I’ve recently been reading about the Millenium Prize problems, specifically the Riemann Hypothesis. I’m not near qualified to even grasp the entire problem, but seeing the hypothesis and the other problems I can’t help wonder: what is the practical use of solving it?
Many researchers have spent a lot of time on it, trying to prove it, but why is it so important to solve the problem?
I’ve tried relating the situation to problems in my field. For instance, solving the $P \ vs. NP$ problem has important implications should it be shown to be either $P = NP$ or $P \neq NP$: for instance, cryptographic algorithms, but it’s hard to say WHY the Riemann Hypothesis, or other problems, are so important.
Perhaps a partial answer could be made by seeing which solutions proof of the Poincaré Conjecture has lead to.
Proving the Riemann Hypothesis will get you tenure, pretty much anywhere you want it.