Private sector professional being screened out of PhD program

Question

A little background:

• I'm a data scientist and machine learning entrepreneur. I co-founded a sorta successful company in the AI space that got top-tier VC investment. Certainly not a unicorn or household name but a solid business that has been going for over 6 years and has a realistic shot of getting acquired by an industry player at some point. After many years, I've stepped down from my operational role and I'm working on other stuff.

• I have an MS, I didn't get anything published, but I worked on computational biology, heavy on statistical methods. I found the atmosphere focused on lab seniority which emphasized pursuing publications to set up future positions in academia sort of empty, so I graduated and started doing my own thing. While I felt disappointed in myself at the time, it ended up being a great decision that resulted in developing a love for building businesses.

The Problem:

• I want to go back to my local University and get a math PhD. There are professors there who have great expertise in fields adjacent to my research interests (theories of statistical learning).

• I got denied last year and I want to apply again, but I will likely get rejected again. The feedback that I'm getting is (1) that I don't have relevant letters of recommendation from academics (they are colleagues I have worked with), and (2) the lack of any substantial math focus in my undergraduate degree.

I can see where they are coming from -- because I didn't publish, they aren't really aware of my statistical work. It wasn't a class on a transcript, it was doing work for my PI. My undergrad was in biochem, at that time I wasn't even really into math, I took the classes I had to take. Grad school was over 13 years ago; people who knew me well are unreachable or dead. People who didn't work with me that closely aren't even sure we worked in the same lab.

Outreach to professors is understandably not very effective. Even though they think my background is great and my research interests are on point, they don't feel comfortable writing a Rec for someone they don't even know. I don't blame them.

But now I'm "locked" out of academia. I know some great young students who got accepted -- they are really just starting out! They are training and building models for the first time ever. They are outstanding young researchers, but they are just really getting their sea legs. They were shocked to find out I can't even get into the program as a PhD candidate, knowing that some graduates have interviewed at my company!

So, for the next application, I'm going to take the Math Subject GRE. The GRE is waived because I have an "advanced degree" but I think it will go a long way. Letters of Rec are trickier - I have been using professional references. Beyond that: what else can professionals like me do to avoid being sidelined for PhD admissions?

Answer 1

This is somewhat jurisdiction dependent but in your case it may be more feasible to aim for a PhD with a particular professor at the university without being enrolled in their classic graduate program. You do want a professor who is willing to supervise you as a PhD student but you don't necessarily need a graduate student stipend (which according to your background I would assume would be financial peanuts for you).

I know that in the German system getting a PhD advisor and getting money for your salary/stipend are two separate questions (although you often get both in a package). Having only a PhD advisor would also give you a lot more freedom in terms of the typical hours/ week commitment to a PhD and allow you to continue working (the total amount of time needed for a PhD doesn't change, so the PhD will take a lot longer if you do that).

I don't know how common this setup is in your jurisdiction but it might be worth looking into.

Answer 2

My gut instinct is that your application may also particularly suffer from focusing on math departments, based on the nicely concise but necessarily limited information in your question. In short: I suspect you're quantitatively very fluent and there's little question that you have the work ethic to see a PhD through. But you may be missing a lot of prerequisites I'd want for a math PhD.

We typically spend a good amount of time teaching math majors to write rigorous formal proofs in undergrad. PhD programs then continue this with additional years of higher level proof-based coursework. For example, at least a year or more of abstract algebra (groups, rings, fields) is a common core requirement, often with a prerequisite of an undergraduate version of the course.

Between being out of school for awhile and probably not having taken prerequisites, I'd be pretty concerned about how you'd do with these kinds of courses. Maybe you'd be able to pull out all the stops and develop a proof-writing skill set very quickly, but that's a risky bet to make when more straightforward ones could be available.

I hesitate to advise you either way on putting energy into the math subject GRE, but I feel compelled at least to warn you that a good score may not help as much as you'd guess. Many math departments are phasing the test out or already have as an application requirement. The test is in a very unusual format for undergraduate mathematics and doesn't necessarily say much about a student's ability to do research or write proofs.

