Francis Guthrie, a 21-year-old mathematics student at University College in London, was mapping the counties of England in 1852 when he noticed that he only needed four colors for the map. He asked his younger brother, Frederick Guthrie, if this was true for any map. Frederick took the problem to his professor, Augustus de Morgan.
In 1878 Arthur Cayley presented this problem to the London Mathematical Society. He and various others tried to prove it over the next century. In 1976 Wolfgang Haker and Kenneth Appel of the Univeristy of Illinois proved the theorem using a computer. It took them four years to write the computer program for the Cray computer, which took 1200 hours to check 1476 configurations.
Some mathematicians are troubled
by the proof by computer. They feel that a theorem so easy to understand
should be able to be proved by hand. Anyone who can prove the theorem
without the computer may win the Fields Medal, the math equivalent of
the Nobel Peace Prize.