Thomas Callister Hales

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Thomas Hales
Born (1958-06-04) June 4, 1958 (age 58)
San Antonio, Texas
Residence United States
Nationality American
Fields Mathematics
Institutions University of Pittsburgh[1]
University of Michigan
Alma mater Princeton University
Doctoral advisor Robert Langlands
Known for Proving Kepler conjecture
Notable awards Chauvenet Prize(2003)
David P. Robbins Prize(2007)
Fulkerson Prize(2009)

Thomas Callister Hales (born June 4, 1958) is an American mathematician working on the Langlands program. He is known in the area for having worked on the fundamental lemma, and proving a special case of it over the group Sp(4). Many of his ideas were incorporated into the final proof, due to Ngô Bảo Châu. He is also known for his proof of the Kepler conjecture on sphere packing.


He received his Ph.D. from Princeton University in 1986, his dissertation was entitled The Subregular Germ of Orbital Integrals.[2] Between 1993 and 2002 he worked at the University of Michigan.[3]

In 1998, Hales submitted his paper on the computer-aided proof of the Kepler conjecture; a centuries-old problem in discrete geometry which states that the most space-efficient way to pack spheres is in a tetrahedron shape. He was aided by graduate student Samuel Ferguson.[4] In 1999, Hales proved the honeycomb conjecture, he also stated that the conjecture may have been present in the minds of mathematicians before Marcus Terentius Varro.

After 2002, Hales became the University of Pittsburgh's Mellon Professor of mathematics. In 2003, Hales started work on Flyspeck to vindicate his proof of the Kepler conjecture. His proof relied on computer calculation to verify conjectures. The project used two proof assistants; HOL Light and Isabelle.[5][6][7][8] Annals of Mathematics accepted the proof in 2005; but was only 99% sure of the proof.[8][9] In August 2014, the Flyspeck team's software finally verified the proof to be correct.[8]

Awards and memberships[edit]

Hales won the Chauvenet Prize in 2003[10] and a Lester R. Ford Award in 2008.[11] In 2012 he became a fellow of the American Mathematical Society.[12]


  • Hales, Thomas C.; Ferguson, Samuel P. (2011), The Kepler Conjecture: The Hales-Ferguson Proof, New York: Springer, ISBN 978-1-4614-1128-4 
  • A formal proof of the Kepler conjecture, (2015) by Thomas Hales, Mark Adams, Gertrud Bauer, Dat Tat Dang, John Harrison, Truong Le Hoang, Cezary Kaliszyk, Victor Magron, Sean McLaughlin, Thang Tat Nguyen, Truong Quang Nguyen, Tobias Nipkow, Steven Obua, Joseph Pleso, Jason Rute, Alexey Solovyev, An Hoai Thi Ta, Trung Nam Tran, Diep Thi Trieu, Josef Urban, Ky Khac Vu, Roland Zumkeller[14]


External links[edit]