Hi,
I’m a second-year PhD student in mathematics at a large university in the US. I really like the research group that I’ll be working with; my advisor is great. The issue is, we have strict requirements for quals, and I’m teetering right on the edge of being forced out of the program. I have two more attempts, but afterwards, that’s it. And I’m also really bad at the whole test-taking thing, so I don’t like my odds.
So, as a young person with an MS in mathematics, what exactly would the options be for me outside of academia? If I flunk out, I want to have some idea in mind for what I can do. My interests in math have always tended towards the more abstract (functional analysis and dynamical systems); it’s the quals in either PDEs or numerical analysis (the applied subjects) that are messing me up.
My PhD is stressful and anxiety-inducing, but at least it gives me purpose and direction in life. This time last year after I failed first year PDEs I wound up in a psychiatric ward. So, I want to know what possible options there are so that I don’t end up in the same situation. I have issues with a lot of the “standard” options for industry mathematicians though:
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I utterly despise programming. I can not think of a more miserable, dreary existence than becoming a professional programmer, or working in the tech industry and having to code regularly. I know how to do it. I’m doing as much as I need to to study numerical analysis to get that qual over with so I can go on to things in math that I want to do; and in undergrad I double majored in math and CS. But I just can’t do it 8 hours a day every day for the rest of my life, and this is a lot of what people recommend.
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I don’t want to work in one of those white-collar banking stock brokering environments. From undergrad I know the sorts of people that those places are filled with, and they are not really people that I’ve ever been able to get along with. Even teaching “math for business majors” my students made me feel uncomfortable at times. (Plus, there are people with specialized degrees in these fields who would be better for them; plus, again, those jobs seem to be coding and solving PDEs). In particular I’ve been personally fucked over by the insurance industry enough that I will never work there.
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I could try to go into teaching I suppose. I’ve quite enjoyed it, and I get good reviews. But, aside from my TA duties here, I have no formal qualifications. My understanding is that most places require an advanced degree specific to teaching in order to be a teacher, and I don’t think I can put myself through more years of graduate school coursework just to go for my consolation-prize career.
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I can’t easily fall back on my family for support. We are not on speaking terms.
It’s an absolute long-shot, but are there any careers that feel like the research part of grad school, but without the stuff that’s miserable about it (the coursework and bureaucracy)? Money is not an issue for me at all. If I can get over the hurdle of early-on coursework and quals, I will live a far more fulfilling life in grad school making 19k/year than I would as a wall-street tech CEO investor. But that’s far from a guarantee at this point, and I just don’t even know where to begin looking for any jobs at all I would want to do outside of academia.
I have a friend that had an MS in math and he worked for an airline doing very long term forecasting to determine flight schedules to maximize efficiency. He found it a bit depressing though as what he would submit would never be done as it went to other groups who modified it as it got closer to now. In other words he made idealized plans that would be modified based on reality.
Does your university have a career center? Check them out because a lot of times they have good relationships with large companies and smaller local companies and know what the job market is like. Usually this just involves making an appointment with a career counselor and telling them exactly what kinds of things you like doing (math-related) and don’t like doing (programming, bureaucracy.) There are jobs that have titles with words like “Analyst” and “Design” that might be right for you; the career center will be able to point you in the right direction.
I’ll give it a shot. My undergrad’s career center was basically worthless for me (the one piece of advice that they would give out is, ‘make an account on HandShake’, and then they did nothing else productive), but maybe at a larger school it will be better.
I utterly despise programming. I can not think of a more miserable, dreary existence than becoming a professional programmer
That’s hilarious to me because I feel the exact opposite way. Love programming except when it involves heavy math (e.g. lighting). Saps all the enthusiasm out of me. I hope you find the right career path for you because from reading your comments you seem super stressed and overworked!
I’m glad there are people who like programming more than I do! Thanks for the support.
Do any of these suit your fancy? (For example)
You more than likely could find opportunities outside of the normal office, if you are willing to work outside of an office, possibly relocate.
I myself am pivoting from Offensive Infosec to rebuilding outboard motors (boating), installing marine electronics, Starlink, navigation etc etc, and I also repair laptops, swap out phone screens and general tech I could do 10/20/30 years ago. It does not pay nearly as much, but it’s fun, I’m outdoors, and I absolutely do not deal with Office Types or fucking HR.
