There is a very fun conversation going on over at twitter about people’s favorite theorems. Here are some that showed up so far:

@andy_swallow: #favoritetheorem Of course Euclid’s proof of infinitude of primes is a beautiful thing.

@sumidiot: i like the little theorems, like… khinchin’s constant exists#favoritetheorem

@divbyzero: #favoritetheorem? Gotta be Euler’s polyhedron formula: V-E+F=2

@bakhvalov: My vote goes to Banach-Tarski Theorem can it get more counterintuitive? “…doubling the ball can be accomplished with five pieces; fewer than five pieces will not suffice.” #favoritetheorem

@RobertTalbert: Fermat’s Little Theorem: a^p = 1 mod p (p prime).#favoritetheorem

Join in on the conversation and let us know what your favorite theorem is as well as find out what the favorite theorems are for Combinations and Permutations and Strongly Connected Components.

The Weierstrass approximation theorem: Any continuous function on a close interval can be uniformly approximated as well as you like by polynomials.

It’s not obvious that the theorem should be true, it has an elegant proof, and the theorem is widely applied.