Science: Eureka!

Toiling in an arcane area that totally baffles most ordinary mortals, mathematicians usually despair of even trying to explain their work to laymen. Yet recently two University of Illinois mathematicians announced a breakthrough of such widespread interest that even the reticent American Mathematical Society issued a rare press release. The news: after more than a century of futile brain racking, one of mathematics' most famous teasers—the so-called four-color conjecture—has finally been proved.

First stated in 1853 by a London graduate student named Francis Guthrie, the conjecture is simple. It says that no more...

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