Pure Math in Industry

Question

I have a bachelor's degree in math (from Ghana) and for my final year project, I did something in applied topology; I explored the application of persistent homology to topological data analysis. I am considering applying for a master's degree and would like to do something that directly relates to my undergraduate project. From my research, any master's program that offers algebraic topology will best suit my preference. However, I have no intention of staying in academia. While I enjoy research, I would rather work in the industry, full-time, and then do mathematical research as a sort of pastime.

I am currently learning to be a professional data analyst. I am worried that with if I do my master's in a pure math field I will struggle to transition to industry. Any advice for me will be most appreciated.

Answer 1

The other answers provide decent general advice. But I fear that they lack the urgency that comes from having actually done this recently. For some background, I was just hired in the past 8 months as an assistant professor at a research university for a data science position, was also preparing applications for industry data science positions, and specialize in topological data analysis (TDA).

Say you want to be employable for data science positions (careful: "data analyst" tends to refer a different job) and get an industry job in a reasonable time frame at the end of a masters. You can do this in a theory-heavy course. If you are unfocused, it will cost you time (and salary) brushing up on skills during a job search after you graduate.

What masters courses should you look for?

It is absolutely essential that you find a course that helps you further develop a set of computer skills in addition to theoretical ones that will be visible to potential employers. An anecdote: I took an MSc like this, the courses included a full proof-based run through of Hatcher's algebraic topology. But also multiple courses on modern machine learning with significant coding components.

What won't help you get a job that quickly: Taking a course with no computational lectures, writing a very theoretical thesis without further developing your computational skills, and then throwing in your industry applications against computer science majors who won't cost an employer 6 months of time just to become productive. This isn't hypothetical: I've had multiple friends get done with very theoretical math PhD's, including specializing in algebraic topology, then take 6mo - 1 year of re-skilling and searching to get an industry job.

What skills are your target employers looking for?

I'd encourage you: Go look up job postings for data science positions you think you could be interested in, and look at the list of skills they'd like. They're going to include Python/R, SQL, probably familiarity with neural networks or CNN's, regrettably an increasing interest in Large Language Models, basic statistics, data cleaning, data visualization, etc. Some type of more serious memory management language like C++ couldn't hurt. Data science positions are also often interested in whether you have skills working with different types of data: Images, text/web scraping, "unstructured", geospatial.

You don't need to be an expert in all of them. Also, some demand for certain skills will change over time. You can't just blow building these up because they're all "easy", however.

What about more TDA?

If you take a Masters, TDA projects can be decent vehicles for a thesis that has some serious math while also benefiting from computer skills you want to build up to be competitive for industry position.

Computational topology and computational geometry for data analysis are not, however, particularly in-demand skills outside of academia. For example, persistent homology remains too expensive right now compared to much faster methods that are "good enough" for most use cases businesses currently care about. Obviously there's continual research work going into improving that situation, as the field is relatively young.

Which is to say, if you want to do more TDA/PH related work in a masters, but are angling for industry positions: It's something you can do, but you need to combine it with bulking up other skills.

Answer 2

In pure math, I'd guess that the job opportunities exist, but are very rare. Only a few companies can afford (in their thinking) to support pure research as it has no guaranteed payoff. Research in industry is mostly product focused, even at places like IBM, which does, by the way employ a number of "pure" researchers. But if it is hard to justify how you contribute to the "bottom line" it is hard to find a place.

Google, Oracle, IBM, and some others have a small (by the standards of the company) pure research staff, but most other companies don't, and rely on universities and government to make the fundamental breakthroughs that they ultimately depend upon. One major difficulty with pure research is that it is difficult to set time constraints. Insight and problem solution in math (and some other fields) doesn't and can't happen on a schedule. It happens when it happens if it happens at all. It is a risk, then, that a few companies are willing to take, but only in a limited way.

But if you want to do pure math as a hobby, sure, you can do that provided that financing your lifestyle doesn't take so much out of you that you have nothing left in you at the end of a long day.

If you want to do pure research and get paid for it, then I suggest that you keep open the possibility that it might be in academia. Even in a liberal arts (teaching) college you have more opportunity for pure math research than you would spending your days in a cubicle at a company in, for example, the auto industry. Just be realistic about what industry really cares about.

I think this is especially true for math and probably physics. In chemistry or biology it is probably a bit different, since, for example, the pharmaceutical industry "product" research can be pretty similar to pure research in those fields. Math, not so much.

