An overview of the Kepler conjecture

TL;DR

This paper provides a historical overview and synopsis of a series of works that aim to prove the Kepler conjecture, which states that no sphere packing in three dimensions exceeds the density of face-centered cubic packing.

Contribution

It introduces a comprehensive series of papers that collectively aim to prove the Kepler conjecture, a longstanding problem in discrete geometry.

Findings

Historical context of the Kepler conjecture

Outline of the proof strategy in subsequent papers

Confirmation of the conjecture's significance in geometry

Abstract

This is the first in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this density is the face-centered cubic packing. This paper has a historical overview and a synopsis of the rest of the series. The other papers in the series are math.MG/9811072, math.MG/9811073, math.MG/9811074, math.MG/9811075, math.MG/9811076, math.MG/9811077, and math.MG/9811078.