Ukrainian quantity theorist Maryna Viazovska is among the many 4 winners of the 2022 Fields Medals, one of many highest honours in arithmetic that’s conventionally awarded to folks aged underneath 40. The opposite winners are James Maynard, a quantity theorist on the College of Oxford, UK; June Huh, a specialist in combinatorics at Princeton College in New Jersey; and Hugo Duminil-Copin, who research statistical physics on the Institute of Superior Scientific Research (IHES) close to Paris. The Worldwide Mathematical Union (IMU) introduced the winners at an award ceremony in Helsinki on 5 July.
“The entire medalists are extremely deserving and gifted, showcasing the vibrancy of mathematical analysis throughout the globe,” says Bryna Kra, a mathematician at Northwestern College in Evanston, Illinois, who’s president-elect of the American Mathematical Society.
Viazovska, who relies on the Swiss Federal Institute of Expertise in Lausanne (EPFL), is the second lady ever to earn the award. She is finest recognized for her answer of the sphere packing drawback — discovering the association of spheres that may take up the most important portion of a quantity — in eight dimensions.
In a three-dimensional house, essentially the most environment friendly solution to pack spheres is the pyramid association, akin to how oranges are packed on trays in a grocer’s store (proving this mathematically was extraordinarily laborious and was the topic of a tour-de-force paper within the Nineties). However in 4 or extra dimensions, little or no is thought, says Henry Cohn, a mathematician on the Massachusetts Institute of Expertise in Cambridge. “It’s this horrific hole in our data — virtually embarrassing for humanity,” mentioned Cohn in an tackle following the Fields Medal announcement. Viazovska launched new methods into the issue that got here from quantity idea and the speculation of symmetries in eight dimensions. “Given how poor our understanding is in different dimensions, it’s actually miraculous that Maryna was in a position to get this precisely,” Cohn added. Extra lately, Cohn himself has helped to increase the consequence to 24-dimensional house.
“Viazovska invents recent and sudden instruments that permit her to leap over pure boundaries which have held us again for years,” says Peter Sarnak, a quantity theorist on the Institute for Superior Research in Princeton.
The Fields Medals and different IMU prizes are usually introduced on the opening of the Worldwide Congress of Mathematicians (ICM), which takes place each 4 years. This yr’s congress was scheduled to start on 6 July in St. Petersburg, Russia, however the plan was scrapped following Russia’s invasion of Ukraine in February. As an alternative, the awards ceremony was moved to Helsinki and the congress will happen as a digital occasion.
“We condemn the insanity, the injustice, and the irreversibility of struggle that threatens the very existence of humanity,” wrote 4 members of what had been the native organizing committee assertion on 27 February.
The committee that chooses the Fields winner — whose members’ identities have been saved secret till right this moment — reportedly made its choice earlier than the invasion.
At a satellite tv for pc convention to the ICM on 2 July, one other Ukrainian-born lady, Svetlana Jitomirskaya on the College of California at Irvine, received the inaugural Ladyzhenskaya Prize in Mathematical Physics — the primary main prize for the self-discipline to be named after a lady however open to folks of any gender. The prize celebrates the late Russian mathematician Olga Ladyzhenskaya (1922-2004), who narrowly missed out on her personal Fields Medal when her candidacy was thought of in 1958. Earlier than Viazovska, the one lady to win a Fields Medal was the late Maryam Mirzakhani, in 2014.
This text is reproduced with permission and was first printed on July 5 2022.