Note: due to inability to format superscripts or subscripts (if you know how do this, please send me mail and tell me!), certain things are not superscripted or subscripted as necessary. To make the song scan, just read the letters aloud. Thus, "an" is "a n", etc.

Chorus:

We drink to mathematics, upon whose structure lies

The physics of both space and time, and why the butter flies

We drink our coffee every day, and nightly quaff down beer

The postulate and axioms come out as theorems here

Rene from Chartres was a man who had it all worked out

He said, "I think therefore I am --- of this there is no doubt!

And by some lines in space you can all points therein describe

So with that thought I think I shall another beer imbibe"

Pierre de Fermat out of France, he was a gambling man

He said "I read these books of mine to find out all I can

"xn plus yn's not zn if n does exceed two

"But the margins of this book cannot contain this wond'rous proof!"

An apple fell and Newton saw
it plummet to the ground

He said "I wonder what doth make the Moon to go around?"

Gravity was born that day, and so was calculus,

With its fluxions and its fluents and its dots to torment us.

Bernoulli, father, son, and brother, and an uncle too.

Daniel was a relative, a cousin once removed.

Math and physics gained a lot, for they fought endlessly.

And nothing breeds success so much as sibling rivalry!

Euler did believe in God, just
like his fellow man.

Diderot the atheist said "Prove God if you can!"

"Sir, (a + bn) over n is x so therefore God exists!"

And Diderot could not refute a proof as good as this.

Joseph Louis Lagrange wrote
a book full of mathematics.

In English it would be the *Analytical Mechanics*.

He said "Look high and low, you'll find no pictures here!

So kind sir would you pour for me another pint of beer!"

Laplace, Marquis, did write
some works on motions up in heaven.

He started work when but a lad of only ten and seven.

Napoleon said "I see no sign of God in this!"

Laplace replied "I have no need for that hypothesis."

Gauss, Karl Friedrich, had a
choice at one year ere his score.

To study mathematics, or words forevermore.

With compass and straightedge, he made his choice anon.

He went around and then inscribed a septendecagon.

Cauchy and Bolzano thought that math was in a mess.

Separately they sought to make it much more rigorous!

Bolzano was Bohemian, and Cauchy came from France.

And with their work analysis continued its advance.

Evariste Galois did write the
theory of the group.

And with his knife did toast the King before the course of soup.

And at my age been laid to rest a dozen years or more.

So unto algebra I drink this next drink that I pour.

Linear equations can be solved by anyone.

The cubics and quadratics and the
quartics have been done.

Abel said "The quintics cannot likewise fall!

They cannot be resolved by means of radicals at all!"

Riemann said that parallels need not exist in space.

Lobachevsky said that two or more could be in place.

The axioms of Euclid, which give us only one,

Cannot describe the space near massive bodies like the sun!

Kronecker thought numbers should be things you can count on.

To root of 2 and rationals, he said "Vile things, begone!

Numbers should be whole! Let's get rid of the reals!

And in their place we'll substitute the theory of ideals!"

Cantor showed that aleph null can count the
integers.

And aleph one the reals, and aleph two the curves.

For aleph three or more, we've got no use at all.

So let us sing of aleph one beer bottles on
the wall.

Banach, Tarski and Sierpinski were a bunch of Poles

Creators of pathologies, like gaskets full of holes!

"If you cut a sphere just so, from one you shall make two!"

(To comprehend this proof you
need another pint of brew)

von Neumann was a man of math, from Hungary he came.

He did his work with automats and theories of the game.

He said "By minimax, you might as well coins flip!

"So you can play your game while I will have another sip!"

The saga of mathematics has not yet in full been told.

The story, it goes on and on, it's six millenia old.

And yet I fear this song, has gone on long enough.

So take my glass and fill it with some alcoholic stuff....