This was the most mathematically oriented episode of all: can't get much better than the Riemann Hypothesis ! Scott Aaronson has a review as well: go and read that first !
I agree with much of what Scott says. I think the problem is a little different though: some of the random phrases attributed to mathematicians (which mathematicians refers to an open problem as a "math problem") actually make sense if a non-mathematician uses them, and when Don (the FBI agent) uses them, it doesn't sound incongruous at all. It's just that the writers need to switch gears a little when writing dialogue for the mathematical characters.
They've done a good job getting a sense of the mathematics; just less of a sense of the mathematician.
Plot Summary: Mathematician claims to have proof of Riemann Hypothesis. Hackers kidnap daughter, demanding proof (and algorithm), which they will then use to crack cryptography.
Major beef: there is no direct link between a solution to the Riemann Hypothesis and factoring. It is undoubtedly true that a solution will shed a lot of light on the structure of primes, but it's not the kind of immediate corollary that is commonly implied in the popular press (take this, for example).
But credit goes where credit is due: I was wondering how they would make the conceptual jump from a theorem to an actual algorithm (assuming said connection). At least they tried to make it credible, with Charlie pointing out that an algorithm could take years to develop.
A point that I didn't really consider, but both Scott and my wife noticed, was that by using the Riemann Hypothesis, the plot line introduced the idea of a problem that has remained unsolved for 150 years, and that it's good for people to realize that "math problems" can take a while to solve. In fact, this point is reinforced when Don expects Charlie to solve it in a few hours :).
Trivia note: the mathematician father was played by Neil Patrick Harris, the "original" child prodigy from Doogie Howser, M.D.
Tags: numb3rs, review