Thomas Callister Hales
Encyclopedia
Thomas Callister Hales is an American
mathematician
. He is known for his 1998 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 pyramid shape. Hales also proved the honeycomb conjecture
.
, and now University of Pittsburgh
Mellon Professor of mathematics
, advocates the formalization of mathematics to ensure rigor in an era where proofs are becoming increasingly complex and computers are becoming necessary to perform verification. Hales's current project, called Flyspeck, seeks to formalize his proof of the Kepler conjecture in the computer theorem prover HOL Light.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is known for his 1998 computer-aided proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
of the Kepler conjecture
Kepler conjecture
The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...
, a centuries-old problem in discrete geometry
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,...
which states that the most space-efficient way to pack spheres
Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space...
is in a pyramid shape. Hales also proved the honeycomb conjecture
Honeycomb conjecture
The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter....
.
Career in mathematics
Hales, formerly at the University of MichiganUniversity of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, and now University of Pittsburgh
University of Pittsburgh
The University of Pittsburgh, commonly referred to as Pitt, is a state-related research university located in Pittsburgh, Pennsylvania, United States. Founded as Pittsburgh Academy in 1787 on what was then the American frontier, Pitt is one of the oldest continuously chartered institutions of...
Mellon Professor of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, advocates the formalization of mathematics to ensure rigor in an era where proofs are becoming increasingly complex and computers are becoming necessary to perform verification. Hales's current project, called Flyspeck, seeks to formalize his proof of the Kepler conjecture in the computer theorem prover HOL Light.