TITLE: What do I need to know to understand the Riemann hypothesis
QUESTION [13 upvotes]: Which kinds of fields of mathematics do I have to know about in order to understand the Riemann hypothesis millenium prize problem?

REPLY [4 votes]: I used to try to explain the complex analysis part. I have given up on that. See http://en.wikipedia.org/wiki/Prime-counting_function for details...
The short version is that the prime counting function $\pi(x)$ is approximated pretty well by $$ \frac{x}{\log x}. $$ It is known that a better approximation is given by  $$ \mbox{li} \, (x).  $$
The Riemann hypothesis is equivalent to a specific form of the statement that $ \mbox{li} \, (x)  $ is a really good approximation, see 
http://en.wikipedia.org/wiki/Prime-counting_function#The_Riemann_hypothesis and TABLE