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.

]]>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.

]]>I guess I'm asking, what is the significance of this? Is it as big a deal as I think it is?

]]>PDF file: http://arxiv.org/pdf/0807.0090v2

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