Math jokes: "your lie when you said to me, 'I did this only as a game'"

Famous math-joke punchlines: "Ah-ha, a solution exists!," "thus reducing it to a problem previously solved," "totally true but completely useless," "assume we have a jabberwock," where a jabberwock makes the problem trivial, "there is at least one borogrove at least one side of which is mimsy," and so on. If you've never heard them, you've not been listening to math jokes, you sensible fellow.

But there are others, call them sporadic math jokes (that's one of them), which don't fit into the mold. Those punchlines above are jokes about mathematicians more than math; the closest I can think of to the latter is "let epsilon be less than zero," which presumably is completely cryptic to non-mathematicians (that's the whole joke, not the punchline), or maybe one of the waitress jokes ("one-half x squared,... plus a constant," "in characteristic two"). Here's another one that bridges the gap:

A mathematician keeps a diary. It reads:

• Monday: Tried to prove theorem.
• Tuesday: Tried to prove theorem.
• Wednesday: Tried to prove theorem.
• Thursday: Tried to prove theorem.
• Friday: Theorem false.

Sometimes it's just one of those weeks.

It cuts even more when the "mathematician" is a student and the "theorem" is an assigned exercise. Sometimes this happens, quite by accident, even on an exam (oops! -- I've seen a couple of these), say if a little hypothesis gets left out or if the problem is copied without discrimination from another source.

On the opposite side, firmly in "not funny," are Stiller's monsters. Computer scientists who play chess and have too much computing power sitting idle engage in the following project: to enumerate and evaluate all legal chess positions with some small number of pieces, say, five or six or seven. You can download complete six-man tablebases, as they're called; that's the two kings plus four other pieces. They'll only cost you several gigabytes. It will also be extremely boring to blindly wander through them, although in normal chess praxis from time to time it would be helpful to have a computer program capable of not just crunching moves with grandmaster vision but of perfectly evaluating every six-man endgame.

In the famous rematch Deep Blue v. Kasparov the machine had six-man tablebases, and it must have weighed on Mr. Kasparov's mind that if the board got too light with material the computer would begin to play not just mortal chess but mathematical perfection, as though announced on the trumpet from the throne of god, or if you prefer, gleaned from the immodest prostitution of the Platonic Form of Chess itself.

And god and Plato can be inscrutable: this is where Stiller's monsters come in. They're a couple of six-man endgames, winning for one side, but where the shortest forced win is around 250 moves; they're named for the man who first enumerated the six-man endings and found them while looking for long forced wins. In the linked article, Tim Krabbé writes:

They are beyond comprehension. A grandmaster wouldn't be better at these endgames than someone who had learned chess yesterday. It's a sort of chess that has nothing to do with chess, a chess that we could never have imagined without computers. The Stiller moves are awesome, almost scary, because you know they are the truth, God's Algorithm - it's like being revealed the Meaning of Life, but you don't understand one word.

The seven-man tablebases of course will be downright huge, but a couple of endgames, like KRRN v. KRR (king-rook-rook-knight versus...) have already been worked out. There is a position in this class which is winning for the superior side but it takes 290 moves to prove it. The last ten or so, mind you, are pretty easy; but the first ninety have to be perfect.

It's the dark side of discrete math. Sometime's there's an obscure obstruction to a general claim ("theorem false") and sometimes ("file under Stiller's monsters") it's true but you have to beat the devil to prove it.