Maryna Viazovska is a professor at the Swiss Federal Institute of Technology in Lausanne. She is the first woman to win the Fields medal.
Sixty mathematicians won Fields medals before this year. Until now, the only woman to receive one was a mathematician from the University of California, Berkeley.
Dr. Viazovska is the second woman. Why is that happening? I'm not sure. I hope it won't stay the same.
The work of Dr. Viazovska is similar to the work of Johannes Kepler. The stacking of cannonballs was considered the densest way that they could arrange, filling up just over 75% of the available space.
There was no proof that the statement was true. Thomas Hales succeeded in 1998 with a 250-page proof and the help of a computer program.
It has been difficult to prove that the packing of equal-size spheres in dimensions greater than three is similar.
The answer was found in eight dimensions, and it was shown that the E8 was the best packing structure. She and four other mathematicians showed that the Leech lattice was the best packing in 24 dimensions. The Leech lattice of spheres occupies about 0.2 percent of the volume in high dimensions.
There are eight and 24 dimensions.
Dr. Viazovska thinks that's a mystery. There are things that happen in these dimensions that don't happen in other dimensions.
She said that a method that gives an upper bound on the packing density is the solution in these cases.
High-dimensional sphere packings are related to error-correcting techniques.
The Russian invasion of Ukraine took a toll on her family. She said it was very hard.
Her sisters, nephew and niece left to join her in Switzerland.
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