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'Once in a Century' Proof Settles Math's Kakeya Conjecture

Source: news.ycombinator.com | By Joseph Howlett

Published on: 2025-06-14 10:21:18

Even the Kakeya set that overlaps the most has to take up some space, Fefferman found. That minimum volume depends on how thick the tubes are. Mathematicians quantify the relationship between the tubes’ thickness and the volume of the set using a number called the Minkowski dimension. The smaller the Minkowski dimension, the more you can reduce the set’s volume by thinning the tubes slightly. The three-dimensional Kakeya conjecture says that a set’s Minkowski dimension must be three. This const

Keywords: dimension kakeya minkowski set tubes

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The three-dimensional Kakeya conjecture, after Wang and Zahl

Source: news.ycombinator.com | By Terence Tao

Published on: 2025-07-06 08:53:56

There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set conjecture! This conjecture asserts that a Kakeya set – a subset of that contains a unit line segment in every direction, must have Minkowski and Hausdorff dimension equal to three. (There is also a stronger “maximal function” version of this conjecture that remains open at present, although the methods o

Keywords: case fat grains kakeya tubes

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