What to do during Math PhD to have options in industry?

Question

I have recently been accepted to a top five math PhD program. The department seems to have a good mix of pure and applied math, and there are plenty of opportunities for collaboration with other departments (Stats, CS, Econ, etc.)

I am most interested in pursuing math more on the applied side of things. Moreover, I would like options outside of academia once I graduate. Looking at the previous PhD alumni, this does not seem to be a problem - anyone not in academics is doing pretty interesting stuff in finance, data science, consulting, machine learning. However, I want to make sure I am not missing something along the way that these students did which enabled them to have broad and attractive job prospects.

I am especially interested in Analysis, Probability, Stats, Machine Learning, Econ, Mathematical Biology, Cryptography, and Applied topology. I would be happy to do work involving any one of these.

My questions are these:

1. What should I do during my PhD to be able to have good non-academic job prospects after graduating? (Would something like a PhD minor be helpful?)

2. How does it differ by field? If I want to do something like quantitative finance, what do I need to do versus if I want to do something like data science?

3. How can I find out more information about question two. As things change and evolve, how can I find out what it is I need in order to be accepted for positions and jobs involving areas that interest me?

I am not sure if I am exactly asking the right question, so if someone else has suggestions of what I should be asking, please suggest.

Note: There are a number of questions on this site that ask similar questions, ("I'm doing math but I want to go into industry") However I think my question is rather different. Firstly, I am hoping to pursue research with applications during my PhD, rather than focusing on super pure math. Secondly, I am asking this question before I have even started my PhD, hoping to know what I should do before, during, and after my program. Most of the other questions basically have the theme "I did a PhD in pure math, now what?"

Answer 1

Based on my own interactions with graduate students and post-docs, I would suggest:

1. Develop skills that are useful to potential employers. This includes basic communication skills and a broad background in data analysis and modeling as well as buzz-word computer skills (R, Python, Deep Learning, etc.)

2. Develop cultural-competence for the corporate world. Learn how to dress and act the part, preferably by immersing yourself in the corporate world through an internship.

3. Have some examples of your work (besides your papers and dissertation) to show to potential employers.

Answer 2

Another important factor here is choice of advisor. Look through the faculty profiles and see if you can find a good fit. This would be someone with industry experience, or that has managed to assign their students to industry jobs past graduation. It would be good to be advised by someone who'll be able to help you get internships at relevant companies and direct your research in the direction you want.

In my experience, math PhDs (with a smattering of CS/Econ/Stats) are highly employable in industry, even if they err on the purer side of research. I know several people who studied pure math and applied their problem solving skills in internships with very good outcomes, let alone if you are learning applied skills on the way. Other soft skills that you acquire will be extremely useful in industry - writing papers, speaking skills, problem solving and so on.

PhD studies are also an excellent time to try out transitioning your ideas into startups. Most good universities have tech connections to help you do that, try to look into that.

Good luck!

Answer 3

As a former arithmetic geometer currently on the industry job market, here's some advice/observations, current as of 2021 (things in industry do rapidly change though, so stay vigilant). I'm speaking from a US perspective and don't know anything about how this changes in other countries. I'm also talking about the labor market in a big US city with a large tech sector (e.g. SF, Seattle, Boston, NYC, LA...) - regardless of where you get your PhD, you'll likely find way more industry opportunities for math PhDs somewhere like this.

General advice:

