The ProblemHow densely can identical spheres be packed in n-dimensional space? In one dimension, the problem is trivial, and in two dimensions, elementary proofs have existed for decades. In three dimensions, a solution was conjectured by Kepler in 1611, but it was not proved until Thomas Hales settled it in 1998, in a heavily computer-assisted proof that subsequently took over a decade to formally verify.
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Sales of the glasses tripled in 2025, CNBC reported, with more than 7 million units sold.