The Ukrainian mathematician became the second woman to win the prestigious Fields Medal

Ukrainian number theorist Marina Vyazovska is among four recipients of the 2022 Fields Medals, one of the highest honors in mathematics, traditionally awarded to people under 40. The other winners are James Maynard, a number theorist at the University of Oxford, United Kingdom; Jun He, a combinatorics specialist at Princeton University in New Jersey; and Hugo Duminil-Copin, who studies statistical physics at the Institute for Advanced Studies (IHES) near Paris. The International Mathematical Union (IMU) announced the winners at an award ceremony in Helsinki on 5 July.

“All of the medalists are incredibly worthy and talented, demonstrating the vitality of mathematical research around the world,” said Bryna Kra, a mathematician at Northwestern University in Evanston, Illinois, who is president-elect of the American Mathematical Society.

Wiazowska, who works at the Swiss Federal Institute of Technology in Lausanne (EPFL), is the second woman to win the award. She is best known for her solution to the sphere packing problem—finding the arrangement of spheres that can occupy the largest volume—in eight dimensions.

In three-dimensional space, the most efficient way to pack spheres is in a pyramidal arrangement, similar to how oranges are packed on trays in a grocery store (proving this mathematically was extremely difficult and was the subject of a tour de force paper in the 1990s years). 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 terrifying gap in our knowledge — almost embarrassing to humanity,” Cohn said in an address after Fields’ medal was announced. Viazovska introduced new techniques to 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 truly a miracle that Marina was able to get just that,” Cohn added. More recently, Cohn himself helped extend the result to 24-dimensional space.

“Wiazowska is inventing fresh and unexpected tools that allow her to leap over natural barriers that have held us back for years,” says Peter Sarnak, a number theorist at Princeton’s Institute for Advanced Study.

The Fields Medals and other IMU awards are usually announced at the opening of the International Congress of Mathematicians (ICM), held every four years. This year’s congress was supposed to start on July 6 in St. Petersburg, Russia, but the plan was canceled after Russia’s invasion of Ukraine in February. Instead, the award ceremony was moved to Helsinki and the congress will be held as a virtual event.

“We condemn the madness, injustice and irreversibility of the war that threatens the very existence of humanity,” four members of the local organizing committee wrote in a February 27 statement.

The committee that selects Fields’ winner – the identity of whose members has been kept secret until today – is said to have made its decision before the invasion.

At an ICM satellite conference on July 2, another Ukrainian-born woman, Svetlana Zhitomirskaya of the University of California, Irvine, won the inaugural Ladyzhenskaya Prize in Mathematical Physics—the first major award for the discipline named after a woman but open to people of any gender. The award honors the late Russian mathematician Olga Ladizhenskaya (1922-2004), who narrowly missed out on her own Fields Medal when her candidacy was being considered in 1958. Before Vyazovska, the only woman to win a Fields Medal was the late Mariam Mirzakhani, in 2014

This article is reproduced with permission and was first published on July 5, 2022