The Four-Color Theorem Gets a Rare New Proof
Some math problems continue to haunt researchers long after they’ve been solved. A proof emerges, is even celebrated, and yet dissatisfaction lingers. Perhaps the argument is too convoluted — the hunt persists for the elusive one-page paper — or perhaps it fails to give a deeper theoretical insight into why something is true. Whatever the reason, mathematicians return, again and again… Source
Some math problems continue to haunt researchers long after they’ve been solved. A proof emerges, is even celebrated, and yet dissatisfaction lingers. Perhaps the argument is too convoluted — the hunt persists for the elusive one-page paper — or perhaps it fails to give a deeper theoretical insight into why something is true. Whatever the reason, mathematicians return, again and again…
Source
The four-color theorem is simple to state: Given a contiguous map, is it possible to color each region with one of four colors such that no neighboring regions share a color?
One of the most famous such cases is that of the four-color theorem, a problem that transformed how mathematicians think about their subject.
The first purported proof , announced in 1879, stood for 11 years before it was proved incorrect. More wrong answers would follow, from lawyers and doctors and famous graph theorists, too. “Here we have a problem that even a child can understand,” said Carsten Thomassen , a graph theorist at the Technical University of Denmark. “I think that’s the reason why it has been such a big challenge.”
The theorem was finally proved nearly a century later — but with computer methods that were considered scandalous at the time, causing mathematicians to question what they considered a proof in the first place. The status of the problem remained a source of debate until 1997, when the use of computers became more common and a simpler computer-assisted proof was found.
