Computer-assisted proofs | Conjectures that have been proved | Discrete geometry | Spheres | Packing problems

Kepler conjecture

The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is around 74.05%. In 1998, Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales' proof, and the Kepler conjecture was accepted as a theorem. In 2014, the Flyspeck project team, headed by Hales, announced the completion of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assistants. In 2017, the formal proof was accepted by the journal Forum of Mathematics, Pi. (Wikipedia).

Kepler conjecture
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What is the Riemann Hypothesis?

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From playlist Mathematics

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Science Bulletins: Kepler Discovers Dozens of Worlds

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From playlist Science Bulletins

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Generalized Kepler Problems - Guowu Meng

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From playlist Mathematics

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From playlist Math

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3 - Kick-off afternoon : Thomas Hales, Formalizing the proof of the Kepler Conjecture

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From playlist T2-2014 : Semantics of proofs and certified mathematics

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The Gravity of Kepler Systems - Eric Agol

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From playlist Joint IAS/PU Astrophysics Colloquium

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From playlist Kepler's Laws

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From playlist Math

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From playlist Wolfram Technology Conference 2014

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From playlist ASTROPHYSICS 1 BINARY SYSTEMS & KEPLER'S LAWS

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From playlist Mathematics

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IMS Public Lecture: Mathematics in the Solar System

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From playlist Public Lectures

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Astrophysics: Binary Star System (14 of 40) Kepler's Law

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From playlist ASTROPHYSICS 1 BINARY SYSTEMS & KEPLER'S LAWS

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Weaire–Phelan structure | Axel Thue | Isabelle (proof assistant) | Finite set | Lattice (group) | Sphere packing | László Fejes Tóth | Theorem | Atomic theory | Circle packing | David Hilbert | Hilbert's eighteenth problem | Proof by exhaustion | Voronoi diagram | Delaunay triangulation | Dodecahedral conjecture | Mathematics | Packing density | Sphere | Gigabyte | Euclidean space | Honeycomb conjecture | HOL Light | Discrete & Computational Geometry | Ulam's packing conjecture | Claude Ambrose Rogers | Linear programming