In geometry, sphere packing refers to the arrangement of non-overlapping spheres within a containing space. An everyday example would be how oranges may be stacked as closely and thus efficiently as possible. What appears to be a rather ordinary task, has stumped mathematicians for centuries. It was only in 1998 that it had been proven that the best solution for packing spheres in a three-dimensional space was in the shape of a pyramid. In 2022, Maryna Viazovska received the prestigious Fields Medal, often described as the Nobel Prize of Mathematics, for solving the sphere-packing problem in 8 and 24 dimensions. Viazovska, who holds the Chair of Number Theory at École Polytechnique Fédérale de Lausanne, proved that the E8 lattice provides the densest packing of identical spheres in eight dimensions. At Falling Walls, Viazovska discusses how she solved the long-standing problem in a particularly elegant way. She also provides a sense of what it was like to conduct her research in the context of the war in Ukraine.

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