**Ramsey theory** is a branch of

mathematics concerned with

combinatorics. It's central

theorems are rather broad, (and I lack the information currently to clarify) but the main

contention is "the complete absence of

patterns is impossible". It puts into a

formal mathmatical

framework the idea that in some situations, an amount of what

*appears* to be

coincidence is certain to occur.

One example could be; take a number of points spread

**randomly** within a defined area, how many points do you need to be certain that at least one line of three points will occur.

Ramsey theory problems are often very easy to state, and very difficult to solve.

I've been told good introduction can be found in Graham & Rothschild, "Ramsey Theory", in Studies in Combinatorics, Gian-Carlo Rota, ed., MAA Studies in Mathematics, Volume 17, MAA, 1978.