Does solving math problems make you a good programmer?
nostrademons: It makes you a better programmer.  It does not, in itself, make you a great programmer, and probably does not make you as good a programmer as if you'd written lots of code in problems that stretch yourself.Similarly, if you test for math ability in interviews, you will get better candidates, on average, than if you don't.  But you aren't guaranteed a great candidate, and you'll like miss a few people that are qualified but just don't do well with those sort of problems.  And it's not as reliable an indicator as having written lots of code in interesting problem domains, but the number of people who are hacker-famous is less than the size of most large companies.