Ukrainian mathematician Maryna Viazovsk is one of four winners of The Fields Medal 2022, as a means of recognizing outstanding mathematical achievement for both existing work and the promise of future success.
Viazovska, who is based at the Swiss Federal Institute of Technology in Lausanne (EPFL), is the second woman ever to earn the award.
The sphere packing problem
Viazovsk received the award for her solution of the sphere packing problem, finding the arrangement of spheres that can take up the largest portion of a volume, in eight dimensions.
In a three-dimensional space, the most efficient way to pack spheres is the pyramid arrangement, akin 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 an address following 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.