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The next two films in our' Show Me the Maths' series demonstrate two contrasting aspects of the mathematics that we do here in Oxford. 

In the first, Josh Bull, talks about the challenge of making mathematical models have application to real patient data, in Josh's case in the field of oncology. In the second, Nathan Creighton discusses his work on Dirichlet-L functions.

'Show Me the Maths': short films that unashamedly get down to the detail.

Mathematical oncologists apply mathematical and computational models to every aspect of cancer biology, from tumor initiation to malignant spread and treatment response. A substantial amount of medical research now focuses on the molecular biology of individual tumors to selectively target pathways involved in tumor progression, leading to careful manipulation of these pathways, and new cell-specific approaches to cancer therapy are now being developed. 

At the same time, advances in cancer immunotherapies have led to a reemergence of their use and effectiveness. Using data-driven computational models is a powerful and practical way to investigate the therapeutic potential of novel combinations of these two very different strategies for clinical cancer treatment.

Trachette will showcase mathematical models designed to optimize targeted drug treatment strategies in combination with immunotherapy, to gain a more robust understanding of how specific tumor mutations affect the immune system and ultimately impact combination therapy. Combined with existing and newly generated experimental data, these models are poised to improve the ability to connect promising drugs for clinical trials and reduce the time and costs of transitioning novel therapeutic approaches from “equations to bench to bedside.”

Trachette Jackson is Professor of Mathematics at the University of Michigan and recipient of many awards for her work in her field and for her commitment to increasing opportunities for girls, women, and underrepresented minority students.

Please email @email to register to attend in person.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Thursday 21 March at 5-6pm and any time after (no need to register for the online version).

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

Our new short film series 'Show Me the Maths' doesn't beat about the mathematical bush. It gets right down to it. Down, that is, to the maths, in all its crucial, complex, sometimes incomprehensible (even to other mathematicians) guises. It's what mathematicians do.

The series will feature research in Number Theory, Mathematical Biology and the History of Mathematics, amongst others. First up: Arun Soor.

We continue to expand our social media presence with YouTube shorts being the latest addition. These one-minute (or less) films will often act as a taster for the longer public and students lectures that are already on the Channel, but we will also include the short films that go on other social media platforms. 

They will enable people who don't have access (or prefer not to have access) to social media to watch the many films we make about our mathematicians and their mathematical lives. Here is Professor Pointyhead.

The first of six 'Probability' lectures we are showing, taken from the first year undergraduate course, is now available to watch.

The First Year Probability lectures are for students of Mathematics, Computer Science and joint degree courses between Mathematics and Statistics and Mathematics and Philosophy. First year lectures are supported by lecture notes and complemented by one problem sheet for every two lectures, which students are asked to solve in preparation for discussion in pairs with their tutors in tutorials. 

Lecture 1 takes the intuitive notion of randomness (and perceived randomness) in the real world and introduces mathematical models, in which events that may be observed are captured as sets of possible outcomes to which we can assign probabilities. 

This lecture joins another 85 undergraduate lectures that can be watched via the playlist.

Oxford Mathematician Roger Heath-Brown has been been appointed Officer of the Order of the British Empire (OBE) for services to Mathematics and Mathematical Research in the 2024 New Year Honours List.

Roger Heath-Brown is one of the foremost analytic number theorists of his generation. His important works on prime numbers and related topics include, among many others:

- "Heath-Brown's identity", an important way of decomposing the primes into multilinear pieces, used in many other works such as Zhang's work on bounded gaps between primes

- There are infinitely many primes of the form x^3 + 2y^3 (currently the sparsest natural sequence where one can find primes)

- if a is coprime to q, there is always a prime a (mod q) of size < q to the power 5.5

- at least one of 2,3,5 is a primitive root modulo infinitely many primes.

His contributions to solving equations in integers and rationals include, for instance:

- every nonsingular cubic form in 10 variables has a rational point (and 10 is best possible)

- every cubic form in 14 variables has a rational point

- development of "the determinant method"

- breakthrough quantitative results on the number of rational points up to a given height

Roger Heath-Brown was educated at Cambridge (a student of Alan Baker) and moved to Oxford in 1979. He was made FRS in 1993, and was twice a speaker at the International Congress of Mathematicians. He remained at Oxford throughout his career, first at Magdalen College and then, upon being promoted to a personal statutory professorship in 1999, at Worcester College. He retired in 2016. Among his many graduate students was James Maynard, who was awarded the Fields Medal in 2022.

Roger said: "Naturally I am thrilled to receive this honour. It is a reflection of the ever growing importance of mathematics in modern life. Indeed, I have been delighted to see the corresponding growth in the subject at Oxford over the past 40 years, and also within Number Theory - my own research area. I would like to take this opportunity to acknowledge the friendship and support of my colleagues both at Oxford and across the globe. They have made my work a pleasure."

You can watch an interview with Roger by Ben Green on occasion of his retirement (a loose term for a mathematician) .

Here's the answer to yesterday's Christmas puzzle. If you missed it, you can find it here although James Munro recaps it in the answer video below.

In a roasted chestnutshell, it's a story of three kings bringing gifts (sound familiar?). However, they are not all telling the truth. Your job is to work out who is and who isn't telling the truth and what gifts they have really brought.

Not too taxing, easy to digest, just follow the star. Merry Christmas.