Most importantly the people and clientele I deal with treat me as a seasoned professional and a whole human being, not some cog to be muscled around.
My last contract was a 6m remote position with Interpol (France) working in the Financial Crimes division, and if that could have turned into a FTE role I would have jumped on it. The French are a WONDERFUL people to work for & with.
Good luck my friend, keep positive.
All of them except the licensed trades. You can get any of those jobs by undergoing the proper training.
But basically go on indeed and browse the list of jobs. You can have any one of those jobs, in principle.
I know a little about the academic system. it’s not an easy market to succeed in. but if you do it’s a wonderful life. you’re free to work on problems you find interesting, without worrying about whether or not they are profitable.
sounds like you genuinely love doing research in math, given that you put in a lot of time and voluntarily turned down a cushy job.
my suggestion is to put your nose to the grindstone and pass your quals. it’s not easy and not everyone makes it… but it sounds like the path to the career you want is this way.
What about the public service? I don’t know about where you live, but in my country the public service doesn’t care what degree you have, just that you have one. Look into the graduate programs of your local/state/federal governments.
Your MS degree already puts you ahead of 95% of everyone else, all the PhD would do is add 4%. :)
I gotta be honest though, I don’t know what jobs require a math degree, maybe something in aerospace? Could be a good gig under a new Trump/Musk administration, lots of money going to SpaceForce I expect.
Maybe? With the recent DOGE stuff I’m not convinced that the NASA budget will do anything but shrink, and if I were to do aerospace I would probably want to do it under NASA. (I’m a pacifist, and don’t think I can work for the militarized SpaceForce nor contractors like Boeing while still maintaining my personal code of ethics).
But, I will definitely look into it as a possibility.
Oh, not NASA, the MONEY is in private industry. Boeing, Northrup, JPL, etc. etc. etc.
https://mckelveyconnect.washu.edu/blog/2022/02/04/top-10-aerospace-companies/
Huh, Honeywell, they could be a good choice. GE Aviation too… I’m mostly aware of GE engineering from their medical equipment division.
Isn’t JPL NASA?
Again, I don’t think I can personally work for military contractor companies like Boeing, Northrup, etc.
I think generally speaking mathematicians are hired by insurance companies, the government, local administration. Random facilities that deal with studies and statistics… There is some overlap with computer science and there are a lot of technology companies out there, dealing with all kinds of domains, Analysis such as signal processing, statistics, more applied things that require maths for engineering, more abstract things like proofs that algorithms do the right thing. Optimization, robotics…
I mean if you dislike sitting in front of a computer in some office, all day… Teaching might be a good call.
Or see if you like electrical engineering. That includes some more at hands dynamics. And you also do a lot of calculations and integrals. I’m not sure how easy it is to get there without studying it. But some aspects of engineering might require formally trained mathematicians.
I will never work for an insurance company. And just saying “the government” is so vague and nebulous as to be meaningless; at least in the US where I am I think it’s mostly either military/‘defense’ stuff, or essentially spying on people. Neither of which I’m comfortable doing.
I’ve never heard of random facilities, but it warrants looking into given all of the things that you’ve mentioned. I’m not interested in all of these things, but it definitely sounds like it has a lot more to offer than most other “mathy” jobs. You also say “more abstract things like proofs”, but proofs are the entirety of what math is if you have a math degree.
Electrical engineering is its own discipline, separate from math. Unless I go back to undergrad and study EE from scratch, I will never be competitive in that job market against people who have specialized degrees in it.
If you have used Matlab, Or R, there is a huge range of data science that only really requires an undergrad in math. Hospitals that run their own Clinical Trials usually have a consistent need.
Really you’re eligible for anything statistics related, and there is a lot out there. Some job titles to look for:
- Data Scientist
- Statistical Analyst
- Statistical Programmer
- Signal Analyst (this is usually government related)
- Data curator
I will never work for an insurance company.
Sure, you do you. I read your complete post only after commenting, so it’s the common advice, but won’t suit you. I mean you’re probably just another corporate drone there, and if you have some negative experience, some more reason to avoid them.
