Re:Okay, assuming this proof to be correct... (Score 5, Informative)

The Riemann hypothesis has nothing to do with the foundations of calculus, or what most undergrads learn. Maybe he's thinking of the continuum hypothesis(which was proven to be undecidable). The Riemann hypothesis is a conjecture in analytic number theory. What it gives us is the best possible information on the distribution of prime numbers among all numbers. One common heuristic interpretation of the Riemann hypothesis is that the primes are as randomly distributed as possible. How is this useful in the real world? For instance, the proof that primality could be tested in polynomial time that came out last summer made use of difficult analytic estimates to show that the algorithm would give an answer quickly enough. Agrawal was able to avoid using the Riemann hypothesis, but presumably the Riemann hypothesis could allow one to get a better bound on the time the algorithm takes to run. That's just one example.. the Riemann hypothesis would allow the solution of many other more easily statable conjectures in number theory. For instance one can use it to prove the odd Goldbach conjecture-every odd number greater than five is the sum of three primes.