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I have posted a similar question to this previously, but would like to reword it and re-ask it.

I just recently completed my undergraduate studies with a degree in mathematics from a relatively well-known US university. During my time as an undergrad I took many advanced (first and second year graduate courses) as well as one-one reading courses with professors on topics in Probability and mathematical analysis (topics like stochastic differential equations, large deviations theory, linear/nonlinear PDE at the level of Caffarelli and Cabre, as well as topics in Calderon-Zygmund and Littlewood-Paley theory).

Due to my indecisiveness and the insistence of my family for me to find "gainful employment", I chose to not apply to graduate school, and instead work full-time in private-industry (quantitative-finance). The work is challenging and sufficiently interesting, and of course pays well, but I still feel that I would be remiss if I did not purse a PhD in mathematics (or related fields). My main issue (in my mind) is letters of recommendation. While I am confident that the professors I have worked with would be willing to recommend me, I am in some sense taking a non-traditional route by delaying my application (for example after one year of working). In turn, I am afraid that the more time I take for asking a recommendation, the less-likely it is that my professors will remember me and be able to write a strong letter for me.

Does anyone have recommendations as to a best course of action here? I am wondering whether I need to bite the bullet and apply to programs this year, and hope they offer deferrals (for say, one year of time) although I'm not sure how the current situation (with covid etc.) could impact this. If anyone here is on mathematics graduate decision boards (or any graduate decision boards for that matter), I would appreciate your input. I am also wary as to the perception of "non-traditional" applicants as my self and how they might be perceived by admissions committees, although it is too late to modify that status.

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    I doubt working for a year between undergrad and PhD would be considered "non-traditional". I think around half the PhD students in my department did something between undergrad and PhD. One even had a 20 year career in another field before switching to physics. I don't think you'll be at a disadvantage.
    – astronat
    Aug 12, 2020 at 16:10
  • Futhermore, what is motivating you to get a PhD? "Feeling remiss" is not going to cut it on a personal statement, and lukewarm motivation will hinder your application just as much as a weak reference.
    – astronat
    Aug 12, 2020 at 16:11
  • So just to be clear on the timeline, your plan is to start a PhD program in Fall 2022, so that you'd be applying in the winter of 2021-22? Aug 12, 2020 at 16:18
  • @NateEldredge Yes - that would be my ideal timeline. Aug 12, 2020 at 16:24

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There's an easy way out of this dilemma: talk to your professors now, tell them that you intend to apply to graduate programs in another year, and that you hope they will be willing to write recommendations. The professors can then draft a letter right away, or at least notes for a letter, while their memories of you are still fresh. When the time comes for you to apply, they can update their draft to discuss any additional accomplishments you have achieved in the intervening year, and send it in.

I don't think that a two-year gap between undergrad and grad school is likely to make a big difference in admissions, especially if you describe it as your plan all along. You just want to avoid giving the impression of "I went to go work in industry but immediately discovered I hated it / got fired / etc, so now I'm applying to grad school because I can't think of anything else to do with my life". If it were five or ten years, there might be some impact, but that's not the case here.

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