Hong Wang Solves Kakeya Set Conjecture

March 6, 2025

Hong Wang, Associate Professor of Mathematics, appears to have solved the infamous Kakeya set conjecture. First introduced by Sōichi Kakeya in 1917, it revolves around the question of the smallest possible area required to rotate an infinitely thin needle in every possible direction. Professor Wang presents a novel solution to the geometry problem in a new paper co-written with the University of British Columbia's Joshua Zahl: "Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions." This research has far-reaching implications, particularly in geometric measure theory and homogeneous dynamics. Professor Wang's paper is still in the peer-review process, but experts are excited by the work's potential. "The latest work follows years of progress that has enhanced our understanding of a complicated geometry and brings it to a new level," says Professor Guido De Philippis, "I am expecting that these ideas will lead to a series of exciting breakthroughs in the coming years!"