{"id":"openai-math/The-symmetric-Mahler-conjecture-and-its-equality-cases","pdf":"https://github.com/openai/math/blob/main/preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026","tags":["convex-geometry","functional-analysis","mahler-conjecture"],"score":0,"title":"The symmetric Mahler conjecture and its equality cases","domain":"Convex and metric geometry","family":"087","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-09-22","reactions":{},"discussion":[{"url":"https://rotemassouline.github.io/symmetric-mahler/#:~:text=The%20following%20note%20is%20based%20on%20ongoing%20conversations","kind":"web","site":"rotemassouline.github.io","text":"The following note is based on ongoing conversations between me and Claude about OpenAI's recent claimed proof of the symmetric Mahler conjecture . While the main ideas are taken from the original proof, some of the details are being rewritten to facilitate my understanding, and some figures and…","added":"2026-11-03","title":"Notes on OpenAI's proof of the symmetric Mahler conjecture","author":"Rotem Assouline"},{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=proofs%20of%20both%20the%20symmetric%20and%20general%20Mahler%20conjectures%20in%20every%20dimension","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"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…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans","author":"Gil Kalai"}],"formalized":true,"family_title":"The Mahler conjectures, functional inequalities and polar-product symplectic width"}