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Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.
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Where can I find a catalog of known Ramsey numbers?
MathWorld has a pretty decent list (scroll down in the link) and cites numerous papers with good bounds
http://mathworld.wolfram.com/RamseyNumber.html
28
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Erdos Conjecture on arithmetic progressions
Introduction:
Let A be a subset of the naturals such that $\sum_{n\in A}\frac{1}{n}=\infty$. The Erdos Conjecture states that A must have arithmetic progressions of arbitrary length.
Question:
I w …