Let $m^*(n)$ be the minimum number of edges in an $n$-uniform simple hypergraph that is not two colorable. We prove that $m^*(n)=��(4^n/\ln^2(n))$. Our result generalizes to $r$-coloring of $b$-simple uniform hypergraphs. For fixed $r$ and $b$ we prove that a maximum vertex degree in $b$-simple $n$-uniform hypergraph that is not $r$-colorable must be $��(r^n /\ln(n))$. By trimming arguments it implies that every such graph has $��((r^n /\ln(n))^{b+1/b})$ edges. For any fixed $r \geq 2$ our techniques yield also a lower bound $��(r^n/\ln(n))$ for van der Waerden numbers $W(n,r)$.