Knuth says his cheques are much more often cached than cashed.

This algorithm is more obviously correct than Buffon's needle, though.

I always assumed $U$ was for subspaces because you call a topological space $T$ for topological space, and when you take a subspace of it, you just take the next letter.

The $A$ is not needed, but it makes the presentation of inverse functions more symmetrical and allows one to define partial functions with fixed domains so that functions are partial functions.

Another problem with this definition is that it's wrong -- in modern mathematics (though less so in the informal language of some analysts, IME) a function has a codomain. Under this definition a function has an image, but any superset of the image could be its domain. As an undergraduate, I was given this definition several times, and it bothered me. A function is a triple $(A, B, R)$ where R is a subset of $A\times B$ such that...

I think that there is a nice pictorial proof for this fact, but I don't think this is it. It's a proof for a specific $n$. To make it a general proof, the inductive step needs to be illustrated.

Another WWII statistics idea: the German tank problem (recently used to estimate Apple's production of iPods, among many other things)

I like this quote which gives some impression of pre-decimal arithmetic. It is advice given to a German man (I think) on his son's education. I have lost the source. "If you only want him to be able to cope with addition and subtraction, then any French or German university will do. But if you are intent on your son going on to multiplication and division—assuming that he has sufficient gifts—then you will have to send him to Italy."

Clearly the use of "natural" is increasing, but is it increasing faster than the volume of MathSciNet? I would presume that both the total rate of mathematics production is going up, and also that MathSciNet comes much closer to indexing the full text of 2000 mathematics than 1945 mathematics.

I don't know the etiquette on this: is my inclusion of a citation enough to turn Chris Eagle's comment into an answer?

The fact that bubbles are round only demonstrates a local, not gloabal, minimum, surely? The bubble can't explore arbitrary regions of phase space: it can only go downhill.

What makes you think humans proof checkers are less buggy than computer ones? :) At least in a computer program, you only have to get it right once: a brain can make any number of different mistakes each time it runs.

Also, the conic sections are the shapes which can be formed by shining a torch (i.e. a point light source with output restricted to rays passing through a circle) on a surface at various angles.

I suppose that incrementing also restarts the "polynomial time" clock?