In July 1976 a mathematical mystery that had puzzled mathematicians for more than a century was finally solved. The Four Color Theorem states that no more than four colors are needed to color the regions of any map so that no two adjacent regions share a color. Its authors, Kenneth Appel and Wolfgang Haken, credited an unconventional collaborator: a computer that did much of the heavy lifting, running for 1,200 hours and making 10 billion decisions. Computer programmer John Koch helped Appel and Haken with the algorithmic work.
Appel and Haken later said the system "began to teach us things about how to proceed that we never expected," conceding that it had "surpassed its creators" in certain intellectual tasks. The result opened a debate about whether a proof too vast for any human to check can count as mathematics. Reactions were far from universal praise. Herbert Wilf of the University of Pennsylvania said, "God wouldn't let the theorem be proved by a method as terrible as that!" Paul Halmos of UC Santa Barbara wrote that "the present proof relies in effect on an Oracle, and I say down with Oracles!"
Age appeared to shape attitudes. After a presentation by Haken's son, the audience reportedly split: "over-40s could not be convinced that a proof by computer was correct, while the under-40s could not be convinced that a proof containing 700 pages of hand calculations could be correct." Some critics went further. George Spencer-Brown of Cambridge University called the affair "the most ridiculous case of 'The King's New Clothes' that has ever disgraced the history of mathematics."
The proof did win notable endorsements. Bill Tutte, who had once doubted the computer-aided method, conceded it had solved the problem and marked the occasion with a poem. German mathematician Heinrich Heesch accepted the proof, though reluctantly, having spent four decades on the problem and developed key algorithmic methods the pair used.
Source: Hacker News · Summarized by HeadlinesBriefing