A Revision of the Proof of the Kepler Conjecture

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. The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end wit...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 44; no. 1; pp. 1 - 34
Main Authors Hales, Thomas C., Harrison, John, McLaughlin, Sean, Nipkow, Tobias, Obua, Steven, Zumkeller, Roland
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.07.2010
Springer Nature B.V
Subjects
Combinatorics
Computational Mathematics and Numerical Analysis
Euclidean space
Geometry
Linear programming
Mathematics
Mathematics and Statistics
Spheres
Theorems
Formal proof
Interval analysis
Linear programming
Hypermap
Sphere packings
Higher order logic
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Summary: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. The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end with the publication of the proof. This article summarizes the current status of a long-term initiative to reorganize the original proof into a more transparent form and to provide a greater level of certification of the correctness of the computer code and other details of the proof. A final part of this article lists errata in the original proof of the Kepler conjecture.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-009-9148-4