# Ukrainian mathematician becomes the second female Fields Medal recipient

Ukrainian mathematician Maryna Viazovska has become the second woman ever to win the Fields medal, often referred to as the Nobel Prize for mathematics.

Viazovska is one of four recipients of the medal, each of whom was chosen by the executive committee of the International Mathematical Union. The other three recipients are Hugo Duminil-Copin (from France), June Huh (US), and James Maynard (UK).

The Fields medal is awarded every four years to at least two, and preferably four, mathematicians who’ve completed “outstanding mathematical achievement for existing work and for the promise of future achievement”.

Each recipient must be under 40 years of age.

Viazovska, who currently works at the Swiss Federal Institute of Technology in Lausanne, Switzerland, was awarded the medal for, among other things, solving the sphere packing problem in eight dimensions.

We know that a hexagonal arrangement is the most efficient way to pack circles together, and in 1998, Thomas Hales proved that the densest way to pack spheres together in three dimensions was an arrangement called “faced centred cubic lattice packing”.

Until Viazovska’s work with colleagues, no one had been able to prove sphere packing for any higher dimensions. She has also used the maths that solved this problem to make developments in Fourier analysis.

Before her win, the only woman to have won the Fields Medal in its 86-year history was Maryam Mirzakhani, who won in 2014 and died in 2017.

In an interview organised by the International Mathematical Union, Viazovska said that the first step towards solving the eight-dimensional sphere packing problem came to her on a train trip back from a conference in Bonn, Germany.

“It was summer, it was rather stuffy on the train. On the train, I thought, since nothing seems to work, let me write the problem out one more time,” said Viazovska.

“In school, they taught us that your head is full of rubbish until you write things down to put them in order. So, I am writing it out, and I get this functional equation. I look at it and I think: ‘I should be able to solve it.’ And, indeed, I solved it – it only took a couple of months.”

Viazovska also commented on the Russian invasion of her home country of Ukraine.

“I know people in Moscow, educated and well-read people, who at the same time support everything that is going on at the moment, everything that Russia does. Some of these people even go to church. Unfortunately, neither education nor profession can prevent people from turning into cannibals,” she said.

“I realise that all of this is happening 3,000 kilometres away from me – I don’t see bombs flying at me, children are safe and healthy. No one will break into my place and ‘denazify’ me.

“But I want the people in Ukraine to know that they have our support. That I feel solidarity with them and it’s not only me who feels that way.

“For me, mathematics and strong emotions are incompatible. When the war started, at first I couldn’t do anything at all.

“Now I have the sense that something must be done. I read the news about a professor from Uzhhorod University, who gives lectures by Zoom directly from the trenches. This story has inspired me a lot.”

Viazovska, who was aware of her Fields Medal win before the invasion started, wished particularly to highlight the plight of Ukrainian refugees, and the effect the war is having on Ukrainian education.

“For example, Kyiv did not suffer as much as cities in the East, but 25% of students left Kyiv University. A huge number of children from Ukraine have now left for Europe, and they have to adapt to a completely different education system in a different language. And if school education is free almost everywhere, the situation with university students is more difficult –- it is hard for them to find a place in a European university,” she said.

“I would like to thank everyone who helps refugees. Especially now, when the initial rally of support may be gradually fading away.”