Thomas C. Hales is an American mathematician renowned for his contributions to discrete geometry, representation theory, and formal verification. Born on June 4, 1958, Hales is best known for proving the Kepler Conjecture, a centuries-old problem in mathematics concerning the most efficient way to pack spheres in a given space.
Kepler Conjecture:
The Kepler Conjecture, proposed by Johannes Kepler in 1611, posits that no arrangement of equally sized spheres filling space has a greater average density than that of the face-centered cubic packing or hexagonal close packing. This problem remained unsolved for nearly 400 years. In 1998, Hales announced a proof of the conjecture. Due to the complexity of the proofâwhich combined traditional mathematical techniques with extensive computer verificationâit underwent a rigorous and lengthy peer review process.
To address any remaining uncertainties, Hales initiated the Flyspeck Project (Formal Proof of Kepler), aiming to create a fully formalized and computer-verified proof of the Kepler Conjecture. In 2014, the project was successfully completed, providing a definitive verification and serving as a significant milestone in the field of formal methods and proof verification.
Honeycomb Conjecture:
In addition to his work on sphere packing, Hales also proved the Honeycomb Conjecture in 1999. This conjecture states that a regular hexagonal grid (like that seen in honeycomb structures) is the most efficient way to partition a surface into regions of equal area with the least total perimeter.
Academic Position and Contributions:
As a professor at the University of Pittsburgh, Hales continues to advance the fields of mathematics and computer science. His work emphasizes the importance of formal verification in mathematics, advocating for the use of computer-assisted proofs to enhance the rigor and reliability of mathematical results. He has published numerous papers and continues to contribute to research on representation theory and other areas of mathematics.
Hales's contributions have had a profound impact on mathematics, not only by resolving longstanding conjectures but also by pioneering methods that bridge traditional mathematics and computer science.
| Coauthor | Papers Together |
|---|---|
| Sean McLaughlin | 7 |
| Tobias Nipkow | 6 |
| Julia Gordon | 6 |
| Steven Obua | 6 |
| Roland Zumkeller | 6 |
| John Harrison | 5 |
| Josef Urban | 3 |
| Rodrigo Raya | 3 |
| Jason Rute | 3 |
| Alexey Solovyev | 3 |
| Clifton Cunningham | 3 |
| Victor Magron | 3 |
| Hoang Le Truong | 3 |
| Gertrud Bauer | 3 |
| Samuel P. Ferguson | 3 |
| Ky Vu | 3 |
| W. Casselman | 3 |
| Jorge E. Cely | 3 |
| Cezary Kaliszyk | 3 |
| Joseph Pleso | 3 |
| Jeremy Avigad | 2 |
| Trung Nam Tran | 2 |
| Truong Quang Nguyen | 2 |
| An Hoai Thi Ta | 2 |
| Dat Tat Dang | 2 |
| Vladimir Voevodsky | 2 |
| Mark Adams | 2 |
| Diep Thi Trieu | 2 |
| Anthony Bordg | 1 |
| Joachim Koch | 1 |
| Yves Bertot | 1 |
| Pieter Hofstra | 1 |
| Robert Harper | 1 |
| Daniel R. Grayson | 1 |
| Michael Nahas | 1 |
| François Loeser | 1 |
| Mark Raymond Adams | 1 |
| Daniel R. Licata | 1 |
| S. McLaughlin | 1 |
| Emily Riehl | 1 |
| Peter Aczel | 1 |
| MartıÌn Hötzel EscardĂł | 1 |
| Peter LeFanu Lumsdaine | 1 |
| Marc Bezem | 1 |
| Peter Dybjer | 1 |
| Alexey Solovyev | 1 |
| Nicola Gambino | 1 |
| Thorsten Altenkirch | 1 |
| Steve Awodey | 1 |
| Eric Finster | 1 |