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Are there are any jobs in industry that involve more mathematics than just what a (good) undergrad program would cover: calculus, differential equations, real and complex analysis, some basic group theory, etc.? I'm stuck without an academic position but would love to do research, and I just don't see anything out there that isn't trivial. It's incredibly frustrating how little math there is available to me, and I have zero interest in doing mathematical modeling or becoming an actuary. So, what kinds of jobs--- salary, location, etc. are irrelevant--- involve math that's advanced enough to be interesting and challenging?

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    $\begingroup$ I don't think there is any non academic job where higher math is useful. I have a job in finance and I find the math either trivial, or boring even when it isn't trivial. The job still manages to be interesting though. $\endgroup$ – Matt Samuel Sep 10 '16 at 1:02
  • $\begingroup$ @MattSamuel: What's the interesting part of it? (My experience with finance consists of one undergrad course and some stochastic calculus.) Your profile says that you got a PhD a couple of years ago in math, so you obviously are deeply interested in the subject; what did you find in finance that was a substitute for it? $\endgroup$ – anomaly Sep 10 '16 at 1:09
  • $\begingroup$ Nothing. I still work on my research in whatever spare time I can find though. Ever since my daughter was born the combination of the full time job and the child have mostly eradicated my spare time. The job is interesting because of the programming I guess (that's the majority of what I do). $\endgroup$ – Matt Samuel Sep 10 '16 at 1:15
  • $\begingroup$ Blurg. That's depressing, but it doesn't make it any less true. Thanks. (Also, congratulations on your daughter!) $\endgroup$ – anomaly Sep 10 '16 at 1:17
  • $\begingroup$ Thanks. One bonus of a job in industry though is that I'm making almost triple what I would be making if I had stayed in academia. This may be particular to finance though. $\endgroup$ – Matt Samuel Sep 10 '16 at 1:20
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Depending on the areas of mathematics you find interesting, the answer may be an emphatic "Yes" or an emphatic "No".

Microsoft Research has a pretty strong group in Mathematics. Some members of that group, such as Michael Freedman, have background in very abstract mathematics and a world class research record, though their work at Microsoft is naturally geared more towards applications. The math involved in Microsoft Research's projects is certainly highly challenging, but whether it's interesting to you or not, only you can judge.

Google and Facebook also have strong research groups. I don't know what, exactly, you call "mathematical modeling", which is something you have zero interest in, but hopefully some of the focus areas of this group are of interest to you, and they certainly dedicate time for doing things that would qualify as research in academia.

The financial industry hires people with fairly deep mathematical background, usually deeper than what you'd get in a typical undergrad program. DE Shaw is known for having strong mathematical staff, and I have friends with math Ph.D.'s who were hired by Goldman Sachs and found both the interviews and the actual work very challenging. Renaissance Technologies is a pretty secretive firm but they are clearly hiring for mathematicians.

Another possible direction is bioinformatics. There's plenty of research being done in bioinformatics in industry, but again, I can't judge if this is an area you'd find appealing, or sufficiently "mathematical".

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  • $\begingroup$ Right, but (for example) do people in finance actually do any deep mathematics, or do companies just like to hire people who can deal with abstraction and statistics? There are certainly many math PhDs in industry, but it doesn't look like they do anything different than anyone else in the field. $\endgroup$ – anomaly Sep 10 '16 at 1:39
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    $\begingroup$ The computer companies (Microsoft, Google, IBM, etc.) have very particular areas of interest, and they lean far more towards computer science than math, so I wouldn't get your hopes up too high for those unless you have that kind of background. $\endgroup$ – Matt Samuel Sep 10 '16 at 1:41
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    $\begingroup$ @anomaly I'm not sure what you consider "deep mathematics" vs "dealing with abstraction". I also don't know why you say that the math Ph.D.'s don't do anything different than "anyone else in the field"; some of them do, some don't. There are lots of things a math Ph.D. can do at Google that a software engineer can't, and they do do those things. $\endgroup$ – Alon Amit Sep 10 '16 at 1:53
  • $\begingroup$ What exactly can a math PhD do that Google cares about? Searching on Google's career site for jobs requiring a PhD (in any field) show a huge number of positions for engineers, a computational biologist (which, at this level, I would say doesn't require particularly advanced math--- mostly straightforward statistics, but lots of biology), a linguist (ditto, with linguistics), quantitative analysts (so just basic mathematical modeling) , and various mangerial positions. That's it for the first fifteen pages, though I might have missed one. $\endgroup$ – anomaly Sep 10 '16 at 6:57
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Are you interested in reservoir simulation?

https://en.wikipedia.org/wiki/Reservoir_simulation

Or finite element method?

https://en.wikipedia.org/wiki/Finite_element_method

Or aeronautical and aerospace engineering?

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  • $\begingroup$ Not particularly, no. I am familiar with finite element analysis, but is it something that one actively develops in industry, or just a matter of taking a pre-existing algorithm and numerically solving a given problem with it? $\endgroup$ – anomaly Sep 11 '16 at 2:50
  • $\begingroup$ Why the down-vote? $\endgroup$ – cgiovanardi Sep 24 '16 at 14:00
  • $\begingroup$ @anomaly - Technical softwares are developed by mathematicians and physicists, mabe na engineer but with good backgrounds in those areas. $\endgroup$ – cgiovanardi Sep 24 '16 at 14:03
  • $\begingroup$ (cont.) It is not the scope of an industry to develop softwares, but to use them. Unless we talk about specificic companies that invest a lot in R&D. I have just found this company comsol.com $\endgroup$ – cgiovanardi Sep 24 '16 at 14:10

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