My question is quite simple. I understand the basis of Riemann Hypothesis and general idea, what I don't understand is why it hasn't been proven yet. What part of the hypothesis that causes such a problem, that apparently makes it impossible to prove. When Hilbert gave his speech in 1900 he thought the "Prime Number problem" would be squared out and proved in a few years after his famous presentation of 23 ongoing dilemmas, so what is it, that prevents mathmaticians from prooving it.
I'd like to know where exactly or what causes the proove of the hypothesis to be so difficult. And also if anyone know how Riemann derived his zeta function. I know he took the basic concept from Euler', but how he figure out what it suppose to be that I don't know.