University of Pittsburgh
November 7, 2012

Pitt Mathematician Honored for Solving 400-Year Mathematical Mystery

Thomas C. Hales has been selected by the American Mathematical Society as an inaugural Fellow and will have his new book on his mathematical solution published later this month by Cambridge University Press
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PITTSBURGH—University of Pittsburgh Andrew W. Mellon Professor of Mathematics Thomas C. Hales is the world’s only mathematician to crack the 400-year-old mystery of the Kepler conjecture—a theory proposing that a pyramid formation is the most efficient way to stack spheres. Even the 17th-century German astronomer Johannes Kepler couldn’t prove his own idea when he published it in 1611.

For this achievement, Hales has been selected to join the inaugural class of the American Mathematical Society (AMS) Fellows Program in 2013—an honor that recognizes scholars who have contributed to the understanding of deep and important mathematical questions. The AMS is the world’s largest and most influential society dedicated to mathematical research, scholarship, and education.

Hales announced his breakthrough on the Kepler conjecture in 1998 and has spent most of the last decade engaged with the Flyspeck Project, a computer software program verifying every single line of his Kepler proof. Such meticulous examination stems from reviewers’ uncertainty regarding Hales’ proof, noting they could only be 99 percent certain. This decade-long “proving of the proof” has resulted in an up-and-coming book, Dense Sphere Packings: A Blueprint for Formal Proofs, written by Hales and slated to be published later this month by Cambridge University Press.

“My book examines every logical inference of the Kepler conjecture proof by computer and is an indispensable resource for those who want to get up to date with research on the proof,” said Hales. “I am presenting, for the first time, a new proof of the conjecture in a very accessible way to a broad mathematical audience.”

Hales joined Pitt in 2001 as Andrew W. Mellon Professor of Mathematics. He has held postdoctoral and faculty appointments at the Mathematical Sciences Research Institute, Harvard University, the University of Chicago, the Institute for Advanced Study, and the University of Michigan. He received B.S. and M.S. degrees from Stanford University, a Master of Advanced Study in Part III of the Mathematical Tripos curriculum from Cambridge University, and a PhD from Princeton University in representation theory. 

For more information on Hales’ Flyspeck project, visit

The American Mathematical Society was founded in 1888 to further the interests of mathematical research and scholarship and serves the national and international community through its publications, meetings, advocacy, and other programs. The society promotes mathematical research, encourages and promotes the transmission of mathematical understanding and skills, supports mathematical education at all levels, advances the status of the profession, and fosters an awareness and appreciation of mathematics and its connections to other disciplines and everyday life. 




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