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.
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.