I don't know much about this, an it's a little over my head... but isn't this a really bid deal? Like solving one of the millennium problems? I remember reading a book on the subject some time ago, but it was way beyond me at the time (it probably still is).
I guess I'm asking, what is the significance of this? Is it as big a deal as I think it is?
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
The Riemann Hypothesis is connected with many parts of mathematics. One of it's most signficant connection (to Number Theorists) is that it is related to the distribution of primes. But there are many others as well.
However, there is something a bit deeper here. Mathematics is pushed by unsolvable problems. Entire fields were brought up around Fermat's Last Theorem, and the same occured with the Riemann Hypothesis. Then they are in turn studied on their own right, and we have found them to be quite useful in areas we did not expect. However again, the only way to expand mathematics (in a meaningful way) is to solve unsolved problems. The Riemann Hypothesis is simply the king of those right now.
and extending on ricky's speech, the problem with things like this, is that although many areas and fields can be built around them, they can never reach their full potential until the hypotheses and theories they are based upon are proven, otherwise you end up with a string of 'all of this is true, given that this is actually true, which is based on the assumption that this is actually true...' and so on.
The Beginning Of All Things To End.
The End Of All Things To Come.
That isn't typically how fields arise. Certainly they can, and there is one equation which is equivalent to the Riemann Hypothesis. However, typically what happens is that a problem is broken down into smaller parts, abstracted, and then the abstraction is used to hopefully achieve a result which corresponds to the problem.
My main area of focus is algebra, so while I can't speak on the Riemann Hypothesis, I can do so on Fermat's Last Theorem. The idea of a Principal Ideal Domain (PID) and Unique Factorization Domain (UFP) were abstractions of certain rings which arise because of FLT. Then Algebraic Geometry then takes a certain type of UFD, specifically polynomials in n variables over a field, and studies them to find solutions to sets of polynomial equation, basically linear algebra on steroids.