Bear with me, I'm fresh out of high school so my level of mathematical knowledge is quite low (probably too low to be trying to understand the Riemann hypothesis, but at least I'm trying).
At this current time, I'm trying to make sense of John Derbyshire's (fantastic) book Prime Obsession. One thing that hasn't been explained in the book and to which I cannot find answers within the bounds of my understanding through research, is why exactly Riemann thought his hypothesis was true.
From what I understand, Bernhard Riemann was a very intuitive mathematician so it's quite possible that although he did not have a proof for his hypothesis, it made sense to him intuitively. I guess my question is, How does it intuitively make sense that all non-trivial zeros of the zeta function lie on the critical line and not somewhere else?