## kepler98

 swMATH ID: 23625 Software Authors: Hales, Thomas C.; Ferguson, Samuel P. Description: The 1998 Proof of the Kepler Conjecture. The Kepler conjecture asserts that no packing of congruent balls in Euclidean 3-space has density greater than the familiar pyramid-shaped packing used to stack oranges at the market. This repository contains the computer code and other documentation for the 1998 proof of the Kepler Conjecture by Sam Ferguson and Tom Hales. This code is not regularly maintained, but it has been deposited at github as a historical record. Homepage: https://github.com/flyspeck/kepler98 Related Software: Flyspeck; HOL Light; Coq; Isabelle/HOL; Isabelle; HOL; Mizar; seL4; ML; Sledgehammer; Automath; Archive Formal Proofs; VAMPIRE; GitHub; LCF; Isar; RODES; E Theorem Prover; Tame Graphs; SageMath Referenced in: 195 Publications
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### Referenced by 327 Authors

 19 Hales, Thomas Callister 7 Kaliszyk, Cezary 6 Urban, Josef 5 Kallus, Yoav 5 Paulson, Lawrence Charles 4 Bezdek, Károly 4 Nipkow, Tobias 4 Obua, Steven 4 Rabe, Florian 3 Aransay, Jesús 3 Divasón, Jose 3 Fernique, Thomas 3 Hardin, Douglas P. 3 Kohlhase, Michael 3 Koutsoukou-Argyraki, Angeliki 3 Lessard, Jean-Philippe 3 Magron, Victor 3 McLaughlin, Sean 3 Stoyan, Yuriĭ Grygorovych 3 Szirmai, Jenó 3 Theil, Florian 2 Adams, Mark 2 Aspinall, David 2 Avigad, Jeremy 2 Bétermin, Laurent 2 Bogoşel, Beniamin 2 Borodachov, Sergiy V. 2 Bourne, David P. 2 Brauchart, Johann S. 2 Chen, Elizabeth R. 2 Cohn, Henry Lee 2 de Laat, David 2 Elser, Veit 2 Färber, Michael 2 Ferguson, Samuel P. 2 Flatley, Lisa C. 2 Gleixner, Ambros M. 2 Grabner, Peter J. 2 Harland, James A. 2 Hartman, Thomas E. 2 Kerber, Michael 2 Kusner, Wöden 2 Li, Wenda 2 Petrache, Mircea 2 Saff, Edward Barry 2 Schürmann, Achill 2 Solovyev, Alexey 2 Sutcliffe, Geoff 2 Théry, Laurent 2 Torquato, Salvatore 2 Vallentin, Frank 2 van den Berg, Jan Bouwe 2 Wiedijk, Freek 2 Zhao, Yufei 2 Zong, Chuanming 2 Zumkeller, Roland 1 Aarts, Emile Hubertus Leonardus 1 Afkhami-Jeddi, Nima 1 Alama, Jesse 1 Albrecht, Andreas A. 1 Allamigeon, Xavier 1 Alt, Helmut 1 Amato, Daniela A. 1 Andreanov, Alexei 1 Arthan, Rob D. 1 Babenko, Vladyslav Fedorovych 1 Bancerek, Grzegorz 1 Bannai, Eiichi 1 Bannai, Etsuko 1 Barbieri, Ettore 1 Barendregt, Hendrik Pieter 1 Barthe, Gilles 1 Bauer, Gertrud 1 Becker, David A. 1 Bédaride, Nicolas 1 Benzmüller, Christoph Ewald 1 Bertot, Yves 1 Blanchette, Jasmin Christian 1 Bondarenko, Andriy V. 1 Boya, Luis Joaquín 1 Breden, Maxime 1 Brown, Chad Edward 1 Buchin, Kevin 1 Bucur, Dorin 1 Budzyńska, Katarzyna 1 Buldt, Bernd 1 Bundy, Alan 1 Byliński, Czesław 1 Calude, Cristian S. 1 Carette, Jacques 1 Castillo, Ignacio 1 Chaplick, Steven 1 Chen, Hao 1 Chen, Xiaoyu 1 Cheong, Otfried 1 Cherlin, Gregory L. 1 Choudhary, Aruni 1 Clarke, Edmund Melson jun. 1 Colbrook, Matthew J. 1 Corneli, Joseph ...and 227 more Authors
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### Referenced in 92 Serials

