{"id":"openai-math/The-Mahler-Conjecture-for-General-Convex-Bodies","pdf":"https://github.com/openai/math/blob/main/preprints/The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026","tags":["convex-geometry","mahler-conjecture","volume-product","santalo-point"],"score":0,"title":"The Mahler Conjecture for General Convex Bodies","domain":"Convex and metric geometry","family":"087","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"We resolve the Mahler conjecture for general convex bodies positively. For every convex body $`K\\subset\\mathbb R^n`$, n ≥ 1, with Santaló point $`s(K)`$, $`|K|\\,|(K-s(K))^\\circ|\\ge (n+1)^{n+1}/(n!)^2`$, with equality exactly for simplices.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-22","reactions":{},"discussion":[{"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"}],"formalized":false,"family_title":"The Mahler conjectures, functional inequalities and polar-product symplectic width"}