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A FORMAL PROOF OF THE KEPLER CONJECTURE

Part of: Discrete geometry

Published online by Cambridge University Press:  29 May 2017

THOMAS HALES ,
MARK ADAMS ,
GERTRUD BAUER ,
TAT DAT DANG ,
JOHN HARRISON ,
LE TRUONG HOANG ,
CEZARY KALISZYK ,
VICTOR MAGRON ,
SEAN MCLAUGHLIN  and
TAT THANG NGUYEN
...Show all authors
THOMAS HALES
Affiliation:
University of Pittsburgh, USA; hales@pitt.edu, nguyenquangtruong270983@gmail.com
MARK ADAMS
Affiliation:
Proof Technologies Ltd, UK Radboud University, Nijmegen, The Netherlands; mark@proof-technologies.com
GERTRUD BAUER
Affiliation:
ESG – Elektroniksystem- und Logistik-GmbH, Germany; Gertrud.Bauer@alumni.tum.de
TAT DAT DANG
Affiliation:
CanberraWeb, 5/47-49 Vicars St, Mitchell ACT 2911, Australia; dangtatdatusb@gmail.com
JOHN HARRISON
Affiliation:
Intel Corporation, USA; johnh@ecsmtp.pdx.intel.com
LE TRUONG HOANG
Affiliation:
Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam; hltruong@math.ac.vn, ntthang.math@gmail.com, tthan@math.ac.vn, tntrung@math.ac.vn
CEZARY KALISZYK
Affiliation:
University of Innsbruck, Austria; cezary.kaliszyk@uibk.ac.at
VICTOR MAGRON
Affiliation:
CNRS VERIMAG, France; magron@lix.polytechnique.fr
SEAN MCLAUGHLIN
Affiliation:
Amazon, USA; seanmcl@gmail.com
TAT THANG NGUYEN
Affiliation:
Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam; hltruong@math.ac.vn, ntthang.math@gmail.com, tthan@math.ac.vn, tntrung@math.ac.vn
QUANG TRUONG NGUYEN
Affiliation:
University of Pittsburgh, USA; hales@pitt.edu, nguyenquangtruong270983@gmail.com
TOBIAS NIPKOW
Affiliation:
Technische Universität München, Germany; nipkow@in.tum.de
STEVEN OBUA
Affiliation:
University of Edinburgh, UK; sobua@inf.ed.ac.uk
JOSEPH PLESO
Affiliation:
Philips Electronics North America Corporation – Andover, MA, USA; joe.pleso@gmail.com
JASON RUTE
Affiliation:
The Pennsylvania State University, USA; jason.rute@gmail.com
ALEXEY SOLOVYEV
Affiliation:
University of Utah, USA; solovyev.alexey@gmail.com
THI HOAI AN TA
Affiliation:
Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam; hltruong@math.ac.vn, ntthang.math@gmail.com, tthan@math.ac.vn, tntrung@math.ac.vn
NAM TRUNG TRAN
Affiliation:
Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam; hltruong@math.ac.vn, ntthang.math@gmail.com, tthan@math.ac.vn, tntrung@math.ac.vn
THI DIEP TRIEU
Affiliation:
AXA China Region Insurance Company Limited, Hong Kong; trieudiep87@gmail.com
JOSEF URBAN
Affiliation:
Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), Czech Republic; urban@cs.ru.nl
KY VU
Affiliation:
Chinese University of Hong Kong, Hong Kong; vukhacky@gmail.com
ROLAND ZUMKELLER
Affiliation:
Roland.Zumkeller@gmail.com

Abstract

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This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.

MSC classification

Primary: 52C17: Packing and covering in $n$ dimensions

Information

Type
Research Article
Information
Forum of Mathematics, Pi , Volume 5 , 2017 , e2
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2017

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