That all isn't to put you off doing a math degree, but rather just to give some thought on why your application packet may stall. If math's what your heart's set on, fair enough. You may, as others have suggested, need some strategy to do interstitial academic work like a math masters or some postbac undergraduate courses to generate clear evidence of sufficient preparation. If you're a bit more flexible, other quantitative departments are often more flexible than math for PhD work: Computer science, biology/computational biology (or a bio adviser who doesn't need you do wet lab work), and applied math/statistics come to mind as departments where you can do a similar PhD to a computationally-focused math PhD without routing through proofs.

Answer 3

I'm a math professor.

Echoing what @user176372 has to say, a math program seems like an odd match for your stated background and interests. Have you studied abstract algebra, real analysis, or partial differential equations? If not, do you want to spend most of the next two years mastering these subjects?

Programs in data science or statistics (among other possible options) seem like better matches, and I can imagine that your background might carry much more weight in graduate admissions there.

This would involve applying to a variety of programs, and presumably moving.

If it is important to you to stay local, then ask yourself this question: what are your long-term goals with a PhD? The academic job market is difficult and getting worse. (I believe it may be better in statistics and data science than in math; conversely, it is horrifying in the humanities.) Moreover, due to the upcoming "demographic cliff", things are likely to get worse.

If you want a job in academia, you may eventually get one if you are lucky -- but you will certainly not be able to find one locally. More common is that you have to move at least once for a postdoc, and then move again for a tenure-track job (if you are lucky enough to find one).

If you want a job outside academia, then a PhD can help you get a foot in the door. But, it sounds like you have a Goliath-sized foot in the door already! There are some more research-oriented positions in government, industry, and nonprofits which you might be competitive for with your existing background.

Why do you want to get a PhD in math? My impression, without knowing you and only judging based on what you wrote, is that your interests would be much better served going in a different direction. If you really do want to get a PhD in math, then imagine that I'm the one reading your cover letter when you apply, and convince me that you are prepared for it and that it lines up with your long-term goals.

Answer 4

You have an extremely narrow application focus (1 university). It isn't surprising that you aren't sufficiently high on the "likelihood of success" scale if they have competitive admissions. Entrepreneurship isn't the same as research. Creating products isn't the same as extending knowledge. Valuable, but not the same.

One option is just to expand your search to other universities. That will increase your chances of admission, but no guarantees. The other option is to find a way to fill the gaps. Perhaps the math requirements are most important to form a basis for research in your field. You aren't locked out, but you may be knocking on the wrong door.

You can probably go talk to one or more people at that local university to form a direct path to a better outcome.

Answer 5

Lots of great answers already, I upvoted them all.

I very much agree that a focus on math after doing data science will look... strange. I am a math Ph.D. and have worked as a data scientist for almost 20 years now. While my grounding in a "mathematical way of thinking" was invaluable for my career, I have a very hard time picturing starting out in data science and then pivoting into doing classical proof based mathematics. And make no mistake: someone who is doing statistical learning theory in a math department is doing math and proofs, not data science. (They may be branding their work as "data science" because there is much more money for that than for measure theory. Don't be fooled by branding.)

So I would absolutely recommend you dig into formal maths first, just to you are certain you know what you are getting yourself into. Get a couple of undergraduate textbooks, e.g., those from Springer. Read the first couple of chapters. Then think seriously about whether you want to do this for the next five years. This earlier answer of mine might be helpful.

If you are still set on doing this, here are two things I would recommend:

• Talk to those professors whose research you are interested in. Just cold email them with a short mail and invite them for a cup of coffee. (Not everyone will accept, or even reply.) Find out what they think of your CV and portfolio, and whether they think you stand a chance - both of getting accepted, and of being successful and getting a Ph.D. Ask them what they would like to see you do to improve your chances.

  This shades into "figuring out whether you really want to do this" as described above. But beyond this, this may also get you a foot in the door. (Which is why you should not go beyond an invitation to a cup of coffee, to avoid bad optics.)

  Of course, do your homework beforehand. Read their last couple of publications. Find out what courses they offer. Look at their current and recent grad students and their research projects.

