Mathematician Kenneth Appel dies at 80

Mathematician Kenneth I. Appel used an I.B.M. computer in 1976 to prove a century-old problem concerning colors on a map, and from there computers were used to provide proofs for higher and higher math.

Appel died of esophageal cancer in Dover, New Hampshire at age 80. “Like a landmark Supreme Court case, the proof’s legacy is still felt and hotly debated,” Edward Frenkel, a mathematician at the University of California, Berkeley told The New York Times.

In 1852, English mapmaker Francis Guthrie asserted that to create a map in which no adjacent countries are the same color, only four colors are needed.

The so-called four-color theorem went unproved until Dr. Appel and colleague Wolfgang Haken used a computer that took up a whole room to make 10 billion logical decisions over the course of 1,200 hours.

Appel and Haken showed that the set of all possible maps must contain an “unavoidable set” of 1,936 different configurations. They then used an I.B.M. 370-168 computer to prove that each configuration could be rendered in just four colors so that no two adjacent land areas shared a color.

Considered "a major intellectual feat," the proof began a debate on how humans can actually double check a proof they can't see, citing possible computer bugs or malfunctions.

Despite traditionalist concerns, Appel's son Andrew told The Times his father never apologized for using a computer. He said that Appel used to say, "Without computers, we would be stuck only proving theorems that have short proofs."