Take an outline map of the lower 48 U.S. states and four crayons. Can you shade in the map so that every state is a different color than each of its neighbors, without resorting to a fifth color? This ...

In 1852 mathematician Francis Guthrie asked a seemingly simple question that triggered endless dispute, left a trail of overturned publications in its wake and culminated in a resolution that has ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

Imagine you're a mapmaker, ready to finish your masterpiece map of the world. The only thing left to do is add the colors. But how many colors do you need for the countries if you want to make sure no ...

Kenneth Appel, 80, who successfully brought the computer to bear on a celebrated mathematical problem that, in its capacity to perplex, tantalize and frustrate, conformed to a common view of ...