• networking is really valuable, both for general knowledge about industry opportunities and for finding actual positions. Keep up undergrad connections, try to meet people who do quantitative research outside the math department (stats, econ, CS...) e.g. by going to their seminars, and don't be afraid to ask your friends to introduce you to people in their network who might be willing to help. Your university's alumni network is also a good place to look.
• Industry is way more flexible than academia and evolves rapidly; as a corollary, it's much easier to pivot your interests than it is to e.g. change research specialties. Math is awesome because it's extremely portable and ubiquitous, so definitely don't talk yourself out of opportunities because you have the "wrong" experience.
• Work on the job application process early and often. Doing internships during your PhD is a great way to learn about job opportunities, try out a field, and maintain industry connections. Plus you'll make more money than you would doing summer teaching... Keeping an up-to-date resume and LinkedIn and reading about careers on the internet is great too. Many PhD students spend 5 years in a Faraday cage, only thinking about their specific research field: if nothing else, this isn't great for your mental health (ask me how i know...).
• Whatever you do, take the time to build and maintain solid competence in general "quantitative skills". This means statistics, basic programming, and basic data analysis (e.g. working with R or Matlab). Ironically, pure mathematicians might be some of the only STEM PhDs who don't have to do these sorts of things all the time in their research, and industry people don't necessarily get this. You can take courses (including ones for undergrads!), build solo projects, practice with stuff like Project Euler, LeetCode, or Kaggle, etc. Depending on what kind of research you do, maybe you can write some Sage libraries to do computations or run statistical models to test hypotheses, etc.
• If you pick a sufficiently applied research topic, this all could get a lot easier. For example, having an advisor with industry connections or even just a track record of students with industry jobs would be extremely useful. The industry job market isn't bad for math PhDs even if they study extraordinarily useless things like I do (nobody's launching a startup using perfectoid spaces...), but if you become an actual expert in something useful (even from a theoretical/academic perspective), you could open yourself up to a very elite tier of job opportunities.
• Don't sleep on your "soft skills". Mathematicians have tons of opportunities to get really good at technical writing and communication to folks with a wide range of backgrounds. Take the time to get good at teaching, volunteer to talk in student seminars, etc. This is a crucial skill in industry and will be tested directly in interviews.
• Job opportunities for math PhDs are certainly not at all limited to the sorts of heavily quantitative tech-y industry I'm discussing below. There's consulting, law/politics/policy, education, technical publishing/writing, just to name a few. You can really leverage those "soft skills" above plus the prestige of a math PhD and your analytical skills to do just about anything!

Specific industries hiring mathematicians:

