This one is as easy to state as it is hard to prove.
Grab any map and four crayons. It’s possible to color each state (or country) on the map, following one rule: No states that share a border get the same color.
The fact that any map can be colored with five colors—the Five Color Theorem—was proven in the 19th century. But getting that down to four took until 1976.
Two mathematicians at the University of Illinois, Urbana-Champaign, Kenneth Appel and Wolfgang Hakan, found a way to reduce the proof to a large, finite number of cases. With computer assistance, they exhaustively checked the nearly 2,000 cases, and ended up with an unprecedented style of proof.
Arguably controversial since it was partially conceived in the mind of a machine, Appel and Hakan’s proof was eventually accepted by most mathematicians. It has since become far more common for proofs to have computer-verified parts, but Appel and Hakan blazed the trail.
Πηγή: popularmechanics
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