I did a PhD in applied math, was a professor for a bit, and then dove into the startup world working on mathematical software. I'm happy to chat directly if you

I did a PhD in applied math, was a professor for a bit, and then dove into the startup world working on mathematical software. I'm happy to chat directly if you want (ping me by email, address in profile). If I were currently a math PhD, I'd personally look toward some bio-info application since the bioinformatics startup scene seems (in my experience) to have a significantly positive second derivative. I personally went (~10 years ago) down the distributed systems / statistical computing route, which is good fun but (in my opinion) overly crowded right now. As for languages / tools: I'd look at something like Python since Scipy/Numpy will give you a way to ply your trade. I'd also look at Weka if you want to do something more on the statistical / machine-learning side. But, by far, the most important thing is being willing to work "in the trenches." A large part of working in software is solving problems like "Our optimizer's CSV parser is failing when we have nested quotes inside escaped HTML". Just picking the right algorithm for the right job is only 10% of the work; solving all the workflow's edge cases is far more time-consuming.