Thomas Callister Hales

Thomas Callister Hales (born June 4, 1958) is an American mathematician. He works in areas like representation theory, discrete geometry, and formal verification.

In representation theory, he is known for his work on the Langlands program and for helping prove an important idea called the fundamental lemma for a special group called Sp(4). Many of his ideas were used in the final proof by Ngô Bảo Châu.

In discrete geometry, Hales solved big questions about how objects can be packed together. He proved the Kepler conjecture about the best way to arrange sphere packings, as well as the honeycomb conjecture and the dodecahedral conjecture.

In 2014, he finished the Flyspeck Project. This project checked his proof of the Kepler conjecture to make sure it was correct using special computer methods. His work has helped make mathematics more exact and reliable.

Biography

Thomas Callister Hales received his Ph.D. from Princeton University in 1986 and taught at Harvard University and the University of Chicago. From 1993 to 2002, he worked at the University of Michigan.

In 1998, Hales shared a big math discovery about the best way to pack round objects together, called the Kepler conjecture. He used a computer to help prove this old problem in discrete geometry. In 1999, he also solved another math guess called the honeycomb conjecture. After 2002, he became a professor at the University of Pittsburgh. He spent many years making sure his Kepler conjecture proof was correct using special computer programs. In 2017, he started a project to make math ideas easier to share and check using computers. In 2024, he and a colleague solved a new math guess. Hales retired in May of 2025.

Awards

Thomas Callister Hales was invited to speak at the International Congress of Mathematicians in 2002. He received several important awards, including the Chauvenet Prize in 2003, the R. E. Moore Prize in 2004, a Lester R. Ford Award in 2008, and a Fulkerson Prize in 2009. In 2007, he won the first Robbins Prize from the American Mathematical Society. He became a fellow of the American Mathematical Society in 2012 and was invited to give the Tarski Lectures in 2019. In 2020, he received the Senior Berwick Prize from the London Mathematical Society.

Publications

Thomas C. Hales has written many important papers about mathematics. Some of his most famous works are about the Kepler conjecture, which is about how to pack circles or spheres together in space as tightly as possible. He also wrote about the honeycomb conjecture and the dodecahedral conjecture, which are similar problems about shapes fitting together.

Hales has shared his ideas in journals such as The Mathematical Intelligencer, Discrete and Computational Geometry, and Annals of Mathematics. He has also worked with other mathematicians to create a formal proof of the Kepler conjecture, which means he used computers to check every step of his reasoning to make sure it was correct.