In pure math, there is cryptography – using number theory to make unbreakable or almost unbreakable codes, and to try to crack those codes. If you’re interested in this and in working for the government, you could look into getting a scholarship from the National Security Agency. They offer similar deals to what ROTC offers, except that you work in an office in Maryland instead of serving in the military afterwards.

In applied math, there are options in actuarial science (mostly statistics to make insurance tables), mathematical finance, and operations research (applying mathematics techniques to make businesses run more efficiently – for example figuring out the best way to set up routes for deliveries and things like that).

I’ve also seen some math majors score engineering jobs without an engineering degree. good luck