Completing the formal proof of higher-dimensional sphere packing

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Back HomeUsing Gauss, we have helped formally verify the sphere packing problem in dimensions 8 and 24 — certifying that the E8 lattice and the Leech lattice achieve the densest possible arrangements of non-overlapping spheres in their respective dimensions. These results, originally proved by Maryna Viazovska and collaborators, earned Viazovska the Fields Medal at the 2022 International Congress of Mathematicians. After successfully proving several facts about modular forms, radial Schwartz functions, and basic sphere packing theory using a previous version of Gauss, we set our sights on a more ambitious goal: completing the remainder of the project.

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