“the government” is so vague
Yeah, I’m deliberately a bit vague here, since I’m not from the USA. A close friend of mine works for the city as a mathematician. Doing stuff about sustainability and the environment. They do things like measure the emissions from cars throughout the city, come up with projects and plans for the next 10 years, sustainability, bicycle lanes… Recommend what to do and what not to do. I don’t really know what else a city does, but they do a lot of things, requiring a lot of professions. I think the same applies for the state and the national government. And there are some jobs that really make the world a better place. And probably also a lot of mundane ones.
Electrical engineering is its own discipline, separate from math.
In my time at uni, I found a lot of interesting stuff happens where disciplines touch each other. I’m not sure if that’s the right way to phrase it. But a lot of advancement happens at the boundary for example between engineering and computer science. That’s why I brought it up. I’m not sure if it helps, you might be right. If you didn’t go through electrical engineering, you probably won’t be able to work in a lab and do experiments, or design things closer to engineering, since you don’t have the background knowledge on how to do experiments etc. The maths is the same, though. I think it’s a bit questionable what kinds of jobs this entails. Probably at some startup or a research institute. There’s a lot of PhDs at their door signs, but not all of them.
“more abstract things like proofs”, but proofs […]
I meant things like functional programming languages. Proving that something doesn’t have any side-effects. Calculating with mathematical correctness, that a robot won’t be able to harm a human, instead of just coming up with some algorithms that you think do the job. Or optimization or writing algorithms for hard and computionally expensive problems. That’s all kinda pure maths. And I’d say 70% of studying computer science is about mathematical background, not programming.
Might also get you a job teaching quantum physics … which is 90% math. Used to know a physicist who worked for the aeronautics industry doing math to reduce turbulence.
Well, my perspective is shaped by computer science anyways. I think it’s a very broad field these days. I don’t exactly know what OP likes about maths, but not all of CS is about numerical analysis and programming… It’s certainly also not about quantum physics either, except for the few quantum computer people out there. The rest of us like numbers and determinism…
I don’t know quantum physics though. It involves a lot of math, but it also involves a lot of physics which I don’t know. It’s something that I’d like to learn at some point, but right now I just don’t have the available bandwidth to learn it - and I definitely can’t teach something I don’t know.
involves a lot of physics which I don’t know.
Introductory QM is for undergrads, who also know next to nothing about QM and not that much about physics … and who are not usually familiar with all the probability stuff.
I’d bet there are plenty of profs who’d like to unload that job and get back to their desks. Might be worth talking to some places about. There are also physicists who aren’t math wizzes … Einstein always had a mather assistant hanging around, even after General Relativity.
Introductory QM is for undergrads, who also know next to nothing about QM, and I’d bet there are plenty of profs who’d like to unload that job and get back to their desks
Yes, so the job would be given to physics grad students. Which I do not know enough physics to apply to be.
If I’m in a position where I’m being thrown out of my grad program with just a masters, I’m not then going to turn around and say, “well, time to do it all over again, this time with a field I’m less passionate about!”
You didn’t mention passion, you only mentioed jobs. OK, well, if you have passions you might get find that you don’t need a PhD to team up with any of those dozens of current hot topics … just passion and the talent and drive to create good new work. I have no doubt that story’s been repeated many times.
Look up the Paul Erdos story.
Paul Erdos got his PhD in mathematics when he was 20 years old. If you wanted to name a famous academic without a PhD, you should have gone with Freeman Dyson.
But yes, I need to not starve to death in case I need to leave my program. That’s why I mentioned jobs.
How broadly do you dislike programming? Data science kinda stuff could work for you if the main focus is on modleing and understading data, even if that means actually implementing the models and the algorthms by programming.
How broadly do you dislike programming?
After undergrad, it seemed like I had two career paths. I could either apply for PhDs in mathematics, work 90 hours a week for 19k/year in a state a thousand km away from anyone I’ve ever known; or I could have tried for a cushy entry-level coding job making 6 figures starting salary in an area close to all my friends from undergrad, and working something normal like 40 hours a week. I chose the former.
I am currently doing what little coding I currently am in an effort to get it over and done with ASAP. My plan is to never write another line of code again once I’m done with my numerical analysis courses.
