Martin Hairer

Sir Martin Hairer
Hairer in 2014
Sir Martin Hairer
Born	14 11, 1975
Birthplace	Geneva, Switzerland
Nationality	Austrian, British
Occupation	Mathematician
Employer	École Polytechnique Fédérale de Lausanne, Imperial College London
Known for	Theory of regularity structures, stochastic partial differential equations
Education	University of Geneva (PhD, 2001)
Awards	Fields Medal (2014), Breakthrough Prize in Mathematics (2021), Sylvester Medal (2025)
Website	[http://www.hairer.org Official site]

Sir Martin Hairer KBE FRS (born 14 November 1975) is an Austrian-British mathematician whose work in stochastic analysis, particularly the theory of stochastic partial differential equations (SPDEs), has reshaped the landscape of modern probability theory. Born in Geneva, Switzerland, into a family with deep mathematical roots — his father Ernst Hairer is a renowned numerical analyst — Hairer developed an early fascination with mathematics and computation that would eventually lead him to construct one of the most celebrated mathematical frameworks of the twenty-first century. He is Professor of Mathematics at the École Polytechnique Fédérale de Lausanne (EPFL) and at Imperial College London, having previously held positions at the University of Warwick and the Courant Institute of Mathematical Sciences at New York University. In 2014, Hairer was awarded the Fields Medal, often described as the most prestigious prize in mathematics, for his creation of a theory of regularity structures for stochastic partial differential equations. In 2020, he was named the sole winner of the 2021 Breakthrough Prize in Mathematics, carrying a $3 million award, for what the prize committee called "transformative contributions to the theory of stochastic analysis."

Early Life

Martin Hairer was born on 14 November 1975 in Geneva, Switzerland. His father, Ernst Hairer, is a professor of mathematics at the University of Geneva, known internationally for his contributions to numerical analysis and the theory of ordinary differential equations. Growing up in an environment where mathematical thinking was part of daily life, Hairer showed aptitude for both mathematics and computing from a young age.

As a teenager, Hairer developed an interest in software and audio processing. He created a software program called Amadeus, a sound editor for macOS (then Mac OS), which gained recognition in the Apple software community. The program was notable enough to receive an Eddy Award from Macworld magazine in 2007. This early venture into programming demonstrated the combination of mathematical precision and creative problem-solving that would later characterize his academic work. Hairer continued to maintain the software even as his mathematical career advanced, an unusual duality that became a notable part of his public profile.

Hairer grew up in the French-speaking part of Switzerland, and his doctoral thesis would later be written in French. His upbringing in Geneva, a city that hosts both the University of Geneva and the nearby CERN, placed him at the crossroads of European scientific culture. The intellectual environment of the city, combined with his father's academic career, provided a foundation for his eventual pursuit of mathematics at the highest level.

Education

Hairer pursued his higher education at the University of Geneva, where he studied mathematics. He completed his doctoral studies there under the supervision of Jean-Pierre Eckmann, a mathematical physicist known for his work in dynamical systems and statistical mechanics. Hairer's doctoral thesis, titled Comportement Asymptotique d'Équations à Dérivées Partielles Stochastiques (Asymptotic Behaviour of Stochastic Partial Differential Equations), was completed in 2001. The thesis addressed fundamental questions about the long-time behaviour of SPDEs, topics that would form the basis of his subsequent research programme. The choice of Eckmann as supervisor was significant, as Eckmann's expertise bridged physics and mathematics, an orientation that would influence Hairer's approach to stochastic analysis as a discipline connected to physical modelling.

Career

University of Warwick

Following the completion of his doctorate, Hairer joined the University of Warwick in the Mathematics Department, where he would spend a substantial portion of his early career. At Warwick, he established himself as one of the leading figures in the field of stochastic partial differential equations, publishing a series of papers that progressively expanded the mathematical community's understanding of SPDEs and their applications.

