Thomas Callister Hales

Thomas Callister Hales (born June 4, 1958) is an American mathematician. He studies topics 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 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 got his Ph.D. from Princeton University in 1986. He taught at Harvard University and the University of Chicago. From 1993 to 2002, he worked at the University of Michigan.

In 1998, Hales shared an important math discovery about the best way to pack round objects together. This is called the Kepler conjecture. He used a computer to help solve this old problem in discrete geometry. In 1999, he also solved another math guess known as the honeycomb conjecture. After 2002, he became a professor at the University of Pittsburgh.

Hales spent many years checking that his Kepler conjecture proof was correct using special computer programs. In 2017, he began a project to make math ideas easier to share and check with computers. In 2024, he and a colleague solved a new math guess. Hales retired in May of 2025.

Awards

Thomas Callister Hales spoke at the International Congress of Mathematicians in 2002. He won many important awards. These include 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. He was also invited to give the Tarski Lectures in 2019. Finally, in 2020, he received the Senior Berwick Prize from the London Mathematical Society.

Publications

Thomas C. Hales has written many important papers about mathematics. His famous works include the Kepler conjecture, which is about packing circles or spheres together as tightly as possible in space. 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 also worked with other mathematicians to create a formal proof of the Kepler conjecture using computers to check every step.