I went to take my Generals, I knocked boldly at the door,
And there sat Harish-Chandra, Weil, Eilenberg and Zsa-Zsa Gabor.
"Come in" said Andre with a grin that cut me right in two.
"And tell us what you know about the group of order two."
I said: "Well,
You integrate dx dy and multiply by z
Expand about the origin and compute Homology
If the field is irreducible, normal, regular, free,
Complete, compact, connected, the answer is twenty-three.
But if it's Archimedian, discrete, Abelian, what's more
A Hausdorff, Banach, pre-Hilbert space,
The answer is twenty-four."
Then Harish-Chandra scratched his scalp and gravely said to me:
"Give me a function on the line that's Lipschitz of order three."
I said: "Well,
Take a wildy knotted torus in an Alexander horned sphere,
And take its Blaschke product with a can of Schaeffer beer.
Disintegrate the cycle and take Tor and Ext and Hom,
Tensor with SO(extra) and apply the lemma of Thom.
Then Zorn to get a maximal tree with fibered sheaf of germs.
The answer can be read off from the lowest order terms."
"I'm a modest man," said Eilenberg, "I'm sure you will agree.
You may talk about any theorem that first was proved by me."
I said: "Well,
In the category of categories two functors which commute
Must have a common fixed-point, which has a unique square-root.
In the weak-star-prime topology pick an extremal cluster-point;
Frobenius was sure this is the Gauss-Greene-Saks adjoint.
But in the punctured disk it is not safe to carry tea,
So wave your hands, erase the board and shout out QED."
Then Zsa-zsa moseyed up to me a wiggling her hips,
"Just slip me fifty dollars, I'll arrange for you to pass."
Well I don't know if I passed or failed, but I'm fifty bucks in debt.
I left them to deliberate --- they haven't come out yet.