The Fields Medal, established to compensate for the lack of a Nobel Prize in Mathematics, is awarded every four years at the International Congress of Mathematicians to 2 to 4 scientists who must be younger than 40 at the beginning of the year of the award. The current awardees, Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska, were awarded on 5 July 2022.
Maryna Viazovska is only the second woman to be awarded the Fields Medal. She received the prize primarily for her solution to the problem of the densest sphere packing in dimension 8. Her proof impressed experts in particular because, in the words of Peter Sarnak, "it is impressively simple, as all great things are". Together with co-authors, Viazovska then went on to crack the dimension 24 case in a related paper.
The question of how to pack spheres of the same size as close together as possible has fascinated mathematicians for more than four centuries. As early as 1611, Johannes Kepler suspected that the best way to do this in the case of dimension 3 was to stack the spheres on top of each other in a pyramid shape. That this is indeed correct was only proven in 1998 by Thomas Hales through a combination of theoretical arguments and extensive computer calculations. Answers are also known for dimensions 1 and 2. Viazovska's work provides the first and so far only complete solutions in higher dimensions.
Maryna Viazovska comes from Ukraine. After completing her Bachelor's degree in Kiev, she did her Master's degree at TU Kaiserslautern. She then joined Don Zagier in Bonn as a doctoral student, where she completed her doctorate in 2013. One station of her postdoc period was the Humboldt University in Berlin. Today Viazovska is a professor of number theory at the École polytechnique fédérale de Lausanne (EPFL), Switzerland.
Her Master's thesis in Kaiserslautern was written in 2007 in the Algebra, Geometry and Computer Algebra group of the Department of Mathematics, her supervisor was Gerhard Pfister. The topic of the thesis was the calculation of Weierstrass semigroups of singularities of space curves and the implementation of a corresponding algorithm in the computer algebra system Singular, which is being developed in Kaiserslautern.
Further information on the Fields Medal and the current prize winners can be found on the website of the International Mathematical Union (IMU).