Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

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**The Fields Medal is considered the Nobel Prize of mathematics. This year the International Mathematical Union chose to award it to Maryna Viazovska, who wrote her doctoral thesis at the Max Planck Institute for Mathematics with Don Zagier and received her PhD from the University of Bonn in 2013. The Ukranian mathematician is second woman to ever receive this prize.**

Maryna Viazovska is awarded the Fields Medal 2022 "for the proof that the E8 lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis." In doing so, she resolved a question that had stumped mathematicians for more than four centuries: how to pack spheres – such as oranges stacked in a pyramid – as close together as possible. It was in 1611 that Johannes Kepler posited, without proof, that the best solution for packing spheres in a three-dimensional space was in the shape of a pyramid. That hypothesis was finally proved in 1998. With the third dimension resolved, it was time for mathematicians to move on to other dimensions. “Formulating the problem in the same way complicates matters because each dimension is different, and the optimal solution depends very much on the dimension,” says Viazovska. Why did she focus on 8 and 24 dimensions? “Because these are special dimensions, and the solutions are particularly elegant.” The way spheres are packed in these particular dimensions is remarkably symmetrical, and uses the E8 and Leech lattices, respectively. More than a decade ago Henry Cohn and Noam Elkies found that these lattice patterns were close to perfection – to one billionth of a percent – but were unable develop a proof. Viazovska’s brilliant work provided the missing ingredient, demonstrating that these lattices are the densest possible packing patterns in their respective dimensions.

But Viazovska wanted to prove it, suspecting that an auxiliary function existed that could provide the right answer and match the density of the E8 and Leech lattices. In her quest for the right function, she drew on other areas of mathematics – a fact that, according to experts, makes her proof particularly elegant and original. Fueled by creativity and intuition, Viazovska turned to the focus of her dissertation: modular forms, a type of mathematical function with a high level of symmetry. After two years of work, she came up with the right function for 8 dimensions.

**Maryna Viazovska** was born in Kiev in Ukraine in 1984. She obtained her Bachelor degree in Mathematics in 2005 from Kiev National University and a Master's degree in 2007 from the University of Kaiserslautern. She was a doctoral student of Don Zagier in the MPIM graduate school from 2008-2012, working on modular forms. In 2013 she received her PhD from the University of Bonn. After a postdoctoral position at the Humboldt University in Berlin she joined the faculty of the École Polytechnique Fédérale Lausanne, where she became full professor in 2018.

Video portrait of Maryna Viazovska [3]

Official announcement of the Fields Medals 2022 by the International Mathematical Union [4]

**Photo credit:**

Matteo Fieni

**Links:**

[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/44

[2] http://www.mpim-bonn.mpg.de/sites/default/files/4.jpg

[3] https://www.youtube.com/watch?v=yAyuipqM5uQ

[4] https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2022