2022 Fields Medals: some lovely surprises

The Fields Medals, awarded every four years, were announced in early July! France can take pride in a new triumph with Hugo Duminil-Copin. For the second time, a woman, Maryna Viazovska, has been honored. British mathematician James Maynard and American–South Korean June Huh round out this year's medalists.

For only the second time since the highest honor in mathematics was created in 1936, a woman is among the laureates. After the Iranian Maryam Mirzakhani (1977–2017), awarded the Fields Medal in 2014 and sadly deceased shortly afterward, the mathematician honored in 2022 is the Ukrainian Maryna Serhïïvna Viazovska, born in 1984. One of our compatriots is also in the spotlight, as the French probabilist Hugo Duminil-Copin (born in 1985) likewise appears on this year's list, which honors four people this time. Two other young mathematicians have the joy of sharing this prize: the British number theorist James Maynard (born in 1987) and the American–South Korean June Huh (born in 1983), who works at the crossroads of two disciplines that would seem to have nothing in common, algebraic geometry and combinatorics. All have made significant contributions to their respective fields, readily sharing news of their progress in the scientific press.

The art of stacking spheres

Our readers know that Maryna Viazovska is the champion of sphere packing (see Les Secrets des dimensions (The Secrets of Dimensions), Bibliothèque Tangente 66, pages 110 to 114, for example); sphere packing is exactly what earned her the medal. As early as 2016, the young mathematician found the most compact way to pack spheres — not oranges in dimension 3, but… in dimension 8 — using the E8 lattice, thus obtaining a packing with density π ⁴/384 (about 25%). Why stop there? In dimension 24, with the Leech lattice, Maryna Viazovska, Henry Cohn, Abhinav Kumar, Stephen David Miller, and Danylo Radchenko achieve a density of π ¹²/12! (about 0.19%).

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