78 citations · 310 across the 39 of their papers we have counts for
43 papers
The Truncated Octahedral Conjecture
Thomas Hales, Lark Song
Among three-dimensional parallelohedra of fixed volume, the Archimedean truncated octahedron uniquely minimizes surface area, affirming a conjecture of K. Bezdek from 2006. The fin…
Simple Matroids and Alfred North Whitehead's theory of dimension (1906)
Thomas Hales
We give a correspondence between simple matroids and a reconstruction of Alfred North Whitehead's theory of dimension, as developed in "On Mathematical Concepts of the Material Wor…
Packings of Smoothed Polygons
Thomas Hales, Koundinya Vajjha
This book uses optimal control theory to prove that the most unpackable centrally symmetric convex disk in the plane is a smoothed polygon. A smoothed polygon is a polygon whose co…
A review of Alfred North Whitehead's "Introduction to Mathematics"
Thomas Hales
In 1911, Alfred North Whitehead published a short book "Introduction to Mathematics" (IM) intended for students wanting an explanation of the fundamental ideas of mathematics. Whit…
The Formal Proof of the Kepler Conjecture: a critical retrospective
Thomas Hales
The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. In 1998, Sam…
Formal Proof of the Group Law for Edwards Elliptic Curves
Thomas Hales, Rodrigo Raya
This article gives an elementary computational proof of the group law for Edwards elliptic curves. The associative law is expressed as a polynomial identity over the integers that…