Rohan Pandey: "kakeya conjecture in R^3 has been resolved" (conflates two Kakeya problems)

Posted 22:46 UTC on 6 Oct by Rohan Pandey (Periodic Labs, formerly OpenAI research, per his X bio), quoting Andrew Curran's link to the repo, with a screenshot of family 074 from the overview: "kakeya conjecture in R^3 has been resolved (fields medal for hong wang this yr was for progress on this problem)".

Correction: the Kakeya set conjecture in R^3 (every Kakeya set there has dimension 3) was already proved by Hong Wang and Joshua Zahl in February 2025 (arXiv 2502.17655, https://arxiv.org/abs/2502.17655); our Fields Medal entry cites that proof for Wang's 2026 medal (2026-07-23-fields-medals-2026). Family 074, "Kakeya in three and four dimensions", claims two other results: the stronger Kakeya maximal conjecture in R^3 (manuscript dated 23 Sep) and the Hausdorff-dimension Kakeya conjecture in R^4 (manuscript dated 24 Sep). Neither has a Lean scope note in the repo; both are unrefereed. Jared Lichtman's thread also reads the release as four-dimensional Kakeya (2026-10-06-jdlichtman-zero-free-strip-hodge). Reach at 11:31 UTC on 7 Oct: ~96k views, 1,274 likes.

kakeya conjecture in R^3 has been resolved

(fields medal for hong wang this yr was for progress on this problem)

Quoting @AndrewCurran_: OpenAI's Math post is up! https://github.com/openai/math

Media: https://pbs.twimg.com/media/HT-2DpBbAAAsJFO.jpg?name=orig

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Archived 2026-10-07 via manual (api.fxtwitter.com, fetched 11:31 UTC).