mathematics

Martin Hairer

Martin Hairer is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Martin Hairer rather than just read about it. In short: Sir Martin Hairer KBE FRS (born 14 November 1975) is an Austrian-British mathematician and mathematical physicist working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at EPFL (École Polytechnique Fédérale de Lausanne) and at Imperial College London.

Key takeaways

Martin Hairer belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Martin Hairer to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Martin Hairer from memory before moving on to harder problems.

Reference excerpt

Sir Martin Hairer KBE FRS (born 14 November 1975) is an Austrian-British mathematician and mathematical physicist working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at EPFL (École Polytechnique Fédérale de Lausanne) and at Imperial College London. He previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve. In 2020 he won the 2021 Breakthrough Prize in Mathematics.

Early life and education Hairer was born in Geneva, Switzerland. He attended the Collège Claparède Geneva where he received his high school diploma in 1994. He entered a school science competition with sound editing software that was developed into Amadeus, and later continued to maintain the software in addition to his academic work; it continued to be widely used as of 2020. He then attended the University of Geneva, where he obtained his Bachelor of Science degree in Mathematics in July 1998, Master of Science in Physics in October 1998 and PhD in Physics under the supervision of Jean-Pierre Eckmann in November 2001.

Research and career Hairer is active in the field of stochastic partial differential equations in particular, and in stochastic analysis and stochastic dynamics in general. He has worked on variants of Hörmander's theorem, systematisation of the construction of Lyapunov functions for stochastic systems, development of a general theory of ergodicity for non-Markovian systems, multiscale analysis techniques, theory of homogenisation, theory of path sampling and theory of rough paths and, in 2014, on his theory of regularity structures. Under the name HairerSoft, he develops Macintosh software.

Affiliations

Awards and honours 2006–2011 Advanced Research Fellowship, Engineering and Physical Sciences Research Council (EPSRC) 2007 – Editors' Choice Award, Macworld 2008 – Whitehead Prize, London Mathematical Society 2008 – Philip Leverhulme Prize, Leverhulme Trust 2009 – Royal Society Wolfson Research Merit Award 2012 – Leverhulme Research Leadership Award, Leverhulme Trust 2013 – Fermat Prize, Institut de Mathématiques de Toulouse 2014 – Consolidator grant, European Research Council 2014 – Elected Fellow of the Royal Society (FRS) in 2014 2014 – Fröhlich Prize, London Mathematical Society 2014 – Fields Medal 2015 – Fellow of the American Mathematical Society 2015 – Member of the Austrian Academy of Sciences 2015 – Member of the Academy of Sciences Leopoldina 2015 – Member of the Academia Europaea 2016 – Honorary Knight Commander of the Order of the British Empire 2017 – Foreign member of the Polish Academy of Sciences 2019 – Substantive Knight Commander of the Order of the British Empire 2021 – Breakthrough Prize in Mathematics 2022 – King Faisal Prize 2022 – Medal of the Erwin Schrödinger International Institute for Mathematics and Physics 2025 – Sylvester Medal of the Royal Society.

Personal life

Hairer holds Austrian and British nationality, and speaks French, German and English; he married fellow mathematician Li Xue-Mei in 2003. His father is Ernst Hairer, a mathematician at the University of Geneva.

References

This article incorporates text available under the CC BY 4.0 license.

Illustrations

Worked examples

Example 1 — a first encounter with Martin Hairer

Start with the simplest possible case. Write down what Martin Hairer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Martin Hairer before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Martin Hairer ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Martin Hairer

In research: Martin Hairer appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Martin Hairer in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Martin Hairer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1975 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Martin Hairer outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Martin Hairer in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Martin Hairer means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Martin Hairer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Martin Hairer in simple terms?

Why does Martin Hairer matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Martin Hairer?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Martin Hairer.