Theorems
Kepler Conjecture
KEP-ler
Also Known As Sphere-Packing Problem
Geometry
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First stated by Johannes Kepler in 1611 while investigating why snowflakes are six cornered, the conjecture concerns the most efficient way to stack identical spheres, the everyday problem of how a greengrocer stacks oranges. It stood unproved for nearly four centuries and was finally settled by a proof that was itself controversial for how it was produced: by exhaustive computer calculation rather than by hand.
Facts
StatementNo arrangement of equally sized spheres filling space has a greater average density than the cubic close packing and hexagonal close packing arrangements, both of which fill about seventy four percent of space. 1 Cross-Tradition Connections
In Branch
Posed By
Kepler first stated the conjecture in 1611; it was proved by Thomas Hales in 1998.
Proved By
Hales announced a proof in 1998; the Flyspeck project completed a formal machine-verified proof in 2014, accepted for publication in 2017.
Sources
1. Kepler Conjecture (Wikipedia)
Wikimedia FoundationBackground sectionQuote, Background section
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.
1. Kepler Conjecture (Wikipedia)
Wikimedia FoundationOrigins sectionQuote, Origins section
The conjecture was first stated by Johannes Kepler (1611) in his paper 'On the six-cornered snowflake'.
1. Kepler Conjecture (Wikipedia)
Wikimedia Foundationmain article body, Hales's proofQuote, main article body, Hales's proof
In 1998, the American mathematician Thomas Hales...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.
1. Kepler Conjecture (Wikipedia)
Wikimedia FoundationA formal proof subsectionQuote, A formal proof subsection
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.
1. Kepler Conjecture (Wikipedia)
1. Kepler Conjecture (Wikipedia)
Wikimedia FoundationProved By: Thomas Hales, Hales' proof sectionQuote, Proved By: Thomas Hales, Hales' proof section
In 1998, the American mathematician Thomas Hales, following an approach suggested by Fejes Toth (1953), announced that he had a proof of the Kepler conjecture.
1. Kepler Conjecture (Wikipedia)
Wikimedia FoundationIn Branch: Discrete Geometry, IntroductionQuote, In Branch: Discrete Geometry, Introduction
is a mathematical theorem about sphere packing in three-dimensional Euclidean space.
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