There are many (well, at least a few) songs out there that involve mathematical topics and themes. At some point I thought about it, and I realized that (as far as I knew), there were no songs that incorporated actual proofs of mathematical theorems. So I wrote a silly little song titled "Q.E.D." in an attempt to fill this gap (and to grab a share of this surely lucrative niche market). Here's an mp3 recording, and here are the lyrics:

Euclid said, there are infinite primes
Well, here's a proof in only two lines:
Suppose they're finite, by assumption
Take their product plus one --- contradiction

Q.E.D., quod erat demonstrandum
Q.E.D., that's what we wanted to show
Q.E.D., quod erat demonstrandum
Q.E.D., quite easily done

Cantor said, the reals are uncountable
Well, take an enumeration in decimal
Now I've got a number that isn't in your list
It differs from the i-th number in the i-th digit

Q.E.D., quod erat demonstrandum
Q.E.D., that's what we wanted to show
Q.E.D., quod erat demonstrandum
Q.E.D., quite easily done

Fermat said, this equation has no solution
It's even so when n is a billion
Well, I've got a proof that isn't very long
But it just doesn't fit into this song

The chords are G D C D, Em C G D.

Explanation for non-experts:
Q.E.D. is commonly used in mathematics to signify the end of a proof.
The first verse refers to Euclid's proof of the infinitude of the prime numbers.
The second verse refers to the diagonalization argument, which was used by Cantor to prove that the real numbers cannot be enumerated.
The third verse refers to Fermat's Last Theorem, and Fermat's marvelous proof thereof...