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A Revision of the Proof of the Kepler Conjecture

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The Kepler Conjecture

Abstract

The Kepler conjecture asserts that no packing of congruent balls in threedimensional 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.

Research supported by NSF grant 0804189.

The original version of this chapter was revised. An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-1-4614-1129-1_12

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Author information

Authors and Affiliations

  1. Math Department, University of Pittsburgh, Pittsburgh, PA, USA

    Thomas C. Hales

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, Hillsboro, OR, 97124, USA

    John Harrison

  3. Carnegie Mellon University, Pittsburgh, PA, USA

    Sean McLaughlin

  4. Department for Informatics, Technische Universität München, Munich, Germany

    Tobias Nipkow & Steven Obua

  5. École Polytechnique, Paris, France

    Roland Zumkeller

Authors
  1. Thomas C. Hales
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  2. John Harrison
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  3. Sean McLaughlin
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  4. Tobias Nipkow
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  5. Steven Obua
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  6. Roland Zumkeller
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Correspondence to Thomas C. Hales .

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Editors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1043, USA

    Jeffrey C. Lagarias

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Hales, T.C., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., Zumkeller, R. (2011). A Revision of the Proof of the Kepler Conjecture. In: Lagarias, J.C. (eds) The Kepler Conjecture. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1129-1_9

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