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Finding a Formula for Fire, Austrian Wins Top Math Award

Martin Hairer during his ICM lecture 02. Source ICM
Martin Hairer during his lecture at the International Congress of Mathematicians in Seoul last month.
  • Why it matters

    Why it matters

    Mathematician Martin Hairer has managed to describe with numbers how irregular, natural phenomena develop, which had never been done before.

  • Facts


    • The Fields Medal is considered the Nobel Prize of mathematics.
    • The prize comes with Canadian $15,000 (€10,636), and is awarded every four years.
    • Brazil’s Artur Avila, Canada’s Manjul Bhargava and Iran’s Maryam Mirzakhani also won the medal this year.
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“Daddy, what do you do all day when you go to work?”

Some parents say “bake bread” or “heal sick people.”

Martin Hairer’s father used to solve differential equations as a professor at the University of Geneva. He infected his son with a love of numbers and abstract reasoning.

In August, Mr. Hairer made his father proud, winning the coveted Fields Medal, considered the world’s top prize for mathematics.

He received the award at the International Mathematics Union Congress in Seoul, South Korea. His achievement: developing a mathematical formula to predict the seemingly unpredictable — in this case the way fire engulfs a piece of paper.

The Nobel prizes are usually awarded years after a scientific breakthrough, meaning only death can prevent a scientist from winning it. For the Fields Medal, there is an age limit and Mr. Hairer came within a few months of being disqualified.

A winner must be younger than 40 years old in the year before the prize is awarded. By their mid-thirties, ambitious mathematicians should have made headway in their findings.

These ambitions are hardly noticeable when sitting opposite Mr. Hairer. The 39-year-old calmly recalls how he received an email from the International Mathematics Union’s chairwoman seven months ago.

She asked if she could schedule a phone call with Mr. Hairer. “At this point, I could already connect the dots,” he said.

Three years ago, Mr. Hairer had conceived a new concept, adding: “I was aware at the time that it was a rather important finding.” He had not thought of winning the Fields Medal but just wanted to get his discovery published as quickly as possible.

Differential equations describe changes of functions, especially dynamic, natural processes. Often, no set formulae can be found to describe them, only local relationships, for instance between position and velocity. The Navier-Stokes equations are a famous example, describing the dynamics of liquids and gases.

Stochastic differential equations are Martin Hairer’s specialty. They are based on the conclusion that processes in nature hardly ever follow a “smooth”, perfectly predictable mathematical formula but contain random elements.


Martin Hairer signing autographs during Seoul's International Congress of Mathematicians. Source: ICM
Martin Hairer signing autographs during Seoul’s International Congress of Mathematicians. Source: ICM


As an example, Hairer explains how a piece of paper burns and the flames develop randomly across the page. Because paper is never fully homogenous,  the flames never have a simple geometric form. Instead, they have a jagged irregularity. Running water or flowing gases are also characterized by such random fluctuations.

Mr. Hairer's discovery has created tremendous excitement well outside the world of mathematics.

To capture the irregularity, mathematicians incorporate a random element in their differential equations.

The resulting functions are not smooth but rough – mathematically speaking, not differentiable.

It makes these equations hard to solve and, more importantly, requires an interpretation. Mr. Hairer found a way to replace the functions by other, easier to understand equations, which results are almost accurate. His discovery has created a tremendous excitement well outside the world of mathematics.

Mr. Hairer’s path from a professor’s curious son to a mathematics scholar was as bumpy as the phenomena his formulas describe. It was a gradual process. In his youth, Mr. Hairer was a passionate software programmer.

At the age of 15, he took part in a Swiss youth research contest and wanted to develop a program, which could extract the notes of all the voices from a digitalized music recording. His aim was a bit too ambitious — only a few years ago, specialized software was developed that is capable of doing that. Young Mr. Hairer took a more humble approach and wrote a program called “Amadeus”, which won him the 1995 Youth Research Prize.

To this day, it is still a standard tool in audio editing.

Mr. Hairer first earned a degree in physics, then got a doctorate in stochastic differential equations and finally switched to mathematics. Today, he teaches at the University of Warwick in Britain, where his wife and fellow mathematician, Xue-Mei Li, is an associate professor.

Incidently, her specialty is differential equations.

This article first appeared in Die Zeit. Gilbert Kreijger translated this into English. To contact the author:

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