In 1852, botanist Francis Guthrie noticed something peculiar as he was coloring a map of counties in England. Despite the counties’ meandering shapes and varied configurations, four colors were all he ...

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 ...

A theorem for coloring a large class of “perfect” mathematical networks could ease the way for a long-sought general coloring proof. Four years ago, the mathematician Maria Chudnovsky faced an all-too ...