Chances for Top Math PhD Programs

Undergraduate Institution: Canadian School (mid-tier)

Program: Business (I know)
GPA: 3.6/4.0; 4.0/4.0 on all (12 one-semester) Math Courses

Type of Student: Asian; International

GRE: 159V, 170Q, 4.5W

Math GRE: 880 (90th %ile)

Program Applying: Pure Math PhD

Work and Research Experience: No formal research experience and no relevant work experience. For the last three years I’ve been doing my own projects/businesses and spend most of my time learning. I have co-founded some 6-figure businesses and run a small fund with some friends that has grown 40x to barely north of a million. I think I can show my interest in mathematics by spinning my story as I have done a lot of independent research on probability, stochastics, numerical analysis, advanced statistics, etc.
Awards/Honors/Recognitions: No substantial awards.

Letters of Recommendation: I have really good connections with some of the math professors. I am confident I can get 2 really good and 1 ok letter of recommendation. My grad real analysis professor, I feel, would write the strongest letter.

Math Subjects: (Took maximum math courses allowed) Calculus, Multivariable Calculus, Applied Linear Algebra (2 Semesters), Introductory Real Analysis, Real Analysis, Algebra I, Graduate Real Analysis, Graduate Functional Analysis, Graduate Harmonic Analysis, Graduate Probability, Graduate Convex Optimization.

*My GPA is awful as I hated my business courses.

Programs: Berkley, Princeton, Harvard, MIT, Stanford, Chicago, UCLA, NYU, Columbia, Cornell, Brown, UPenn,

Question: Do you think given my unconventional background I would have a chance? Is there something I could do that would improve my chances?

A pure math PhD program would be a tough sell as your experience is in applied math. You’d have a better shot for financial math.

Your GPA is not awful. A 3.6 is a good GPA. Awful would be sub 2.5.

PhD admissions can’t be “chanced” the way undergrad admissions can be (and I would argue that even undergrad admissions are tricky). They are holistic, and they really depend on a lot of factors that can’t be easily described in an online forum, including the true strength of your recommendation letters, your research fit with the department, and the quality of your statement of purpose.

That said, here is some feedback:

  • I believe that math programs are a little less strict on this, but no formal research experience would be a dealbreaker in most doctoral programs. In the professors’ eyes, how could you possibly know that you want to spend 5+ years in a PhD program (and a whole career doing research) if you haven’t done any yet? Independent research doesn’t help as much, as there’s no way to verify the quality of that research (unless you got it published in outlets your field cares about).

  • For pure math, running a successful business doesn’t count for much. The skills not really transferable. They want to know whether you can succeed as a researcher, not a business person.

  • That, paired with the fact that you majored in business, is going to raise some questions about your seriousness in pursuing a pure math PhD (as opposed to applied math, business analytics, operations research, etc.) You need to have a really good answer for that question. Other than taking a lot of math classes, there is really nothing here that demonstrates passion for, interest in, and/or experience with pure mathematics concepts/research/scholarship.

  • That said, it is good that you’ve taken so many math classes - you maxed out and that actually is pretty close to what a major would’ve taken. However - and take this with a grain of salt, as I’m not in math - the class listing beyond the basics seems pretty applied.

All-in-all, your portfolio can spur one to ask why you want a pure math degree and not a more applied one? You have to be able to answer that question, either directly in your statement or indirectly through other activities you do between now and then and through your recommenders’ letters.

Also, given the programs you want to apply to, I would say you need to aim for all 3 letters being ‘really good.’

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Chances are extremely low, even with 3 really good letters.

If pure math is your passion, consider a MS degree to take some theoretical courses and start getting into some research. Since you asked about NYU:


I agree with the comments about doing a masters first. The most famous prep course would be Part 3 maths at Cambridge: MASt/MMath: Information for Prospective Part III Students | Part III (MMath/MASt)

This page also links to a lot of past Cambridge course material where you can test your skills and see how you might compare to other top math PhD applicants. It sounds like your interests might be more towards probability and optimization, so look at the material there: Probability | Part III (MMath/MASt)

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Nope: unless (as @juillet said) you have some objective evidence you aren’t going to be able to ‘spin’ that. A research masters will help you see if you like sustained pure math research, and transition you from the strong applied focus you have now, and help you identify your research focus, which will help you identify the programs that are the best match for you.

Remember that it’s not just getting into a PhD program: there’s also the pesky business of successfully (and reasonably happily) completing a 5-6 year comparatively independent (verging on isolated) program.

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