The odds of studying versus applying a mathematics? I went to school to learn programming, but have come to realize that the most fascinating problems are in mathematics or computer science theory. For this reason I am considering studying mathematics at the graduate level. I would like to ask what are the odds that a mathematics graduate will REALLY apply mathematics?
 A: 
Because of the apparent need for STEM majors, 

Demand levels for S, TE, and M are very different things.  The preliminary question that should be addressed is whether there is really a great demand for home-grown STEM specialists. 

Besides academia, I don't know where to find a highly concentrated demand for mathematics majors. 

The academic job market has the least demand per graduate, and effectively zero demand for people without doctorates.
A: Tthere are certainly jobs out there where you will really apply mathematics (i.e. they involve actively learning new math, reading papers, implementing and designing algorithms and possibly inventing new math). Some examples are


*

*Quantitative financial analyst or quantitative trader (at in investment bank, or hedge fund)

*Risk modelling (e.g. as an actuary in an insurance firmm or reinsurer, or in-house)

*Formal verification expert (e.g. in a hardware or software firm)

*Systems modeller (e.g. in traffic management, urban design, crowd modelling)

*Aerodynamics engineer (e.g. for Boeing, for an F1 team, in the military)

*Applied cryptographer (e.g. in security services, NSA, GCHQ)

*Data science (e.g. at a social networking firm - Facebook, Google, Twitter etc employ many of these)

*Data journalism (e.g. the New York Times, Guardian etc are hot on this)


However, these all tend to be very competitive (other applicants will have masters degrees, PhDs or post-doctoral experience) and generally difficult to break into.
