The symmetric Mahler conjecture and its equality cases
We resolve the symmetric Mahler conjecture positively, including its equality classification. Every origin-symmetric convex body in ℝ n has volume product at least $4^n/n!$, with equality exactly for invertible linear images of Hanner polytopes.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
proofs of both the symmetric and general Mahler conjectures in every dimension, including the equality cases of Hanner polytopes and simplices, respectively. Borsuk’s problem in dimension nine. The question of the smallest dimension admitting a counterexample to Borsuk’s conjecture has appeared…