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Why would so many talented mathematicians forsake academia to write outrageous stories and gags for an animated TV show? After all, the contrast between the elegant abstractions of higher mathematics and the foibles of the imbecilic Homer Simpson could hardly be greater.

But perhaps the similarities are closer than it appears. Think of it this way: To write an episode of “The Simpsons,” one begins with a known set of characters — Homer, Bart, Lisa, Marge — and confronts them with a problem. The rest of the episode follows the characters through a complicated series of moves until the problem is resolved.

And while the show certainly allows for a wide range of improbable turns (Homer disappears into the third dimension, Lisa is rescued from an angry mob by Stephen Hawking), not everything is allowable: The characters must remain true to their personalities and the stories must follow their own inner logic, for a story free of the constraints of personality, logic and motivation is no story at all.

Now think of proving a geometric theorem: Once again, one has a certain set of elements — points, lines, triangles, circles — and is confronted with a problem. What is the sum of the angles of a triangle? What is the area of a polygon? The proof then consists of a series of moves that leads to a resolution of the problem.

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