> His result has also revived a debate in the field about the nature of the optimal packing in arbitrarily high dimensions. For a while, mathematicians considered highly symmetric, lattice-based packings to be the best way to arrange spheres as densely as possible. 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. Some mathematicians saw it as evidence that more disorder was needed in the search for an optimal sphere packing.
Clearly, this improvement doesn't apply to the few dimensions for which we already proven optimal packing, but the proof was general.