Oxford Mathematician James Maynard awarded Fields Medal 2022

Professor James Maynard has been named one of four recipients of the 2022 Fields Medal, the most prestigious award in mathematics for those under 40.

The Fields Medal recognises outstanding mathematical achievement for existing work and for the promise of future achievement. Often described as the Nobel Prize of mathematics, the Fields Medal is awarded every four years to recipients under the age of forty.

Professor James Maynard, Mathematical Institute, University of Oxford has been awarded a 2022 Fields Medal for his ‘spectacular contributions’ to analytic number theory, ‘which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation’.

‘It means a huge amount to win such a prestigious prize and to have this sort of recognition from my colleagues around the world. It feels a bit surreal imagining my name alongside giants of mathematics that I read about as a child,’ said Professor Maynard.

‘The system at Oxford has always given me a lot of time and freedom to explore my research interests, and this freedom is vital if you want to make important conceptual advances. I developed my passion for mathematical research as a graduate student. My supervisor, Professor Roger Heath-Brown, was very supportive and helped me develop hugely when I was starting out.’

One of the leading figures in the field of number theory, Maynard became a Professor of Number Theory at Oxford in 2017. Much of his career has focused on the study of some of the most famous questions in number theory, particularly around the distribution and structure of prime numbers.

Prime numbers, divisible by themselves and one, have fascinated mathematicians for millennia, but still pose a number of fundamental questions. In his work on distribution, Maynard has shown that sometimes primes are much more sparse than average, a famous Erdős problem on which no qualitative progress had been made for decades.

Maynard has also produced fundamental work in Diophantine approximation, solving the 1941 Duffin–Schaeffer conjecture with Dimitris Koukoulopoulos, Associate Professor at the University of Montreal in 2019.

His latest work is a series of works on the distribution of primes in residue classes extending principles beyond the Generalised Riemann Hypothesis – a theory on the distribution of prime numbers.

The International Mathematical Union, which has awarded the Fields Medal since the 1930s described Maynard’s approach: ‘His work is highly ingenious, often leading to surprising breakthroughs on important problems that seemed to be inaccessible by current techniques.’

Maynard is keen to encourage others into the field: ‘I certainly hope that the award might help encourage the next generation of mathematicians to become interested in research in number theory – there have been many exciting developments on old problems recently.’