Mathematicians prove decades-old Kakeya Conjecture in major breakthrough

21/07/2025

Hong Wang and Joshua Zahl have solved the three-dimensional Kakeya conjecture, a fundamental problem in geometry that has been open for many decades. The conjecture asks whether the space used to rotate a needle in all directions necessarily has full Hausdorff dimension. Their proof has settled this question positively in dimension three and confirmed deep ties to harmonic analysis.

First posed almost a century ago, the problem rapidly gained prominence through its linkage to other areas of mathematics. Experts hail the work as transformative, potentially unlocking progress on higher-dimensional versions and related open problems. “It’s a once-in-a-century result,” said Nets Katz of Rice University.