Caucher Birkar is one of four winners of the Fields medal University of Cambridge

A Kurdish refugee to the UK is one of the four recipients of the 2018 Fields medals. Caucher Birkar was given the award at the International Congress of Mathematicians in Rio de Janeiro, Brazil.

The Fields medals, often called the Nobel prize of mathematics, are awarded every four years. Medallists must be under the age of 40 by the start of the year they receive the award, with up to four mathematicians honoured at a time.

Caucher Birkar, a mathematician at the University of Cambridge, UK won the award for his work on categorising different kinds of polynomial equations. He proved that the infinite variety of such equations can be split into a finite number of classifications, a major breakthrough in the field of arithmetic geometry. Born in a Kurdish village in pre-revolutionary Iran, Birkar sought and obtained political asylum in the UK while finishing his undergraduate degree in Iran.


Leading mathematicians

Another of this year’s medals was awarded to Alessio Figalli at ETH Zurich, Switzerland. His research concerns the optimal transport problem, which aims to find the most efficient route for carrying an item from one location to another. This seemingly simple problem has a broad range of applications to everything from the formation of crystals to changes in the weather.

Peter Scholze at the University of Bonn, Germany was seen as the odds-on favourite to win a medal this year. At 30 years old he is of the youngest to ever win the award, which like Birkar’s was for contributions to arithmetic geometry. Whereas shapes and numbers are often seen as belonging to separate disciplines, Scholze believes it is possible to translate ideas between the two, leading to what some hope will be a grand unification between these disparate areas of mathematics.

Finally, Akshay Venkatesh at the Institute of Advanced Studies in Princeton, New Jersey, was awarded for work spanning a bewildering array of mathematical fields, including number theory, dynamics and topology. Some hope that his research will allow for progress in solving the Riemann Hypothesis, a tantalising conjecture about the distribution of prime numbers

Previous medallists include Cédric Villani, who is now a member of the French parliament, and Maryam Mirzakhani, the first woman to receive the award. Controversially, Grigori Perelman was awarded one of the medals in 2006 for solving the million-dollar Poincaré Conjecture but declined the award and the monetary prize.