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 individuals aged beneath 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.
“All the 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 is predicated on the Swiss Federal Institute of Know-how in Lausanne (EPFL), is the second girl ever to earn the award. She is finest identified for her resolution of the sphere packing drawback — discovering the association of spheres that may take up the biggest portion of a quantity — in eight dimensions.
In a three-dimensional area, essentially the most environment friendly technique 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 onerous and was the topic of a tour-de-force paper within the Nineteen Nineties). However in 4 or extra dimensions, little or no is thought, says Henry Cohn, a mathematician on the Massachusetts Institute of Know-how in Cambridge. “It’s this horrific hole in our information — nearly embarrassing for humanity,” stated Cohn in an handle following the Fields Medal announcement. Viazovska launched new strategies into the issue that got here from quantity principle and the idea 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 area.
“Viazovska invents contemporary and sudden instruments that enable her to leap over pure boundaries which have held us again for years,” says Peter Sarnak, a quantity theorist on the Institute for Superior Examine 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 a substitute, 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 warfare 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 at this time — reportedly made its resolution earlier than the invasion.
At a satellite tv for pc convention to the ICM on 2 July, one other Ukrainian-born girl, Svetlana Jitomirskaya on the College of California at Irvine, gained the inaugural Ladyzhenskaya Prize in Mathematical Physics — the primary main prize for the self-discipline to be named after a girl however open to individuals 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-about in 1958. Earlier than Viazovska, the one girl to win a Fields Medal was the late Maryam Mirzakhani, in 2014.
This text is reproduced with permission and was first revealed on July 5 2022.