The Four-Color Theorem

MathWorld says:

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color. This problem is sometimes also called Guthrie's problem after F. Guthrie, who first conjectured the theorem in 1852.

I don’t remember when or where I first learned of the four-color theorem, which likely wasn’t covered in any of my elementary school or junior high math classes.

Perhaps it was in 1977, when Appel and Haken published their (computer-generated!) proof. I recall that it made the news, in a Look what the troubledomes are up to now. Aren’t they a riot? sort of way.

Long ago – but still some years after 1977 – I was chatting with a friend, and mentioned the four-color theorem. He didn’t believe me, and spent the next little while trying to devise counter-examples. He’d bring me a piece of paper, on which he’d drawn a map & begun coloring (really, just labeling) the regions.

“Look at this”, he’d say. “It needs a fifth color.”

I’d look at it for a moment; then, “No, if you make this one red, and that one green, then you can use blue for the other one.”

(I paraphrase. It’s been thirty years. At least thirty years.)

One of the many cherished conceits I hold about myself – that may or may not be true, mind – is that I’m more inclined than most to search for underlying causes, systemic deficiences, etc., etc., when confronted with a problem. I’m just more meta than normal people.

So very often, some crisis has the cow-orkers in a lather, but all they’re really saying is, It needs a fifth color.