Kenneth Appel - GoKawiil

Four Color Theorem proof by Appel and Haken sparked 1976 backlash over computer math

In July 1976, mathematicians Kenneth Appel and Wolfgang Haken, aided by programmer John Koch, proved the Four Color Theorem using roughly 1,200 hours of computer processing and 10 billion logical decisions. The achievement, the first major theorem proved with heavy reliance on a computer, drew sharp criticism from mathematicians who argued that a proof no human could fully verify by hand should not count as legitimate mathematics.

newsletter.pessimistsarchive.org · 2026-10-13

Mathematicians offer fresh proof of the Four-Color Theorem

A new mathematical proof revisits the long-standing four-color theorem, which states that any map can be colored with just four colors so no adjacent regions share one. The proof builds on the historical lineage from Alfred Kempe's flawed 19th-century attempt, later fixed conceptually through Kempe chains, and the 1976 computer-assisted proof by Kenneth Appel and Wolfgang Haken that checked thousands of configurations.

quantamagazine.org · 2026-09-10