Math, Inc. Back HomeCompleting the formal proof of higher-dimensional sphere packingUsing 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.
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Months of clashes have flared up again since Thursday, when Afghanistan launched attacks along the frontier and Pakistani forces hit back on the border and from the skies. Pakistan has declared it is in “open war” with Afghanistan.