trailThe three-dimensional Kakeya conjecture has been proved: every three-dimensional Kakeya set has dimension three.
The Wang–Zahl proof of the three-dimensional Kakeya conjecture can be adapted to prove the conjecture in higher dimensions.
The proof of the three-dimensional Kakeya conjecture is a once-in-a-century mathematical result.
The jump from two to three dimensions is the hardest step in resolving the Kakeya conjecture in all dimensions.
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Hong Wang and Joshua Zahl posted an arXiv preprint in February 2025 claiming a proof of the three-dimensional Kakeya set conjecture.
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The mathematical community accepts the Wang–Zahl proof of the three-dimensional Kakeya conjecture as correct.
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The three-dimensional Kakeya conjecture has been proved: every three-dimensional Kakeya set has dimension three.
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