{"id":"openai-math/The-Kakeya-maximal-conjecture-in-three-dimensions","pdf":"https://github.com/openai/math/blob/main/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026","tags":["harmonic-analysis","kakeya-problem","geometric-measure-theory","maximal-functions"],"score":0,"title":"The Kakeya maximal conjecture in three dimensions","domain":"Real and complex analysis","family":"074","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove the Kakeya maximal conjecture in three dimensions. For every ε > 0, the maximal average over unit tubes of radius δ maps $`L^3(\\mathbb R^3)`$ to $`L^3(S^2)`$ with norm at most $`C_\\varepsilon\\delta^{-\\varepsilon}`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=The%20release%20announces%20the%20maximal%20conjecture%20in%20three%20dimensions","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"The release announces the maximal conjecture in three dimensions and the Hausdorff-dimension conjecture in four dimensions . Periodic tiling in dimension three. In An Aperiodic Monotile I also mentioned Greenfeld and Tao’s disproof of the periodic translational tiling conjecture. The new…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"}],"formalized":false,"family_title":"Kakeya in three and four dimensions"}