Image of Roger

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) .

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