Jenga mathematics

I like this: on his blog The Endeavor, John D. Cook draws an analogy between strengthening a theorem and the game Jenga.

Jenga is a game where you start with a tower of wooden pegs and take turns removing pegs until someone makes the tower collapse… I use the phrase “Jenga mathematics” to refer to generalizing a well-known theorem by weakening its hypotheses, seeing how many pegs you can pull out before it falls.

Maybe we can take this analogy in a slightly different direction. It is often the case that a mathematician is willing to accept slightly weaker conclusions if she or he is able to remove some hypotheses. (For example, in my work I take theorems about differentiable dynamical systems and try to extend them to continuous dynamical systems—often there is some analogous, but weaker theorem.) In the same way, a Jenga structure with blocks removed has holes in it, but it is still standing. (On second thought, maybe mine isn’t such a good analogy—I’m using the missing blocks are both hypotheses and conclusions. Oh well.)