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Copyright 2005 by Jeff Suzuki
Technically I'm a historian of mathematics. I wrote this song while a graduate student, and have been steadily correcting its historical accuracy ever since...
I'm actually not sure what the music to this is; it is a parody of “The Engineer's Drinking Song” (from MIT), and I've been told it's the Georgia Tech Marching song.
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.'
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 axioms and postulates come out as theorems here...
Pierre de Fermat out of France, he was a gambing man.
He said 'I read these books of mine, to find out all I can,
x^n plus y^n's not z^n, 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 fluents and its fluxions and its d's to torment us.
Bernoulli, father, son, and brother, and an uncle too,
Daniel was a relative, and cousins there were too.
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 math'matics,
In English it would be the Analytical Mechanics.
He said 'Look high and low, you'll find no pictures here...
So kind sir won't 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 this 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 forever more.
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.
Sep'rately they sought to make it much more rigorous.
Bolzano was Bohemian, and Cauchy came from France.
And under them analysis continued its advance.
Linear equations can be solved by anyone.
Cubics and quadratics and the quartics have been done.
Abel said "The quintic cannot likewise fall.
It cannot be resolved by means of radicals at all."
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 until algebra I drink this next drink that I pour.
Nikolai Ivanovich Lobachevski did
Create a set of axioms that weren't those of Euclid
"Of parallels in space, there can be more than one.
This helps describe the space near massive bodies like the sun."
Kronecker thought numbers should be things you can count on.
Of root of two and rationals he said "Vile things, begone!
Numbers should be whole, let's get rid of the reals.
And in their place let's substitute the theory of ideas."
The aleph null of Cantor can count up the integers.
And aleph one the reals, and aleph two the curves.
For alephs three or more, we've got no use at all.
So sing a song 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 can make two.
To understand this proof it helps to have another 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 games while I will have another sip."
The story of mathematics has not yet in full been told.
The story, it goes on and on, it's six millennia old.
And yet I fear this song has gone on long enough.
So take my cup and in it fill more alcoholic stuff...
The Footnotes
What are now called Cartesian coordinates appear nowhere in Descartes's work. Fermat was the first to use the height of a point above a reference line, but it was Newton who was the first to graph curves in the way that we do today.
Fermat, of course, is known for his Last Conjecture (unfairly called his last theorem, which implies he had a proof): for integers x, y, and z, then the equation x^n + y^n = z^n has no non-trivial solutions if n > 2. Some histories of mathematics will say that Fermat did not claim a result unless he had a proof, but on at least one occasion (the primality of the so-called Fermat numbers), Fermat claimed something without having a proof.
Newton's notation didn't actually include the dx/dy notation so favored in modern calculus texts; that originates with Leibniz. This isn't really a mistake...it's actually more along the lines of a pun (capitalize the "D" and think like a student).
This story was told by Augustus de Morgan, and it is generally believed to be an invention. Diderot, despite what authors like de Morgan and Eric Temple Bell claim, was a competent mathematician (he wrote a number of the mathematical articles in the Encyclopedie) and would have been able to instantly refute Euler's 'proof' of the existence of God.
Lagrange, as a Frenchman of Italian descent, would probably not drink beer. But I couldn't think of a good rhyme for "here".
It's not certain whether this is an apocryphal exchange. Laplace was Napoleon's Examinateur when Napoleon passed through the Military School, and the two had a long relationship with each other that can be summarized as Napoleon showered honors upon Laplace, and Laplace repaid him by being the first in line to demand Napoleon's abdication after the ill-fated Hundred Days.
There's a story that Galois wrote up his great work on group theory the day before dying in a duel at the age of nineteen. Actually, it was the third or fourth version of his ideas on group theory. When I wrote this verse, I was actually less than a dozen years old than Galois at the time of his death. Sadly, this is no longer true...
The Banach-Tarski paradox is the following: given a sphere, there exists a decomposition into a finite number of pieces which can then be reassembled into two spheres, each as large as the original.
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