When 10 billion computer decisions solved the Four Color Theorem and outraged mathematicians in 1976
tdhopper · x · 2026-10-13
A look back at the first time machines beat mathematicians: in 1976, Appel and Haken announced a computer-assisted proof of the Four Color Theorem, using 1,200 hours of compute and roughly 10 billion machine decisions. The math community revolted:
- Herbert Wilf: "God wouldn't let the theorem be proved by a method as terrible as that!"
- Paul Halmos: "the present proof relies in effect on an Oracle, and I say down with Oracles!"
- Frank Bonsall: a solution via computer verification of special cases "does not belong to mathematical science at all"
- George Spencer-Brown called it the most ridiculous case of 'The King's New Clothes' in math history
One department head even barred Appel and Haken from meeting his graduate students. The authors later admitted the system "began to teach us things about how to proceed that we never expected" and had "surpassed its creators" — an eerie parallel to today's debates over AI-assisted proofs.
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