---
title: "Thomas C. Hales"
type: "entity"
entity_kind: "person"
status: "hub"
canonical_name: "Thomas C. Hales"
aliases: []
first_seen: "2026-10-28T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["honeycomb conjecture","hexagonal tiling / plane-tiling optimality","Kepler conjecture","computer-assisted proof","Hexels"]
seek_code_commit: "d40ee39"
---


American mathematician who proved the honeycomb conjecture — that a regular hexagonal grid is the plane-tiling pattern of least total perimeter enclosing equal-area cells, settling a problem traceable to antiquity — published as "The Honeycomb Conjecture" (*Discrete & Computational Geometry* 25:1–22, 2001). He is also known for a computer-assisted proof of the Kepler conjecture on optimal sphere packing, later formally verified by the Flyspeck project.

Matters to this vault as the cited mathematical authority behind a 2026 computer-graphics paper's design choice: Honeycomb-Surfels/Hexels (Kaushik, Paul & Yuille, arXiv:2610.37668) grounds its decision to use a hexagonal, rather than square or triangular, rendering primitive directly in Hales's 2001 theorem, and derives (in an appendix this vault has not yet read directly) a specific area-coverage advantage from it.

## References
- [[claim-hexels-replace-gaussian-kernel-with-hexagonal-support-and-linear-color-field-in-2dgs]]