A Ukrainian mathematician who proved the best way to pack spheres in eight dimensions to take up the least space, and an Oxford expert who has solved conundrums in the spacing of prime numbers are among the winners of the Fields medal, considered the equivalent of a Nobel prize for mathematics.
The winners of the prize, presented at the International Mathematical Union awards ceremony in Helsinki, have been announced as Prof James Maynard 37, from Oxford University, Prof Maryna Viazovska, 37, of the École polytechnique fédérale de Lausanne, Hugo Duminil-Copin, 36, of the University of Geneva and Institut des Hautes Études Scientifiques, and June Huh, 39, of Princeton University.
While the first Fields medal was awarded in 1936, there was a hiatus until 1950, since when it has been presented every four years to up to four mathematicians who are under 40.
Viazovska, who was born and grew up in Kyiv, is only the second woman to receive the award, following the win by Iranian mathematician Maryam Mirzakhani who became a medalist in 2014. Mirzzakhani died of breast cancer in 2017.
Speaking after receiving the 2018 New Horizons in Mathematics prize, Viazovska, said one thing she really like about maths is that it is always clear where the truth is.
“A theorem is always either wrong or right … if you’re doing an exam in history and somebody asks you ‘so what were the reasons for the French revolution?’, how can you know which answer is wrong and which is right? So this was always very mysterious for me,” she said.
Talking to the Guardian from his hotel room in Helsinki, Maynard – who is expecting the birth of his baby imminently – said he learned of his win while up a ladder tackling house renovations.
“I was grabbing my phone to use it as a torch to help to see if I had messed the painting up or not. And I noticed that had I got a email then from the IMU president asking to have a zoom call,” he said. “When I got that email, I suspected what it might mean.”
Maynard’s citation points to his “spectacular contributions in analytic number theory” – among them his work on the distribution of prime numbers.
“Prime numbers are like the atoms for mathematicians,” said Maynard. “In the same way that you can understand an awful lot about chemicals by knowing the atoms that make them up, you can understand the huge amount about whole numbers and how they interact with multiplication – which turns out to be very important for things like cryptography – if you understand things about prime numbers.”
A key step in trying to understand prime numbers, said Maynard, is to look at the size of the gaps between them. “Unfortunately, we don’t really understand this too well, despite the fact that it’s been studied for certainly hundreds of years and possibly thousands of years,” he said.
However Maynard has made a number of breakthroughs, including showing that sometimes prime numbers come unusually close together and sometime unusually far apart.
Prof Andrew Granville, a former mentor, said that when Maynard made an early pivotal discovery in how often pairs of prime numbers occur that are two steps apart – such as three and five – Graville told the young mathematician he must have made a mistake. But Maynard had not.
“It was a real shock,” said Granville. “And the thing is, he’s not a one horse wonder … James has approached one [question] after another and just made massive headway.”
Granville also praised the work of Viazovska, who solved the problem of the densest way to pack spheres in eight dimensions and, working with others, 24 dimensions.
As Granville notes, the conundrum had its origins in Elizabethan England, when Sir Walter Raleigh wondered how to work out the number of cannonballs in a pile. This was solved by Raleigh’s assistant Thomas Harriot who then began pondering how spheres can be packed to take up the least space. The answer, according to Renaissance astronomer Johannes Kepler, was a pyramid pattern – such as that seen on an orange stand. However his conjecture was proved only proved in recent years.
Viazovska, said Granville, took the question even further, finding the solution in higher dimensions. “It turns out that in dimensions eight and 24, the solution is much easier than our common dimension, three,” Viazovska said in 2018.
Maynard told the Guardian that winning the award is a great honour, but surreal.
“It feels certainly a bit weird to imagine my name on some list of great mathematicians when, as a kid, I would read up about lots of these figures, and they would sort of motivate me,” he said. “So then to put my name on that list feels completely bizarre.”