James Maynard

Fields Medal: Kyiv-born professor and Oxford scholar among winners | mathematics

A Ukrainian mathematician who proved the best way to pack spheres in eight dimensions to occupy the least space and an Oxford expert who solved mysteries in the distance of primes are among the Fields Medal winners, identified as Equivalent to a is Nobel Prize in Mathematics.

The winners of the prize, presented at the International Mathematical Union awards ceremony in Helsinki, have been announced: Prof. James Maynard, 35, from the University of Oxford, Prof. Maryna Viazovska, 37, from the École polytechnique fédérale de Lausanne, Hugo Duminil-Copin, 36, from the University of Geneva and the Institut des Hautes Études Scientifiques, and June Huh, 39, from Princeton University.

While the first Fields Medal was awarded in 1936, there was a hiatus until 1950, since when it has been awarded 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, after Iranian mathematician Maryam Mirzakhani, who became a medalist in 2014. Mirzzakhani died of breast cancer in 2017.

James Maynard
James Maynard: “For mathematicians, prime numbers are like atoms.” Photo: Ryan Cowan

Speaking to the Guardian from his hotel room in Helsinki, Maynard – who is expecting the birth of his baby imminently – said he learned of his victory as he climbed a ladder to tackle home renovations.

“I grabbed my phone to use as a flashlight to see if I messed up the painting or not. And I noticed that I had received an email from the IMU president at the time asking for a Zoom call,” he said. “When I received this email, I had an inkling of what it might mean.”

Maynard’s quote refers to his “spectacular contributions to analytic number theory” including his work on the distribution of prime numbers.

“For mathematicians, prime numbers are like atoms,” Maynard said. “Just as you can understand a lot about chemicals by knowing the atoms that make them up, you can understand a whole lot about integers and how they interact with multiplication which turns out to be very important for things like cryptography – if you know anything about prime numbers.”

Hugo Duminil Copin.
Hugo Duminil Copin. Photo: Matteo Fieni

An important step in trying to understand prime numbers, Maynard says, is to look at the size of the gaps between them. Maynard has made a number of breakthroughs, including showing that prime numbers are sometimes unusually close together and sometimes unusually far apart.

Prof Andrew Granville, a former mentor, said that when Maynard made an early crucial discovery about how often there are pairs of primes that are two steps apart – such as three and five – Graville told the young mathematician that he made a mistake must have done. But Maynard hadn’t done it.

“It was a real shock,” said Granville. “And the thing is, he’s not a one-horse wonder… James approached one [question] after another and just made great progress.”

Granville also commended the work of Viazovska, who solved the problem of closest packing of spheres in eight dimensions and in collaboration with others in 24 dimensions.

June Hm.
June Hm. Photo: Lance Murphey

As Granville notes, the puzzle originated in Elizabethan England when Sir Walter Raleigh was wondering how to calculate the number of cannonballs in a stack. This was solved by Raleigh’s assistant Thomas Harriot, who then began thinking about how bullets could be packed to take up the least amount of space. According to Renaissance astronomer Johannes Kepler, the answer was a pyramidal pattern – like that seen on an orange stand. However, his conjecture has only been proven in recent years, relying on tens of thousands of lines of computer code.

Viazovska, Granville said, took the question even further and found the solution in higher dimensions. “It turns out that the solution in dimensions eight and 24 is much simpler than in our common dimension three,” Viazovska said in 2018.

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Peter Sarnak, a professor of mathematics at Princeton and also at the Institute for Advanced Study in Princeton, welcomed Viazovska’s victory.

“Viazovska invents new and unexpected tools that allow her to overcome natural barriers that have held us back for years,” he said.

Duminil-Copin’s work, on the other hand, deals with the mathematical theory of phase transitions – such as when ice melts into liquid water – in statistical physics.

According to Plus Magazine, Huh was more interested in poetry than math at school, but became addicted to math after attending lectures by Heisuke Hironaka. In his work, Huh and his colleague Petter Brändén found a link between mathematical models to optimize situations where variables are continuously related and those where the relationships are discrete.

“It was very satisfying to find this formal bridge,” Huh told the magazine. “And what was even more pleasing to us is that with this bridge you can approach problems that were considered very technical and difficult in a very natural and easy way.”

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