Meet the Ukrainian number theorist who received top honors in mathematics

End of February, Just weeks after Maryna Viazovska learned that she had won a Fields Medal — the highest honor for a mathematician — Russian tanks and warplanes began attacking Ukraine, her homeland, and Kyiv, her hometown.

Viazovska no longer lived in Ukraine, but her family was still there. Her two sisters, a 9-year-old niece and an 8-year-old nephew, made their way to Switzerland, where Viazovska lives today. They initially had to wait two days for traffic to ease; even then, the drive west was excruciatingly slow. After spending several days in a strange house waiting for their turn as war refugees, the four crossed the border into Slovakia one night, proceeded to Budapest with the help of the Red Cross, and then boarded a plane to follow Geneva. On March 4 they arrived in Lausanne, where they stayed with Viazovska, her husband, their 13-year-old son and their 2-year-old daughter.

Viazovska’s parents, grandmother and other family members stayed in Kyiv. As Russian tanks closed in on her parents’ house, Viazovska tried every day to persuade them to leave. But her 85-year-old grandmother, who experienced war and occupation as a child during World War II, refused, and her parents did not abandon her. Her grandmother “couldn’t imagine that she wouldn’t die in Ukraine,” Viazovska said, “because she’s lived there all her life.”

In March, a Russian air raid destroyed the Antonov Aircraft Factory where her father had worked in the last years of the Soviet era. Viazovska had attended the kindergarten nearby. Fortunately for Viazovska’s family and other Kiev residents, later that month Russia shifted the focus of its war effort to the Donbass region of eastern Ukraine. But the war is not over yet. Viazovska’s sisters spoke of friends who had to fight, some of whom died.

Viazovska said in May that although the war and the math existed in different parts of her mind, she hadn’t done much research in recent months. “I can’t work if I’m conflicted with someone or something emotionally difficult is going on,” she said.

On July 5, Viazovska accepted her Fields Medal at the International Congress of Mathematicians in Helsinki, Finland. The conference, organized every four years by the International Mathematical Union along with the Fields Medal announcements, was set to take place in St. Petersburg, Russia, despite concerns about the host country’s human rights record, resulting in a boycott petition signed by over 400 mathematicians. But when Russia invaded Ukraine in February, the IMU switched to a virtual ICM and moved the in-person award ceremony to Finland.

At the ceremony, the IMU cited Viazovska’s many mathematical achievements, most notably her proof that an arrangement is named E8th Lattice is the closest packing of spheres in eight dimensions. She is only the second woman to receive this honor in the medal’s 86-year history. (Maryam Mirzakhani was the first in 2014.)

Like other Fields Medalists, Viazovska manages “to do things that are totally not obvious, that a lot of people have tried and failed,” said mathematician Henry Cohn, who was asked to give the official ICM talk to celebrate their work. Unlike others, he said, “She makes them by uncovering very simple, natural, profound structures, things that nobody expected and that nobody else could find.”

The second derivative

The exact location of the École Polytechnique Fédérale de Lausanne is far from obvious on a rainy May afternoon in front of the EPFL metro station. Known in English as the Swiss Federal Institute of Technology in Lausanne – and a leading research university in mathematics, physics and engineering in every language – it is also sometimes referred to as the MIT of Europe. At the end of a dual lane for bicycles and pedestrians that ducks under a minor freeway, the idyllic signs of campus life come into view: huge two-story bike racks, modular architecture befitting a sci-fi cityscape, and a central plaza lined by Classrooms, restaurants and happy student posters. Across the plaza is a modern library and student center that rises and falls in three-dimensional curves, allowing students to walk under and over each other inside and out. From below, the sky is visible through cylindrical waves punched through the topology like Swiss cheese. A short distance away, in one of these modular buildings, a professor with a security card opens the orange double doors that lead to the sanctum of the math department. Just behind the portraits of Noether, Gauss, Klein, Dirichlet, Poincaré, Kovalevski and Hilbert is a green door with the simple inscription “Prof. Maryna Viazovska, Chaire d’Arithmétique.”

Viazovska conducts video conferences with students at her EPFL office.Photo: Thomas Lin/Quanta Magazine

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