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New sphere-packing record stems from an unexpected source

After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.

Klartag had broken open a central problem in the world of lattices and sphere packing after just a few months of study and a few weeks of proof writing. But in 2023, a team found a packing that didn’t rely neatly on a repeating lattice; before Klartag’s result, it was the record to beat. Klartag, for his part, hopes that his work will set off a return to the practices of Rogers’ time, when the fields of convex geometry and lattice theory were far more connected.

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