During his time at Warwick, Hairer received several recognitions that signalled his growing stature in the field. In 2008, the London Mathematical Society awarded him the Whitehead Prize, given to mathematicians in the early stages of their careers who have made outstanding contributions. That same year, he received the Philip Leverhulme Prize, a significant award recognizing outstanding research achievement by early-career scholars in the United Kingdom.

In 2006, Hairer received recognition from the University of Warwick's Mathematics Department for his contributions to the field. He also received the Fermat Prize in 2013, awarded for outstanding research in fields where Pierre de Fermat made significant contributions, further cementing his international reputation.

Hairer also secured an ERC (European Research Council) Consolidator Grant in 2014, providing substantial funding for his research programme.

Development of Regularity Structures

Hairer's most celebrated contribution to mathematics is the theory of regularity structures, which he introduced in a landmark paper in 2014. The theory provides a systematic framework for making mathematical sense of a large class of stochastic partial differential equations that had previously been considered intractable or even ill-defined. These equations arise naturally in mathematical physics, particularly in models describing phenomena such as interface growth (the KPZ equation), quantum field theory, and other systems where randomness plays a fundamental role.

The core problem that Hairer addressed was that many physically motivated SPDEs involve products of distributions — mathematical objects that, under classical analysis, cannot be multiplied together in a well-defined way. Previous approaches had either avoided these equations entirely or handled them on a case-by-case basis with ad hoc methods. Hairer's theory of regularity structures provided a unified and general framework, creating what colleagues described as an entirely new mathematical world.

The Quanta Magazine profile published upon his receipt of the Fields Medal described how Hairer's work "created a whole world" and noted the "startling creativity" that characterised his approach to the problems of stochastic analysis. The theory drew on ideas from several areas of mathematics, including rough path theory (developed by Terry Lyons), renormalization techniques from quantum field theory, and classical PDE theory, synthesizing them into a coherent and powerful new framework.

The theory's significance lies not only in its resolution of specific long-standing open problems but also in the new conceptual language it introduced. Regularity structures provided a way to describe the local behaviour of solutions to SPDEs with a level of precision that had not previously been possible, enabling mathematicians to prove existence, uniqueness, and regularity results for equations that had resisted all previous attempts at rigorous mathematical treatment.

Imperial College London

Hairer moved to Imperial College London, where he took up a professorship in the Department of Mathematics. At Imperial, he continued to develop and extend the theory of regularity structures while also pursuing broader questions in stochastic analysis and probability theory.

In September 2020, it was announced that Hairer had won the 2021 Breakthrough Prize in Mathematics, the richest academic prize in the world, carrying an award of $3 million. He was the sole winner in the mathematics category that year. The Guardian reported on the award, noting that it recognized his "transformative contributions to the theory of stochastic analysis, in particular the theory of regularity structures in stochastic partial differential equations." Imperial College London issued a press release describing him as "the single winner of the 2021 Breakthrough Prize in Mathematics."

EPFL and Current Work

Hairer holds a professorship at the École Polytechnique Fédérale de Lausanne (EPFL) in addition to his position at Imperial College London. The dual appointment places him at two of Europe's leading research institutions and allows him to collaborate with mathematicians across the continent.

In August 2025, the Simons Foundation announced the launch of the Simons Collaboration on Probabilistic Paths to Quantum Field Theory, a major collaborative research effort in which Hairer's work on regularity structures and SPDEs plays a central role. The collaboration aims to develop probabilistic approaches to quantum field theory, connecting Hairer's mathematical framework to fundamental questions in theoretical physics.

In February 2026, The New York Times featured Hairer in an article about mathematicians testing the capabilities of artificial intelligence in mathematical reasoning. The article described Hairer as "a mathematician known for his startling creativity" and explored the broader question of whether AI systems could replicate or assist with the kind of deep mathematical insight that characterizes work such as Hairer's theory of regularity structures.

Editorial and Service Roles

Throughout his career, Hairer has been active in professional service to the mathematical community. He has served on the editorial boards of several leading journals, including the Electronic Journal of Probability and the Annales de l'Institut Henri Poincaré. He has also served on the Scientific Committee of the Mathematisches Forschungsinstitut Oberwolfach (MFO), one of the most important research centres for mathematics in the world.

