Breakthrough Tracker record
The Kakeya set conjecture in three dimensions
Every Kakeya set in R³, meaning a set containing a unit line segment in every direction, has both Hausdorff and Minkowski dimension 3.
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- Stable ID
math-kakeya-three-dimensions-2025- Revision
math-kakeya-three-dimensions-2025.v1- Field
- Mathematics · Harmonic analysis and geometric measure theory
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Current · Strongly expert-supported preprint
- Last checked
AI role
No generative-AI role was disclosed.
Record details
- Problem or result
- Three-dimensional Kakeya set conjecture
- Authors
- Hong Wang and Joshua Zahl
- Institutions
- NYU Courant and University of British Columbia at announcement
- Result date
- Preprint submitted February 24, 2025
Why it matters
The theorem resolves the three-dimensional case of a central problem linking harmonic analysis, geometric measure theory, partial differential equations and number theory.
Limits
Higher-dimensional cases remain open. No peer-reviewed publication was located for the long and technically demanding preprint.
Sources
- Primary: Hong Wang and Joshua Zahl, Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions
- Independent: Quanta, Once-in-a-Century Proof Settles Math's Kakeya Conjecture
Correction and revision history
- Added on 2026-07-22 with the result confined to three dimensions and higher dimensions explicitly left open.
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