Historical overview of the Kepler conjecture
The Kepler conjecture, of 1611, states that the densest packing of unit balls in three space is attained by the standard `cannonball packing', the densest lattice packing. Thomas C. Hales completed his computer assisted proof of this conjecture in 1998. A revised version of his proof was published in parts. The strategy and structure of the proof are described on 120 pages in [Ann. Math. (2) 162, No. 3, 1065--1185 (2005; Zbl 1096.52010)]; details appear in a series of six papers in volume 36 of Discrete and Computational Geometry. The present paper is the first of this series. Although the whole proof, with its more than 5000 subproblems solved by computer calculations, has probably not been checked completely by others (some of the history is reported in \textit{Frank Morgan}'s review of Szpiro's book on the Kepler conjecture in Notices Amer. Math. Soc. 52, No. 1, 44--47 (2005)), it appears that the proof is now generally accepted by the experts. This initial paper of the series is historical. In its first part, it describes the face-centered cubic packing, the early history of Kepler's problem and related questions, the literature on upper bounds for the density, and suggested proof strategies for the Kepler conjecture, in particular the one by L. Fejes Tóth of 1953. In the second part, the author describes briefly his own strategy, its development and the changes it has undergone, the contents of his earlier relevant papers, and the role of computer verifications and calculations in the work.
scientific article; zbMATH DE number 5614951
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