In July 2022 Maryna Viazovska became the second woman and the first person with a degree from a Ukrainian University to win the prestigious Fields Medal in Mathematics. She was born in Kyiv and showed great mathematical promise from a very young age.
Viazovska won the Fields Medal for solving the sphere packing problem in dimensions 8 and 24. The sphere packing problem is one of the oldest open problems in Mathematics, first proposed by Johannes Kepler in 1611. Kepler conjectured that the familiar pyramidal piling of fruits seen in a grocery store is the densest way to pack spheres of equal volume in three dimensions. Even though the problem is so easy to state, it took centuries to solve. In 1998, Thomas Hale solved Kepler’s original conjecture in three dimensions, but the complete solution in all dimensions is still a mystery.
Visualizing the sphere packing problem in dimensions higher than three is a lot more complicated than in three dimensions. However, dimensions 8 and 24 have long been known to be mysteriously special. Mathematicians have conjectured for a while that the most efficient sphere packings in dimensions 8 and 24 are given by what are called the E8 and the Leech lattice respectively. In 2016 Viazovska, who at that time was a postdoctoral researcher in Berlin, published a paper that finally proved that the E8 lattice is indeed the most efficient sphere packing in dimension 8.
Peter Sarnak, a renowned number theorist from Princeton said about Viazovska’s paper, “It’s stunningly simple, as all great things are. You just start reading the paper and you know this is correct.” Within a week of publishing her paper, Viazovska together with a few other mathematicians extended her method to solve the problem in dimension 24.
Viazovska is currently the chair of number theory at École Polytechnique Fédérale de Lausanne (EPFL). In 2022, while she won the Fields Medal she also suffered great emotional distress as Ukraine, her country, was plunged into a brutal war by Russia. She found solace in teaching and dedicated one of her lectures to Yulia Zdanovska, a young mathematician and computer scientist from Kharkiv. Zdanovska died in a missile attack in Kharkiv. While talking to the Simons Foundation about Zdonovska, Viazovska said, “When someone like her dies, it is like the future dies.”
You can hear Maryna Viazovska talk about her work, her life, and her feelings about the humanitarian crisis in Ukraine in the interview she did for the International Mathematical Union upon winning the Fields Medal, and also in the following video made by the Simons Foundation.
Entry Courtesy of Nissim Ranade