Last week, the International Mathematical Union announced the winners of the 2022 Fields Medal. The most prized award in the world of mathematics, the medal is awarded every four years to four mathematicians aged no more than 40 with outstanding contributions to the discipline.
In 2018, the announcement was made in Brazil, during the International Congress of Mathematicians in Rio de Janeiro. Four years earlier, the Brazilian Artur Avila, a researcher at Impa (Institute of Pure and Applied Mathematics), was among the laureates in South Korea.
This year’s situation is unusual. The 2022 ICM was supposed to take place in Saint Petersburg, Russia, but the Ukraine war prompted the International Mathematical Union to hold the congress online, for the first time in history, and the awards were transferred to Helsinki, Finland.
Still, the announcement of the winners caused a sensation, in part because of the presence on the list of a woman: the Ukrainian Maryna Viazovska, from the Federal Polytechnic School of Lausanne, is only the second woman to be awarded the Fields Medal. The first, in 2014, was the Iranian Maryam Mirzakhani (1977-2017). Viazovska is accompanied by Frenchman Hugo Duminil-Copin, from the Institute for Advanced Scientific Studies (IHES) in Paris; the British James Maynard, from the University of Oxford; and the South Korean June Huh, from Princeton University.
Viazovska’s main work deals with the problem of ball packing, raised more than 400 years ago by a practical question of the British navy, on the way to world hegemony: how to store cannonballs so that as many as possible fit in the basement of each ship?
The problem came to the German astronomer Johannes Kepler (1571 – 1630), who published it in a work published in 1611: how to place identical spheres in a large container, in such a way that as many spheres as possible can fit?
There is a 2-dimensional version of this problem, considering disks in the plane instead of spheres in space. This one was solved (empirically, of course) millions of years ago by bees in the construction of their combs. Viasovska is notable in the opposite direction: she solved the problem of packing spheres in dimensions 8 and 24. I will comment more next week.
