Career for a mathematician outside academia Briefly, the question is: what are sensible career choices for a trained mathematician (with a doctoral degree) outside of academia?

The situation I've found myself in is the following. I have been employed as a teaching assistant at one of the top Polish universities for a year now. The salary of TAs in Poland is borderline acceptable (as in, if it were a little bit less, one wouldn't be able to make ends meet), but when I was signing a contract, I was promised I will be promoted to assistant professor after a year. 

Now, I was informed a few days ago that I am not getting said promotion, but they'll be happy to keep me as a TA. It was stated very clearly that this is happening not because I am not doing my job properly (in fact, I have a pretty solid track record); apparently the university is in financial troubles. As a corollary, I may be stuck as a TA for quite some time. 

I have a family to provide for, so this is unacceptable for me. 

To make matters even worse, the timing of the information left me without any option to pursue a postdoc position. This got me thinking that -- even though I enjoy doing research and teaching very much -- perhaps it's time to take that step and decide on changing career path. The problem is, I don't really have any experience in work outside of academia. I feel that I am professional and disciplined enough to handle any kind of work, but sending resumes at random doesn't seem like a good idea.

I realize the question may be too vague, but I'm thinking maybe someone has already been down that road and has some advices to share.
The past few years, many friends, either mathematicians or people from physics/chemistry who knew how to write code, have gone other to various financial companies to do algorithmic trading, data analysis, that sort of things… and some others have joined web startups. In short: their coding, algorithmic and reasoning skills were more valuable than their specific academic knowledge.

What I would advise you to do is to look where alumni from your department have moved. Ask the department for statistics or listings, if they publish them; otherwise, look up people's names on the web or professional networks (LinkedIn comes to mind). See where they are now: this will give you an idea of who is hiring people with your skills (and network).