Four Color Theorem
A well-known theorem in graph theory stating that any planar map can be colored with no more than four colors such that no two adjacent regions share the same color. First proved in 1976 by Appel and Haken using exhaustive computer verification, it stands as a landmark in computer-assisted proof.
Core Facts
The proofs of the four-color theorem and Kepler's conjecture both involved computer assistance, sparking philosophical discussions about whether humans truly understand these proofs.
The computer-assisted proof of the four-color theorem was first published by Kenneth Appel and Wolfgang Haken in 1976, requiring computer verification of 1,936 irreducible configurations, and is the first important theorem proof in the history of mathematics to essentially depend on a computer
The computer-assisted proof of the four color theorem in 1976 sparked years of controversy in the mathematical community because it contained extensive exhaustive computations that could not be individually verified by hand.
Timeline (last 90 days)
Lean's mathlib library continues to accumulate formalized theorems, and the four color theorem, the Kepler conjecture and others have all been partially or fully formalized.
The computer proof of the four color theorem was once not fully accepted by some mathematicians because it was too lengthy and difficult to verify manually.
The computer-assisted proof of the four color theorem once sparked controversy and was ultimately accepted only through a combination of formal verification and human review.
The four-color theorem is the first major theorem in the history of mathematics to be verified primarily by computer.
The four color theorem was proved in 1976 by Appel and Haken by reducing the map coloring problem to computer-verified case analysis of approximately 1,936 configurations.
Several important theorems have been formalized in Lean, such as the four-color theorem and partial results of Fermat's Last Theorem
Some mathematicians believe that proofs which cannot be verified step by step by the human brain do not carry sufficient mathematical meaning.
The proofs of the four-color theorem and Kepler's conjecture both involved computer assistance, sparking philosophical discussions about whether humans truly understand these proofs.
In 2005, Georges Gonthier proved the four color theorem using Coq.
The formalization of the four color theorem was completed in 2005 by Georges Gonthier using Coq
1 more timeline events
All Facts (13)
The proofs of the four-color theorem and Kepler's conjecture both involved computer assistance, sparking philosophical discussions about whether humans truly understand these proofs.
65%VerifiedThe computer-assisted proof of the four-color theorem was first published by Kenneth Appel and Wolfgang Haken in 1976, requiring computer verification of 1,936 irreducible configurations, and is the first important theorem proof in the history of mathematics to essentially depend on a computer
65%VerifiedThe computer-assisted proof of the four color theorem in 1976 sparked years of controversy in the mathematical community because it contained extensive exhaustive computations that could not be individually verified by hand.
65%UnverifiedThe computer-assisted proof of the Four Color Theorem was completed in 1976, requiring a computer to exhaustively check 1,936 cases.
70%UnverifiedLean's mathlib library continues to accumulate formalized theorems, and the four color theorem, the Kepler conjecture and others have all been partially or fully formalized.
50%UnverifiedThe computer proof of the four color theorem was once not fully accepted by some mathematicians because it was too lengthy and difficult to verify manually.
50%UnverifiedThe computer-assisted proof of the four color theorem once sparked controversy and was ultimately accepted only through a combination of formal verification and human review.
50%UnverifiedThe four-color theorem is the first major theorem in the history of mathematics to be verified primarily by computer.
50%UnverifiedThe four color theorem was proved in 1976 by Appel and Haken by reducing the map coloring problem to computer-verified case analysis of approximately 1,936 configurations.
50%UnverifiedSeveral important theorems have been formalized in Lean, such as the four-color theorem and partial results of Fermat's Last Theorem
50%UnverifiedSome mathematicians believe that proofs which cannot be verified step by step by the human brain do not carry sufficient mathematical meaning.
50%UnverifiedIn 2005, Georges Gonthier proved the four color theorem using Coq.
50%UnverifiedThe formalization of the four color theorem was completed in 2005 by Georges Gonthier using Coq
50%