Ukrainian number theorist Maryna Viazovska is among the four winners of the prestigious mathematics prize
Maryna Viazovska is known for work on sphere packing
5 July 2022 – Ukrainian number theorist Maryna Viazovska is among the four winners of the 2022 Fields Medal, one of the highest honours in mathematics, which is conventionally awarded to people under 40. The other winners are James Maynard, a number theorist at the University of Oxford, UK; June Huh, a specialist in combinatorics at Princeton University in New Jersey; and Hugo Duminil-Copin, who studies statistical physics at the Institute of Advanced Scientific Studies near Paris. The International Mathematical Union (IMU) announced the winners at an award ceremony in Helsinki on 5 July.
“All of the medallists are incredibly deserving and talented, showcasing the vibrancy of mathematical research across the globe,” says Bryna Kra, a mathematician at Northwestern University in Evanston, Illinois, who is president-elect of the American Mathematical Society.
Viazovska, who is based at the Swiss Federal Institute of Technology in Lausanne (EPFL), is the second woman ever to earn the award. She is best known for her solution to the sphere-packing problem — finding the arrangement of spheres that can take up the largest portion of a volume — in eight dimensions.
In 3D space, the most efficient way to pack spheres is the pyramid arrangement, similar to how oranges are packed on trays in a grocer’s shop (proving this mathematically was extremely hard and was the subject of a tour-de-force paper in the 1990s). But in four or more dimensions, very little is known, says Henry Cohn, a mathematician at the Massachusetts Institute of Technology in Cambridge. “It’s this horrific gap in our knowledge — almost embarrassing,” said Cohn in a statement after the Fields Medal announcement. Viazovska introduced new techniques into the problem that came from number theory and the theory of symmetries in eight dimensions. “Given how poor our understanding is in other dimensions, it’s really miraculous that Maryna was able to get this exactly,” Cohn added. More recently, Cohn worked with Viazovska and others to extend the result to 24-dimensional space.
“Viazovska invents fresh and unexpected tools that allow her to jump over natural barriers that have held us back for years,” says Peter Sarnak, a number theorist at Princeton University.
“Spectacular contributions”
Of Maynard, who is known for breakthrough discoveries about the spacing of prime numbers, Sarnak says that “a number of his results were viewed as pure fantasy before he announced them”. Maynard’s citation from the Fields Medal committee notes that he has “made spectacular contributions in analytic number theory”.
Duminil-Copin has achieved a number of fundamental results on a mathematical model that “describes how a piece of iron loses its magnetization when it reaches a certain temperature”, says his former mentor Wendelin Werner, a mathematician at the Swiss Federal Institute of Technology (ETH) in Zurich.
Huh’s citation said that, together with colleagues, he had “transformed the field of geometric combinatorics”. He did so by importing tools from another field of maths, algebraic geometry.
Fields medallists June Huh, James Maynard and Hugo Duminil-Copin (left to right)
Relocated ceremony
The Fields Medal and other IMU prizes are normally announced at the opening of the International Congress of Mathematicians (ICM), which takes place every four years. This year’s congress was scheduled to begin on 6 July in St Petersburg in Russia, but the plan was scrapped after Russia invaded Ukraine in February. The awards ceremony was moved to Helsinki and the congress will be a virtual event.
“We condemn the madness, the injustice, and the irreversibility of war that threatens the very existence of humanity,” wrote four members of what had been the local organizing committee in a statement on 27 February.
The committee that chooses the Fields Medal winners — whose members’ identities were kept secret until today — reportedly made its decision before the invasion.
At a satellite conference for the ICM on 2 July, another Ukrainian-born mathematician, Svetlana Jitomirskaya at the University of California Irvine, won the inaugural Olga Alexandrovna Ladyzhenskaya Prize in Mathematical Physics — the first major prize in the discipline to be named after a woman but open to people of any gender. The prize celebrates Russian mathematician Olga Ladyzhenskaya, who narrowly missed out on her own Fields Medal in 1958. Before Viazovska, the only woman to win a Fields Medal was Maryam Mirzakhani, in 2014.