Ukrainian mathematician Maryna Viazovska, second woman to win the Fields Medal

The Ukrainian mathematician Maryna Viazovska (Kiev, 37 years old) received this Tuesday the 2022 Fields Medal, one of the highest honors in mathematics, which is considered the equivalent of the Nobel Prize. Viazovska is a professor at the Federal Polytechnic School of Lausanne (Switzerland) and has been awarded for her solution to the problem of packing spheres in the most compact way possible, that is, with the least free space between them, in 8 and 24 dimensions.

The award is awarded every four years, on the occasion of the International Congress of Mathematicians, to scientists under 40 years of age. Of the 60 medals awarded since 1936, Viazovska is the second woman to receive one. The first was the Iranian Maryam Mirzakhan, who died in 2017 of cancer, who won it in 2014. Viazovska’s name was already circulating in the previous edition of the Fields Medal, in 2018, and the fact that she was not awarded then caused some disappointment in large part of the scientific community.

This year’s recognition, however, takes on an even greater dimension, following the expulsion of Russia from the congress and the transfer of the ceremony from St. Petersburg (Russia) to Helsinki (Finland) in retaliation after the invasion of Ukraine by the army of Vladimir Putin. Along with Viazovska, the British James Maynard, the Frenchman Hugo Duminil-Copin and the American June Huh have also been awarded.

A “tremendously complex” problem

Until the discovery of the E8 network (8 dimensions) in 2016, this problem had only been solved in 2 and 3 dimensions. For example, the best way to package two-dimensional spheres, such as CDs or coins, is in a hexagonal shape – one coin in the middle and six around it forming a hexagon -, as was discovered in 1892; while the most compact way to pack spheres in three dimensions is to stack them in the shape of a pyramid, as fruit sellers do with oranges in the market, as demonstrated in 1998 by Thomas Hales, although the test was not considered valid until 2005, because he made computer use is missing. Now it seems obvious, but for years it was a real headache for the scientific community.

«The usefulness of solving these problems in any dimension ranges from crystallography to big data, and has many applications. It is very advanced mathematics. They are problems of great importance in many areas of knowledge,” says Clara Grima, professor of Mathematics at the Higher Technical School of Computer Engineering at the University of Seville and researcher in Computational Geometry in statements collected by the Science Media Center Spain.

Grima highlights the “tremendous complexity of these problems” and the “brilliant, spectacular and not within the reach of anyone’s understanding” way in which Viazovska has solved them, first alone in dimension 8, and then jointly in dimension 24. «I am very happy that they have granted it to Maryna because she is possibly one of the most brilliant mathematical minds that we have in the 21st century, and she is very young, she was born in 1984, so she has a lot left to contribute and I hope that she become—and I hope the media collaborates with it—into a great reference for the girls and boys of this world,” says Grima.

“The techniques developed by Viazovska to calculate the packing density of spheres in dimensions 8 and 24 could help solve the problem in other dimensions or advance knowledge in many other areas of science,” adds Marta Macho-Stadler, professor at the Department of Mathematics of the University of the Basque Country (UPV/EHU).

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