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

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

Maryna Viazovska in an image from the YouTube channel of the Institut des Hautes Études Scientifiques. / IHÉS

Science | Math

Follow in the footsteps of the Iranian Maryam Mirzakhan, who died of cancer in 2017, who received this award in 2014

Elena Martin Lopez

Ukrainian mathematician Maryna Viazovska (kyiv, 37 years old) received the 2022 Fields Medal on Tuesday, 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 as compactly as possible, that is, with the least free space between them, in 8 and 24 dimensions.

The award is granted 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 it 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 Saint Petersburg (Russia) to Helsinki (Finland) in retaliation after the invasion of Ukraine by the army of Vladimir Putin. Together with Viazovska, the British James Maynard, the French Hugo Duminil-Copin and the American June Huh have also been awarded.

An "extremely complex" problem

Until his 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 pack spheres in two dimensions, like CDs or coins, is in a hexagonal shape -one coin in the middle and six around it forming a hexagon-, as discovered in 1892; while the most compact way of packing spheres in three dimensions is to stack them in the form of a pyramid, as the greengrocers do with oranges in the market, as Thomas Hales demonstrated in 1998, although the test was not considered valid until 2005, because it did no use of computer. Now it seems obvious, but for years it was a real headache for the scientific community.

“The utility of solving these problems in any dimension ranges from crystallography to big data, and has many applications. It's very advanced math. 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 of the University of Seville and researcher of Computational Geometry in statements collected by the Science Media Center Spain.

Grima highlights the "tremendous complexity of these problems" and the way "brilliant, spectacular and not within the reach of anyone's understanding" in which Viazovska has solved them, first alone in dimension 8, and then in dimension 24 together. «I am very happy that they have awarded 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 to contribute and I hope she will become —and hopefully the media will collaborate with it—, in a great reference for girls and boys in this world”, says Grima.

"The techniques developed by Viazovska to calculate the density of the packing 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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