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Applied math, on the other hand, has many more opportunities, including in finance, insurance, and others. But, applied math is very different from pure math, with different techniques and goals. The same would be true for other applied fields - applied physics, for example.

Answer 3

A pure mathematics program will teach you two sets of skills, one of which will be highly applicable in any career you choose, the other of which may or may not be.

1. First and foremost, a pure mathematics program will teach you general cognitive skills with respect to rigorous thinking, problem solving, and how to deal with impossibly complex tasks by tackling tractable pieces.

2. Second, the specifics of the work that you engage in will teach you particular skills that may or may not be applicable anywhere else. For example:

• Abstruse mathematical theorems and specific proof techniques will likely not be useful.
• Learning how to search through research literature to find useful theorems and proof techniques is more likely be useful.
• Even some pure mathematics may include computational exploration and data analysis, which is definitely useful.

Somebody hiring in industry will likely be interested in both what you can do right now and what your potential for growth looks like.

• If you are learning and producing visible evidence of competence with data analysis somewhere (whether in your program or outside of it), that will give you skills for "right now".
• The cognitive skills from your research program will more address potential for growth, if you can demonstrate flexibility of mind in how you apply them outside of the narrow context in which you've learned them.

Bottom line: there are valuable skills for industry available in a pure mathematics program, if you are flexible enough to understand how to apply them across disciplines.

Answer 4

A math degree is the last reason why anyone would struggle in the industry. While it may be country dependent, fields like data science/insurance/logistics etc. are full of people with math degrees and some positions even require one. I would argue that math is the best degree to have for those jobs, since understanding and using the correct math is the difficult part of the job. Using the IT tools (R, python, Excel, sql etc.) is the much much easier part.

Answer 5

I second everything Buffy said, but my undergrad was in pure math and I started on a masters program in pure math before ultimately transferring to law school so I may be able to offer some relevant experience.

As Buffy said, finding industry jobs that are truly in pure math is very difficult. I never succeeded. But finding industry jobs that appreciate someone with a background in mathematics, even if it is pure mathematics, is quite easy. I held jobs in programming, database administration, and data analysis in more than one separate industry.

Also while my current firm certainly cares more about my J.D. than my work in mathematics, the skill of thinking rigorously is always useful and I even make use of basic mathematical concepts surprisingly often in my work as a lawyer.

To somewhat add to what Buffy said, I can say that trying to do mathematical research as a hobby while having a full time job is challenging to put it mildly. While I still enjoy mathematics, the closest thing I have managed to do to research since I transferred out of the master's program is that I can still help my son with his math homework even though he's in college to be an electrical engineer. (I did manage to publish a couple of articles about relational algebra, but those were in trade magazines for database administrators about applying relational algebra to practical database administration and did not really develop a new idea so much as summarize old ones with practical examples). Perhaps you are more skilled or more disciplined than I am. Fermat quite famously did significant research as a hobby while being a judge. I have not managed to live up to Fermat's example.

Answer 6

Effectiveness in industry jobs requires some software engineering experience. Math majors without significant demonstrated software development under their belt require a lot of on-the-job training by a peer, and that's assuming that the position even has such a peer available. Employers will not consider such an applicant if someone comparable but with developer skills is available.

If you didn't have code in several small projects reviewed by a professional, you'll face many hardships IMHO. I have dealt with numerical code written by grad students in math fields - and one thing novices have a lot of trouble with is tendency to copy-paste and inability to factor out concepts at different levels of abstraction. They even have trouble just figuring out what those levels of abstraction might be to start with - a fact perhaps puzzling given their math background.

I've seen plenty of numerical code written for Ph.D. dissertations by people without guidance/review by a software engineer that was an impenetrable mess that could be shortened to 1/4 the length while making it self-documenting, easy to understand in terms of the application rather than implementation details, amenable to unit testing, and so on.

If you can contribute to open-source math libraries/projects that have code reviews in place for contributors - that might be a good way to gain experience. I have no idea how much of it does with topology, though. Open source data analysis is all the rage though so it shouldn't be hard to find something where you could gain experience.

It helps already if you can "code your way out of a box" for simple repetitive data wrangling tasks - say scripting with Python, numPy and other relevant libraries. Even that is a leg up over some applicants. The ability to write maintainable code takes a long time to develop, so you won't be an expert in a year or two anyway. But at least some familiarity with industrial software development processes - a familiarity that can be built contributing to open source - will go a long way towards making you a more desirable candidate.