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Full Idea
The celebrity of the famous proof in 1976 of the four-colour theorem of maps is that a computer played an essential role in the proof.
Clarification
What is the minimum number of colours needed for a good map?
Gist of Idea
Computers played an essential role in proving the four-colour theorem of maps
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch.10)
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.154
A Reaction
The problem concerns the reliability of the computers, but then all the people who check a traditional proof might also be unreliable. Quis custodet custodies?
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| 10885 | Computer proofs don't provide explanations [Horsten] |