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I think anybody who needs smart people who can work with difficult domain problems will be happy to interview you. The chief worries with a PhD mathematician would be:

1. Will you take a pragmatic engineering approach when it's warranted, or will you be a cranky loner scribbling differential equations that supposedly prove which brace style is superior?

2. Will you be bored when you're not doing "real" math?

3. Will you demand a salary that exceeds your current ability to contribute?

Sounds like you are clear on all three counts. Now it's a matter of finding the right opportunities. If you want a job locally, meetups for topics like machine learning are a good place to find out where mathematically inclined programmers are working. (Though you might find that a lot of them are at meetups because they're bored at their current jobs.) If you're targeting a certain city, you can join local mailing lists for (e.g.) functional programming to which local employers might post job opportunities.

You can also check out job postings to see which high-tech companies are hiring programmers. A company that employs a lot of PhD scientists in other positions is more likely to hire PhDs into programming positions, if only for the sake of effective communication and a consistent culture. One of your biggest qualifications to work as a programmer in such an environment is that when the physicists or molecular biologists talk to you about the problems they're trying to solve, you are much better equipped to understand them and build good software for the company than a guy who didn't go beyond undergraduate linear algebra.

You're going to do fine. Finding your way into the right circles might be a slow process, though. Don't be afraid to take a boring job if you can't find a better one, because at least you'll get something to put on your resume, experience dealing with mundane crappy stuff that you might have avoided so far -- things like debugging, messy merge/rebase problems, and working with other people's retarded code. Good programmers have to be efficient at that stuff. Good programmers also have to be good at working with people, and the crappiest jobs have the most challenging people problems. It's better to be getting your hands dirty with that stuff than sitting at home sending out resumes and solving Project Euler problems. HOWEVER, don't lose faith that you are a highly valuable performer with rare capabilities even if that isn't true in the initial crappy jobs you find yourself in. Soon enough you'll find your way into the right companies, meet the right people, and you'll be fine.




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