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A formal proof of the Kepler conjecture. (English) Zbl 1379.52018
Kepler’s conjecture says that the density of any packing of unit balls in Euclidean three space cannot be larger than \(\pi/\sqrt{18}\), the density of the face-centered cubic packing. The complex proof of that conjecture by T. C. Hales and S. P. Ferguson, published in [Discrete Comput. Geom. 36, No. 1, 5–20 (2006; Zbl 1186.52010); ibid. 36, No. 1, 21–69 (2006; Zbl 1186.52014); ibid. 36, No. 1, 71–110 (2006; Zbl 1186.52011); ibid. 36, No. 1, 205–265 (2006; Zbl 1186.52013); ibid. 36, No. 1, 111–166 (2006; Zbl 1186.52012); ibid. 36, No. 1, 167–204 (2006; Zbl 1186.52009)], has left the referees with some degree of incertitude concerning its correctness. Therefore Hales initiated the Flyspeck project of a formal proof of Kepler’s conjecture using the HOL Light and Isabelle proof assistants. The paper under review reports on that proof.

MSC:
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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