• Another, possibly longer-term method to improve your chances: you note that you haven't published anything, but have been doing scientific work. If there is anything at all out of that work you might be able to publish, then try to do so. You don't need a Ph.D. or an academic affiliation to publish (although the latter helps).

  Yes, getting a publication accepted can be a long slog. But if you do manage to do this, this can be quite impressive.

  In figuring out where to submit, that part about reading those professors' recent research will be very helpful. If you can place something in a conference or journal where one of them also publishes, this will provide instant name recognition. And conversely, if you find out (possibly the hard way, unfortunately) that your work is not appropriate for any of those particular venues, that gives you another important piece of information about the match between your interest and that of the people you are looking to work with.

Good luck!

Answer 6

Your skill set seems more like the competency that you'd need for a physics or computer science PhD than a maths PhD. The way you describe your goals, "I am convinced there are particular disciplines within Theories of Learning that I would like to study, and after lots of learning, become an expert in", sounds quite vague. This might be okay if you can back up your skills with an undergraduate degree in maths, but probably won't carry you if you can't demonstrate evidence of skill. I also get the feeling you view maths as a tool, closer to a physicist mindset (or possibly computer scientist) than a mathematician's mindset. Its also hard to judge if your statistical work is relevant, without training in the field you may think you did something difficult while in actuality to a mathematician its like a script kiddy saying what they do makes them a brilliant programmer. The other thing to be aware of is that master's level research generally just teaches you tools and skills that are used in research, but not actually how to do academic-level research itself (that is what PhD is for).

From this I don't think you are being screened out because you were a private sector professional, but probably because you don't demonstrate (yet) sufficient competency/mindset for a maths PhD.

I'm also not sure if a maths PhD best aligns with your goals. Why do you want to learn about theories of statistical learning? Are you trying to provide deeper understanding of the models that are taking over the world so they are less of a black box? Are you wanting to improve your models so that your business is stronger? Are you wanting to gain deeper insight into human intelligence by learning about artificial intelligence? Do you just want to know the maths behind the models?

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In what follows I'll assume you are financially independent/don't need to worry about money and can dedicate at least 2 or 3 full working days a week to studying without distractions.

If you want to learn the maths, enroll in a undergraduate or master level maths degree. This will teach you how to think formally as a mathematician does and provide you with a grounding if you decide to go into a maths PhD. You can then also begin to read reviews and books on your subject, for example https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/ might be relevant, though it is a relatively simple introduction to a mathematical view of machine learning.

If you want to do research, you may need to do the previous suggestion first. But you should also look at the webpage of the researchers and groups who look interesting to you, see if they have a colloquium or talk series and try to go along to one of them. At the colloquium you can try to talk to some of the researchers, ask them about their research and try to understand the big picture/their motivations. Focus on listening and asking them what they think you'd need to know/do to contribute to similar kinds of research if it interests you. They would be able to judge your level of compentence better than anyone over the internet can. Doing this for a while, you can get a better feel of the landscape and raise the idea of collaborating on some research, be aware that you are essentially asking them to take on another PhD student without recognition but if they think you are competent and have the potential they might be willing to guide you.

If you really want the maths PhD (either to move into academia or just for the title) you probably need to do a combination of 1 and 2 if you are restricting yourself only to the local university. You need to demonstrate that you are worth their time, since even if you are self funded, this is time that they could dedicate to another student who has a safer background and may promote their name/work if they go into academia.

Answer 7

Two more thoughts:

1. Start a masters program for math. There you will learn math, get in touch with professors, and maybe create some attention. This will help with your application, publications, and letters of recommendation. And it helps you to re-evaluate, if you really want to do Maths.
2. Have you enough money to pay for your own project? If you can provide enough money to cover your salary for four to five years plus the expenses of the university, you might be able to fund your own PhD position. Might be unorthodox, but why not profit from your success as a startup founder?

Answer 8

An additional idea: You could absolve the admission exams (having the subjects "math" and "probability theory") for an actuary certification path. Doing this might show the university that you have a working knowledge of probability theory at a high level and are fast at solving mathematical problems in this area such that your knowledge is applicable.

Note that to be successful the university should know what an actuary is. Example exams à la "I have solved a difficult exam like this one under high time pressure" may be helpful.