*Princeton Companion to Mathematics*

"The fundamental theorem of enumeration, independently discovered by several anonymous cave dwellers, states that

|A| = Σ_{a∈A}1.

In words: the number of elements of A is the sum over all elements of A of the constant function 1."

Sounds kind of silly, but it's true. The whole chapter is a nice fourteen-page answer to "what is enumerative combinatorics?", mentioning most of the classic problems and most common methods of solution, which appears to be its

*raison d'être*; I know most of this stuff but I can imagine how useful similar blurbs on subjects I'm not so familiar with would be, and indeed most of the book is intended to be at about the first-year undergraduate level; that's low enough that I should be able to read it without stopping for breath. (The guidelines for contributors say that the articles about various subjects should be something like the beginning of a very good colloquium talk, the sort where you really get the feeling that you know something about how some other area of mathematics works.) The PCM has a semi-official blog, which is Tim Gowers' blog. Several dozen of the component articles are available online, on a password-protected site; the password is in the linked-to post by Gowers. I suspect I'll have more to say about the

*PCM*in the future.

## 1 comment:

Worthy of Lewis Carroll, perhaps?

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