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 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:
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.
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.
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.
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.
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.
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.