Question:
I heard that a computer has solved the famous four-color problem. I was
wondering if someone could tell me why this is so. (The four-color problem
is having to use four colors on a map so that no two colors that are the
same are next to each other). I realize that for the two to be neighbors
they must share infinitely many boundary points, but am still confused as to
why this is true. Could someone tell me why you need four colors in either
non mathematical or mathematical terms please.

Replies:
A few years ago two mathematicians at the University of Illinois created a
proof that any map can be colored with four colors (or fewer). The proof is
VERY long and is a challenge to understand. It proceeds by first reducing
the infinitely many possible maps to a finite number of special cases (still
a lot of cases) and then, wit assistance of a computer, checking all of
these cases. There was an article describing the method of proof in the
Scientific American a few years ago. That would be a good place to start in
studying the proof.

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