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Context

I am a few years out of undergrad and have been working in a finance job since I graduated. As an undergraduate I identified going into a math PhD as a very likely plan for myself early on. I was very successful on paper, and I think if I had stayed fully committed to that path I would have had a very typical and rather strong application (at least as far as your typical undergrad knows how to self evaluate, which I could be easily convinced is very poorly). But I lacked confidence in the softer skills that I believe to be required for graduate school, such as making connections and choosing the right advisor. I also did not believe the research I had done realistically approximated typical PhD research, even though I loved it and thought it went well. I ended up choosing to look for an internship instead of a second REU, was accepted into an unexpectedly prestigious place which lead to a full time job offer that I took.

I have gained some social confidence since then, and am seriously considering returning for a PhD in math. I believe the opportunity to spend several years fully focused on a subject I love will not be something I would be likely to regret.

I suspect that the answer to this question might be different for pure versus applied math. My personal topic interests lean toward applied, but I'd be curious to hear the answer for both.

My Working Understanding:

  • For math specifically, it is somewhat uncommon for someone to have industry experience prior to starting a PhD. This is less true in other fields.
  • Many professors may look poorly on the potential of those who choose to go to industry first, because it demonstrates a lack of commitment to the field.
  • Admissions committees will worry that a student who has been away from math has forgotten too much and will be behind. (The GRE subject test is a way to try to mitigate this, though many schools do not accept it anymore and it has major flaws.)
  • Experience in industry is of limited interest to admissions committees in most cases.

Why I Want to Check My Understanding:

  • It will help inform how I discuss this experience in my application materials.

  • It allows me to more accurately self evaluate my application strength, useful for managing expectations and picking schools.

  • While I have found answers to this that discuss the question more generally for Stem PhDs, I have heard it is less common for math and would expect the answer could be different.

  • Input on this would help others in my situation, or undergrads who are considering trying industry before trying a PhD.

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If your undergraduate degree is in math then I think the question of industry experience is irrelevant other than at the margins. In finance it might be a small plus if you were applying math in the job.

Most US doctoral admissions is based only on the undergraduate education and the selection is done by committees that evaluate your likelihood of success. Most early doctoral students in math in the US take quite a lot of coursework to prepare them for comprehensive/qualifying exams. If you haven't forgotten everything you learned you start at about the same place as everyone else.

One normally chooses a dissertation advisor later, after they have coursework and maybe comps behind them. You and the potential advisor will be in a much better place to evaluate one another at that point than at admission time.

One issue I see, however, is whether you can still get the important positive letters of recommendation from your previous professors who will attest to your likelihood of success. In that, it is easier to apply directly from the undergraduate program when people remember you.

This would be different other places, where individual professors select, and probably fund doctoral students; Germany IIRC.

Gaining confidence in yourself is a good thing, however. You might mention that somewhere, perhaps in your request to professors for letters.

And, if the finance was heavily mathematical and the program you want to enter is applied math, especially with a finance-adjacent option, it would be a plus. But in general, other things will count far more.

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