TITLE: What areas of pure mathematics research are best for a post-PhD transition to industry?
QUESTION [58 upvotes]: I have a student who is looking to start a PhD in pure mathematics. She is talented and motivated, and will do quite well. She is still in a phase of her development where she is still open to the possibility of working in a broad range of research areas. In order to offset the risk of not finding an academic job post-PhD she would like to write a dissertation that will give her increased likelihood of finding work in industry. She wants to do research in pure mathematics however, i.e. prefers proving theorems to writing code or testing models.

Question: What areas of pure mathematics research are best for a post-PhD transition to industry? Please be as specific as possible.

Answers to the questions here and here are certainly relevant, but these questions are obviously distinct from my question. I think this question is useful to the pure mathematics community in that it addresses the fact that there are so many qualified academic job applicants in recent years. (For this reason, I hope the community gives the question a chance.)

REPLY [2 votes]: You say that your student "... would like to write a dissertation that will give her increased likelihood of finding work in industry. She wants to do research in pure mathematics however ...". The assumption is that she isn't really motivated to work outside academia, and would only take an industry job as a last resort.
That attitude/approach is just not appealing to employers. It's possible to get a job in industry with a mathematics PhD, but you have to want to do it in the first place.  If an interviewer asks why you applied for the job, and you say "Well, I couldn't get a postdoc" then it's game over.
For the rest, I agree with Timothy Chow's answer.