90 hours a week math? Sounds unrealistic, reminds me of somebody at the faculty who said he would spend similar hours at the office during his phd. He also said it was out of guilt and the extra work didn’t really amount to anything due to fatigue.
To me it sounds like you should first address whatever mental issues you have going on.
Looking at my calendar from this past semester I was in 3 courses, which each met for 3 hours had 8-10 hours of homework each week. I attended 4 weekly seminars (1 of which I was helping organize; two of which I presented in some weeks). I taught one course which met for 4 hours, double that for class prep. I had 5 hours regularly scheduled in the tutoring center, plus an office hour. I’m slow at grading, so it often took me 4-6 hours per week. Plus an hour a week for my advising meeting, and we’re at 60 hours before I even begin talking about when I’m doing my own research - I typically try to devote my weekends and also Thursday afternoons in their entirety to either reading math books of interest to me or papers of interest to me (I do the rest of that stuff MTWF).
So it’s not quite 90 hours a week every week. There are weeks when the tutoring lab was shortstaffed so I needed to pick up an extra three hours there. There were times when I would proctor a 3-hour exam. There were lots of severe injuries in my department this semester so I’ve covered people’s classes too. So there were a lot of 90 hour work weeks just due to the structure of everything, but I guess saying that every week is a 90 hour week is an exaggeration. I don’t think I’ve worked fewer than 75-80 hours a week all semester though.
I am not unconvinved that you actually do spend an insane amount of time at the office.
I am also convinved that you could be 50%+ more efficient if you just cut corners where you needed to. And also, not on the brink of a mental breakdown.
I only spend one hour a week in my office for my office hour.
Is your brain unable to comprehend what I mean by ”at the office”?
Evidently.
are you good with digital signal processing? every radar manufacturer needs this
In undergrad I did a project on harmonic analysis and wavelets, with some attention having been paid to the signal processing applications. (And by that I mean I learned enough to say ‘this has applications in the fields of signal processing and image compression’ in the abstract). But at this point it’s years ago and I don’t remember too much.
AI is currently all the rage. I know a guy who does neural networks training, and it’s the closest job to Pokemon trainer that you can have. He does not know any programming language, it’s all purely data processing, and it requires a heavy math background. It’s still an 8 hours per day job in a corporate environment, and a half of it is fixing his computing farm, because there’s no dedicated sysadmin for replacing burned videocards.
Another math-heavy option is signal processing. I’ve worked in a company which produces wireless communication hardware, it’s like 200 people, and there were two signal processing guys who patented an algorithm which increases data throughput by something like 0.5% in some specific high-noise scenarios, they are listed together with CEO on their website About page. That said, all the easier tasks for signal processing are already done, we’re already at the theoretical limit of Shannon theorem, so you’ll only be making gradual improvements.
I would also recommend cryptography research, but it requires a lot of coding knowledge, even if you’re not writing any actual code, and paranoia is pretty much a requirement.
It’s an absolute long-shot, but are there any careers that feel like the research part of grad school, but without the stuff that’s miserable about it (the coursework and bureaucracy)?
There’s no getting away from the bureaucracy, but it is possible to get career positions in academia – and I don’t mean as a professor, either. Check your university’s job site. If they’re big, they almost certainly have one. Get to know your professors too, and make sure they’re aware of the things you’re good at (even beyond your immediate subject area if you have additional hobbies/interests/skills) so they can help you find a landing place if things don’t work out where you are. If you’re willing to do programming – even if you don’t like it – there is a hell of a lot of stuff that needs to be done in academia, and some of it pays enough to live on. It’s possible to carve out a niche and evolve a role into a mix of stuff that you’re good (enough) at but dislike, and stuff that you like but which doesn’t necessarily always have funding if there’s some overlap…
Do you want fries with that?
Real talk, programming is your best bet. Companies don’t hire “smart” people anymore in the hopes they can teach them to do the job, so the math background doesn’t really put you ahead of someone with specific training.
If you hate programming though, I would pop back into undergrad and get a second bachelors in Accounting (you should be able to skip all the gen ed reqs). You could prob do it in 3-4 semesters.
