A Once-in-a-Century Proof: The Kakeya Conjecture

By Quanta Magazine

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A simple question about a spinning needle has haunted mathematicians for more than a century. It led to the Kakeya conjecture, a cornerstone of modern analysis connecting geometry, fractals, and the behavior of waves. Now, mathematicians Hong Wang and Joshua Zahl have cracked the 3D case — a once-in-a-generation breakthrough that could reshape how we understand the Fourier transform. (Also featuring Terence Tao and Jonathan Hickman.) Read more at Quanta Magazine: https://www.quantamagazine.org/once-in-a-century-proof-settles-maths-kakeya-conjecture-20250314/ Please note two corrections to this video: - At 4:00 and 4:12, some of the Hausdorff dimension boxes appear rectangular. They should all be squares. - At 4:43, the proof described should be attributed to Antonio Cordoba rather than Roy Davies, who used a slightly different argument. --------- Quanta Magazine is an editorially independent publication supported by the Simons Foundation. We focus on developments in mathematics, the

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