Hairer has delivered invited lectures at numerous institutions worldwide. He gave the Minerva Lectures at Columbia University and the Lipschitz Lectures at the Hausdorff Center for Mathematics in Bonn. In 2014, he participated in the Euler Lecture series in Berlin. He also visited the Illinois Institute of Technology's Department of Applied Mathematics in October 2016 as a guest lecturer.

He has participated in programmes at the Institut Henri Poincaré in Paris.

Personal Life

Martin Hairer is the son of Ernst Hairer, a mathematician at the University of Geneva known for his work in numerical analysis and geometric integration. The mathematical lineage is notable — having a parent who is also a distinguished mathematician in a different field of the discipline is relatively uncommon.

Hairer holds both Austrian and British citizenship. He was made a Knight Commander of the Order of the British Empire (KBE). While non-Commonwealth citizens who receive honorary knighthoods typically do not use the title "Sir," Hairer's knighthood was reported to have been converted to a substantive knighthood, reflecting his British citizenship, and he uses the title accordingly.

Hairer is a Fellow of the Royal Society (FRS), one of the highest honours in British science.

Beyond his mathematical career, Hairer's creation and maintenance of the Amadeus sound editing software for macOS has been a consistent feature of profiles written about him, serving as an illustration of his broad intellectual interests and technical skill beyond pure mathematics.

Recognition

Hairer has received an extensive list of honours and awards throughout his career. The most prominent among these are:

• Fields Medal (2014): Awarded at the International Congress of Mathematicians in Seoul for his "outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations."
• Breakthrough Prize in Mathematics (2021, announced 2020): Awarded as the sole laureate, with a $3 million prize, for "transformative contributions to the theory of stochastic analysis, in particular the theory of regularity structures in stochastic partial differential equations."
• Sylvester Medal (2025): Awarded by the Royal Society for "outstanding contributions in the field of" mathematical research, as reported by Felix Online, the student newspaper of Imperial College London.
• Fermat Prize (2013): Awarded by the Institut de Mathématiques de Toulouse.
• Whitehead Prize (2008): Awarded by the London Mathematical Society.
• Philip Leverhulme Prize (2008): Awarded by the Leverhulme Trust.
• ERC Consolidator Grant (2014): Awarded by the European Research Council.
• Knight Commander of the Order of the British Empire (KBE)
• Fellow of the Royal Society (FRS)

Legacy

Martin Hairer's theory of regularity structures has had a profound and lasting impact on the field of stochastic analysis. The framework he introduced in 2014 resolved problems that had been open for decades and opened up entirely new directions of research in probability theory, mathematical physics, and partial differential equations. Colleagues quoted in Quanta Magazine described the work as having "created a whole world," a characterization that reflects the scope and ambition of the theory.

The significance of regularity structures extends beyond the specific equations they were designed to handle. The theory introduced new algebraic and analytic tools that have been adopted and adapted by mathematicians working in adjacent fields. In particular, the connections between regularity structures and renormalization group techniques from quantum field theory have opened a productive dialogue between pure mathematics and theoretical physics, a development that the Simons Collaboration on Probabilistic Paths to Quantum Field Theory, launched in 2025, seeks to deepen and formalize.

Hairer's receipt of both the Fields Medal and the Breakthrough Prize in Mathematics — two of the most selective awards in the discipline — within a span of six years underscores the mathematical community's assessment of his work as among the most important of his generation. The fact that the Breakthrough Prize committee chose him as the sole laureate in 2021, rather than splitting the award among multiple recipients, further reflects the singular impact of his contributions.

His involvement in discussions about the role of artificial intelligence in mathematics, as reported by The New York Times in 2026, suggests that Hairer continues to engage with questions about the future of mathematical practice and the nature of mathematical creativity. As the field of stochastic analysis continues to develop, Hairer's regularity structures remain a central reference point and a continuing source of new research directions.