Hal-9001's Journal: Musings on pure mathematics

While reading today's story on the Riemann hypothesis, I was led to a very cogent explanation of the Riemann hypothesis that I wanted to save for future reference. The Slashdot journal system, which I've neglected for over a year now, seemed like a perfect place for recording it. A choice line from the comment is

...for me to explain it [the author's PhD thesis in mathematics] fully to him [the author's physicist friend] would probably necessitate him doing at least one mathematics degree first. And that's not really something I'd wish on one of my friends :)

I can vouch for the claim that pure mathematics is very difficult to explain to a nonmathematician. As a graduate student in electrical engineering, I believe I am pretty adept at applied mathematics (algebra, calculus, matrix arithmetic, differential equations, integral transforms and such), but my understanding of pure mathematics (rigorous proof, analysis, abstract algebra, number theory, set theory and such) is probably at the level of an undergraduate junior in mathematics, at best. I recall that Richard Feynman, Nobel laureate in physics, mentions in Surely You're Joking, Mr. Feynman that his mathematician friends in graduate school used to give him a hard time by presenting topological paradoxes or by giving him integrals that could not be evaluated except by special methods like contour integration, so I believe I'm in good company. ;-)