The winners of the award, presented at the International Mathematical Union awards ceremony in Helsinki, were announced as Professor James Maynard 37, of the University of Oxford, Professor Maryna Viazovska, 37, of the École polytechnique fédérale de Lausanne, Hugo Duminil- Copin, 36, of the University of Geneva and the 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 then it has been presented every four years to up to four mathematicians under the age of 40. Viazovska, who was born and raised in Kyiv, is only the second woman to receive the award, following Iranian mathematician Maryam Mirzakhani’s victory 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 likes about mathematics is that it’s always clear where the truth lies. James Maynard: “Prime numbers are like atoms to mathematicians.” Photo: Ryan Cowan “A theorem is always either wrong or right… if you take a history exam and someone asks you “what were the reasons for the French revolution?”, how can you understand which answer is wrong and which is right? So that’s always been quite a mystery to me,” he said. Speaking to the Guardian from his hotel room in Helsinki, Maynard – who is currently expecting his baby – said he learned of his win while climbing a staircase to renovate the house. “I was grabbing my phone to use as a torch to see if I messed up the painting or not. And I noticed that I had received an email then from the IMU president asking me to do a zoom call,” he said. “When I received this email, I suspected what it might mean.” Maynard’s citation notes his “spectacular contributions to analytic number theory” – among them his work on the distribution of prime numbers. “Prime numbers are like atoms to mathematicians,” Maynard said. “In the same way that you can understand a lot about chemicals by knowing the atoms that make them up, you can understand a 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, Maynard said, is to look at the size of the gaps between them. “Unfortunately, we don’t really understand it very 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 discoveries, including showing that sometimes prime numbers come unusually close and sometimes unusually far. Professor Andrew Granville, a former mentor, said that when Maynard made an early critical discovery about how often pairs of prime numbers occur two steps apart – such as three and five – Graville told the young mathematician that he should he made a mistake. But Maynard wasn’t having it. “It was a real shock,” Granville said. “And the thing is, it’s not a miracle horse… James has come close to one [question] after the other and just made huge progress.” Granville also praised the work of Wiazowska, who solved the problem of the densest way to pack spheres in eight dimensions and, in collaboration with others, in 24 dimensions. Subscribe to First Edition, our free daily newsletter – every morning at 7am. BST As Granville notes, the riddle had its roots in Elizabethan England, when Sir Walter Raleigh wondered how to count the number of shells in a pile. This was solved by Raleigh’s assistant Thomas Harriot, who then began to think about how spheres could be packed to take up the least amount of space. The answer, according to Renaissance astronomer Johannes Kepler, was a pyramid design – like the one seen on an orange base. However, his guess has only been proven in recent years. Viazovska, Granville said, 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’s definitely a bit strange to imagine my name on some list of great mathematicians when, as a kid, I read about a lot of these elements and they would kind of motivate me,” he said. “So to put my name on that list is totally weird.”
