Professor Sir Martin Hairer is the single winner of the 2021 Breakthrough Prize in Mathematics.

Professor Hairer is recognised “for transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations.”

Maths is truth. Once you discover something in maths, it applies to all eternity. Professor Martin Hairer

He receives three million USD and a trophy, to be presented at a live awards ceremony next year, and will engage in a program of lectures and discussions.

The Breakthrough Prizes are the largest prizes in science, and aim to “help scientific leaders gain freedom from financial constraints to focus fully on the world of ideas; to raise the profile and prestige of basic science and mathematics, fomenting a culture in which intellectual pursuits are validated; and to inspire the next generation of researchers to follow the lead of these extraordinary scientific role models.”

The Breakthrough Prizes were founded by Sergey Brin, Priscilla Chan and Mark Zuckerberg, Yuri and Julia Milner, and Anne Wojcicki. The Prizes have been sponsored by the personal foundations established by Sergey Brin, Priscilla Chan and Mark Zuckerberg, Ma Huateng, Jack Ma, Yuri and Julia Milner and Anne Wojcicki.

'Creativity and deep insights'

On winning the award, Professor Hairer, from the Department of Mathematics at Imperial, said: “I was surprised but obviously very honoured. I’m very happy if I can inspire some people to study mathematics or even just understand a little bit better what maths is all about. Maths is truth. Once you discover something in maths, it applies to all eternity.”

Professor Alice Gast, President of Imperial College London, said: “Martin Hairer’s breakthroughs have profoundly shaped our understanding of stochastic processes. He has brought clarity to previously incomprehensible random phenomena and equations.

“His creativity and deep insights have led to powerful advances in mathematics, physics, computing and finance. Martin is an inspiring ambassador for Imperial, for mathematics, and for science – he is highly deserving recipient of the Breakthrough Prize.”

Professor Hairer is a world leader in probability theory and analysis. He was born in Geneva and is a British-Austrian citizen, joining Imperial in 2017. He won the Fields Medal in 2014 and was knighted in 2016. His father is Professor Ernst Hairer, a mathematician at the University of Geneva.

An interview with Professor Hairer, including more detail about his research, his inspiration, and what it feels like to win, can be listened to below.

Describing randomness

Professor Hairer’s work focuses on generating equations to accurately describe seemingly random motion in time and space, such as how droplets of water spread across the surface of a napkin, the growth of bacteria on a Petri dish or the chaotic activity of millions of individuals making stock trades.

He made serious progress in understanding these equations, called stochastic partial differential equations (PDEs), with his theory of regularity structures. These structures model random effects on physical systems, effectively creating an analytical toolkit for studying stochastic PDEs.

“While the exact details of the fluctuation of the stock market and the movement of water atoms are very different, their probabilistic outcome is the same,” said Professor Hairer.

Professor Hairer moved to London when he joined Imperial three years ago with his wife, mathematician Professor Xue-Mei Li. He says they have been renting ever since, but now plan to use the $3m to finally buy a place to call their own.

Professor Hairer presented Imperial’s annual Schrödinger lecture in 2020, taking the audience on a journey through probability, and the way seemingly dissimilar events can be described in a similar way by probability. You can watch the full lecture below.

Professor Hairer is Imperial’s second Breakthrough Prize winner – joining Professor Sir Simon Donaldson, who was awarded one of the inaugural Breakthrough Prizes in Mathematics in 2014.