 22 Discrete & Computational Geometry 16 Journal of Automated Reasoning 6 Advances in Mathematics 4 Communications in Mathematical Physics 4 Journal of Statistical Physics 4 Experimental Mathematics 3 The Mathematical Intelligencer 3 Theoretical Computer Science 3 Formal Aspects of Computing 2 Artificial Intelligence 2 Archive for Rational Mechanics and Analysis 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Proceedings of the American Mathematical Society 2 European Journal of Combinatorics 2 Journal of Complexity 2 Bulletin of the American Mathematical Society. New Series 2 Mathematical Programming. Series A. Series B 2 Annals of Mathematics and Artificial Intelligence 2 International Transactions in Operational Research 2 Journal of High Energy Physics 2 Journal of Statistical Mechanics: Theory and Experiment 2 Journal of Formalized Reasoning 1 Discrete Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Reports 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Mathematics of Computation 1 Beiträge zur Algebra und Geometrie 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 BIT 1 Duke Mathematical Journal 1 International Journal for Numerical Methods in Engineering 1 Journal of Computational and Applied Mathematics 1 Journal of Geometry 1 Journal of Mathematical Economics 1 Journal of Pure and Applied Algebra 1 Mathematische Zeitschrift 1 SIAM Journal on Computing 1 Acta Mathematica Hungarica 1 Computer Aided Geometric Design 1 Physica D 1 Journal of Symbolic Computation 1 Constructive Approximation 1 Information and Computation 1 Facta Universitatis. Series Mathematics and Informatics 1 Computational Mechanics 1 Journal of the American Mathematical Society 1 SIAM Journal on Matrix Analysis and Applications 1 AI Communications 1 Computational Mathematics and Modeling 1 Annals of Operations Research 1 The Annals of Applied Probability 1 Differential Geometry and its Applications 1 Journal of Global Optimization 1 Elemente der Mathematik 1 SIAM Review 1 Notices of the American Mathematical Society 1 Chinese Science Bulletin 1 Journal of Nonlinear Science 1 Journal de Théorie des Nombres de Bordeaux 1 Journal of Functional Programming 1 INFORMS Journal on Computing 1 Geometry & Topology 1 Data Mining and Knowledge Discovery 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Erkenntnis 1 Journal of Mathematical Logic 1 Annales Mathematicae Silesianae 1 Logic and Logical Philosophy 1 Sādhanā 1 JP Journal of Algebra, Number Theory and Applications 1 Computational Biology and Chemistry 1 Mediterranean Journal of Mathematics 1 Discrete Optimization 1 Mathematics in Computer Science 1 Logica Universalis 1 Optimization Letters 1 Journal of Physics A: Mathematical and Theoretical 1 Journal of Topology and Analysis 1 Symmetry 1 Analysis and Mathematical Physics 1 S$$\vec{\text{e}}$$MA Journal 1 Forum of Mathematics, Pi 1 Forum of Mathematics, Sigma 1 Journal of Computational Dynamics 1 Research in the Mathematical Sciences 1 Journal of Logical and Algebraic Methods in Programming 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Referenced in 41 Fields

 74 Convex and discrete geometry (52-XX) 73 Computer science (68-XX) 23 Number theory (11-XX) 23 Operations research, mathematical programming (90-XX) 22 Mathematical logic and foundations (03-XX) 18 Numerical analysis (65-XX) 17 Combinatorics (05-XX) 15 Statistical mechanics, structure of matter (82-XX) 9 General and overarching topics; collections (00-XX) 7 Probability theory and stochastic processes (60-XX) 5 History and biography (01-XX) 5 Algebraic geometry (14-XX) 5 Partial differential equations (35-XX) 5 Geometry (51-XX) 5 Mechanics of deformable solids (74-XX) 5 Quantum theory (81-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Approximations and expansions (41-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 3 Algebraic topology (55-XX) 3 Statistics (62-XX) 3 Fluid mechanics (76-XX) 2 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Manifolds and cell complexes (57-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)