I also hesitate to give this answer but here it goes.

You do not have to work in the most obvious jobs to help the society. As a mathematician you must be fully aware of the fact that many useless looking abstract mathematical tools turned out to be extremely useful in practice only later.

Besides how do you know that education is helping the society where we have an increasing evidence that our educational system is very wrong. So in reality, you might be doing the exact opposite what you wish initially i.e. making people love math and make them suffer by a pursuing a degree among those mean and arrogant alpha-males (Exaggeration police was here! But you can see this,this and especially this for the fun of it).

Moreover, you might do more good if you really love your subject and create a use of it. Many concepts like Street-Fighting Mathematics and Freakonomics showed that the academia is missing something that is truly crucial for its self-sustained dignity. The relevance.

By relevance, I don't mean that poem starting with math is pure, would you know that it is relevant from the start. I know what R&D departments do, because I worked for quite some time in one particular industry. Hence, I know how to measure how much of my work will be complete fun and useless (for the time being) and how much of it will spin-off to something that would be good for a product. Same holds for the academia, you can't expect every single person to publish and turn everything upside down with one 3-page article. Some people don't want to publish anyway. Some people love to get their hands dirty and work on applied math problems which most of them are not even publishable. Some even go into private companies and carry on their stuff applied to a special (and possibly boring but, hey who cares) practical problem (Not to mention the Google's PageRank).

Long story short, you would better off if you follow nobody's instincts but yours. Try to materialize your career plan with the given limited resources and surplus of happiness that it provides. Sounds cliché but it became a cliché, in the first place, for a reason. By itself, it is a damn hard problem. So you might work on it as a mathematician starting from the Lagrangian :P