Wolfgang HakenKenneth Appel at the University of Illinois in Urbana, Illinois, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color.
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."
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