Things like the
Riemann Hypothesis make me wish I understood more about
mathematics. This write up is aimed at explaining why the
hypothesis is important, not at explaining the
minutiae of how it works. That piece of the puzzle is
over my head.
In its simplest form, the Riemann Hypothesis states that all non-trivial zeros of the Riemann Zeta Function lie on the line 1/2 + it as t ranges over real numbers. The reason this is important is that you can use these zeros to predict where prime numbers will crop up. Nobody has proved the Riemann Hypothesis as of this writing, although number theorists would like it very much if someone would hurry up and do the damn job.
See, the thing is, lots of work in number theory starts: "If the Riemann Hypothesis is true . . ."
This is a big problem. Huge. Number theory lies at the heart of mathematics, and if the Riemann Hypothesis is bunk then an awful lot of number theory falls down goes boom. There's a big gap in maths, and it would be great if some nice fellow would come along and fix it.
They've managed to show that it works for everything through the 1020th (100,000,000,000,000,000,000th) zero. But there are always more zeros, and there's nothing keeping zero number 100,000,000,000,000,000,001 from lousing up the pot. Really all we need is a nice proof that it works for all zeros. Ever.
So if anyone has any ideas, please go to. It would make me very happy.
This write up would like to thank http://www.math.ubc.ca/~pugh/RiemannZeta/RiemannZetaLong.html for lots of nice information. Thank you.