I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! https://arxiv.org/abs/2502.17655 I discuss some ideas of the proof at https://terrytao.wordpress.com/2025/02/25/the-three-dimensional-kakeya-conjecture-after-wang-and-zahl/
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