The Kakeya maximal conjecture in three dimensions
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 $C_\varepsilon\delta^{-\varepsilon}$.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
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…