The proof is one of the most controversial of modern mathematics because of its heavy dependence on computer "number-crunching" to sort through possibilities. Even Appel has agreed, in numerous interviews, that it lacks elegance and provided no new insight that has guided future mathematical research.

Others, however, have pointed to this work as the start of a sea-change in mathematicians' attitudes toward computers - which they had largely disdained as a tool for engineers rather than for theoreticians - leading to the creation of what is sometimes called "experimental mathematics."

From 1993 through 2003, Appel was head of the mathematics department at the University of New Hampshire in Durham, New Hampshire.

Appel's implementation of highly optimised code solving the N-body problem by numerical integration was celebrated by Jon Bentley in his book *Programming Pearls*.

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