• Quantitative finance: these firms often seem happy to hire math PhDs who can demonstrate strong skills in statistics and competent programming (e.g. being able to write some Python or C++ code to run a statistical model; software engineering background isn't so necessary). "Quantitative researchers", especially at small hedge funds/proprietary trading firms, often work in a fairly academic/research-oriented environment, sometimes even publishing papers. These firms care about pedigrees a lot, so the prestige of your program and university matter (unfortunately!). If you have Putnam or Math Olympiad background, that's very helpful (I've even seen companies ask about standardized test scores?!?). To a lesser extent, having a strong publication record might help. Very few people have studied math directly relevant to quantitative finance (derivative pricing, stochastic PDE, etc.), so doing a PhD in that area would set you up very well. Doing something related to stats or probability is also a big plus, but all sorts of mathematicians are attractive applicants. These firms are willing to invest quite a lot of resources into training and care mostly about finding the "smartest"/most prestigious people. Jobs are 90% concentrated in New York and sometimes Chicago (plus e.g. London and Hong Kong outside of the US).
• Data science: here, you're really expected to have some legitimate domain expertise when you apply, at least if you're looking at jobs with the word "researcher" in the name (lots of "data science" jobs are things like database engineering with a fancy name). Jobs involving a large amount of theoretical research on ML models (e.g. at somewhere like DeepMind) are particularly competitive, and you'll be competing with people with machine learning PhDs. If you can do actual research related to machine learning, even if it's 1-2 side projects/papers, you're in a very good position. You're very strongly encouraged to have built a non-trivial ML project and have the code up on GitHub, e.g. competing in Kaggle data challenges. Programming skills are important, but mostly on the level of being able to hack together a solid model in Jupyter or R. Coursework or a PhD minor would definitely be useful here, and you should at minimum take some machine learning courses at your university. Strong stats/data/modeling experience puts you ahead of a "non-quantitative" pure mathematician.
• "Defense"/government cryptography: the NSA and similar organizations (e.g. the "Center for Communications Research") seem to consistently hire very many mathematicians. Background in cryptography or applied/computational number theory is great but definitely not a requirement. These are institutions with deep and immutable sources of funding working over a very long time horizon, and they appear to be rather happy to collect talent and provide space for fairly open-ended research in a wide range of subjects as well as specific domain training. Some general competence with programming is likely helpful but not critical. Having a strong academic/publication record is useful. There are a number of "postdoc" type positions and some "tenure-track" type positions; unlike universities, the NSA actually has the resources to promote a large number of its junior researchers. Obviously, you'll need to pass extensive background checks, much of your work will be secret, and you may or may not ever know what your work is being used for.
• Software engineering: this is an enormous and very wide field which appears to never stop growing. Outside of "FAANG", there can be stiff competition among companies for qualified applicants. Math PhDs are attractive and will likely help you get interviews and possibly bump you up a pay grade relative to even fairly strong undergrad CS majors. But you'll be expected to do the same technical interview as everyone else, which requires you to be able to solve tricky coding problems on a whiteboard. Taking undergrad or grad CS courses at your university is very helpful here, and you'll be expected to be familiar at a minimum with basic algorithms and data structures along with decent fluency in a programming language of your choice. Advanced CS course work helps. Building some sort of cool project/app and putting it on GitHub helps a lot. Big tech companies like "FAANG" (maybe now it's called "MAANA"?) have a lot of competition for jobs but also have better hiring pipelines for PhDs and lots of experience training people without a software engineering background. Startups are more likely to expect you to be able to build something useful right out of the gate. Networking is helpful, especially at smaller companies, so it might be a good idea to hang out at the CS department and make some friends.
• Blockchain/industry cryptography research: this is a fairly new industry and will likely look very different by the time you finish your PhD. At the moment (fall 2021), there's a lot of demand for talent but not an incredibly large pool of people with specialized knowledge. This field is developing very rapidly and ideas often flow between academic cryptography and industry, so being able to read a research math paper is a useful skill. Doing a PhD minor or doing math research on the theoretical side of cryptography would make you pretty attractive. It would definitely be worth your time to take a course or two in the subject if this is something you're interested in. Contributing to open-source projects or otherwise participating in the "ecosystem" would be a good idea too. Basic programming skills are necessary, and some software engineering background could be helpful. [Warning: when I started my PhD in 2016, one might have said similar things to the above about the data science industry. Since then, the talent pool has exploded and the growth in demand for industry research has tapered off].
• Industry general research labs: e.g. Microsoft Research or Google Research. I've seen such institutions recommended a lot on this site as industry destinations that allow you to keep doing something very similar to academic math research. The caveat here is that the job market at these places is also similar to academic math research - these are basically faculty positions with a different funding structure, and they hire accordingly.

Answer 4

Instead of thinking in vague terms about how your mathematical training can be applied in industry, I think it is much more fruitful to focus on problems in the real world that excite you. Most math PhDs pursue research problems by letting curiosity guide them. Things don't suddenly change just because you're going into industry. Particularly in the current era because of the tech boom, there are tremendous opportunities for bright, mathematically minded people in industry.

It isn't just power point presentations and talking to clients. Of course there's nothing wrong with that if that's the kind of thing you like. My point is just that mathematicians have a rare ability to think deeply and get to the core of a technical problem and many corporations are realizing the value they can bring.

If you haven't heard of them, two people to read about are Eric Lander and Jim Simons. Both started out as mathematicians and went on to become great figures in the fields of biology and finance respectively. It is notable that Jim started out trading in a discretionary manner and only later incorporated quantitative techniques. So rather than viewing "industry" as some monolith, think about what problems you want to solve and be confident that your mathematical training will give you a leg up.

Answer 5

I added a PhD minor in computer science to my mathematics PhD. It's helped market me for industry jobs. Every recruiter has mentioned it. One still needs to have the skills (and be able to demonstrate them in the interview) but the minor does seem to get you phone calls.