" discussion on this last week, and have set up a number of working groups that will consult closely with students. I look forward to updating you about our plans once we've done more work. In the meantime I hope to see many of you at Mathematical Institute events over the coming months, and wish you all well.