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While I love research and academia and would prefer to continue there, I've found myself in industry and haven't felt it's a good match for my interests. Moreover, I'm constantly frustrated by the lack of opportunity to do math research. I'd like to find something I'm genuinely excited about (not to mention using all the mathematics I've spent years and years learning), but I'm not sure what exactly is available in industry for people with backgrounds and interests in pure math. Math research, for example, is not really something that industry does at all. (In fairness, there are a couple of small exceptions, like Microsoft Research and probably something over at Google, but the era of large, well-funded industry labs is over.) As far as I can tell, there are three options:

  1. Work for a finance or insurance company doing some sort of mathematical modeling.

  2. Work for some sort of government lab, probably in cryptography or a closely related field.

  3. Work in something completely unrelated to mathematics, like software engineering.

Those options exist (and, in fact, I've had offers from each of them), but I'm not enthusiastic about them. Is there anything that's more compelling from a theoretical-mathematical standpoint?

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    $\begingroup$ Trading Houses and Hedge Funds absolutely have research groups. Goldman Sachs and Morgan Stanley are only two examples of successful I-Banks that have huge research budgets in the areas of quantitative research for derivative products and algorithmic trading. And before you turn away from applied math, the money can be phenomenally good - would you be more interested working at Goldman if your annual bonus was $500K or more? $\endgroup$
    – Mark Viola
    Aug 13, 2015 at 4:17
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    $\begingroup$ Well, I've known fresh PhD's to enter with a base at $100K+, with a first year bonus that is equal to a 1 or 2 multiple of the base. That is 1st year. $\endgroup$
    – Mark Viola
    Aug 13, 2015 at 4:30
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    $\begingroup$ And sincere best wishes next week! I hope you bedazzle them. Just act humble, smile a lot, and ask questions back if their questions are challenging to answer. Some of those places will still conduct stress interviews to test the prospect's nerves. Do not get rattled and you'll do well. $\endgroup$
    – Mark Viola
    Aug 13, 2015 at 4:33
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    $\begingroup$ @anomaly I wish you the very best. And I hope that the function at the fund actually provides some interesting mathematical challenges for you - more than you might be anticipating now. Alongside this, the compensation can be outrageously high! So, once you've made your first $10 MM you can do whatever the heck you want!! $\endgroup$
    – Mark Viola
    Sep 10, 2015 at 19:01
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    $\begingroup$ @Dr.MV: Has anyone actually done that? A full-time math professor, spending almost all of his waking hours on research, usually produces one major paper per year. It's unrealistic to expect that I can produce anything of value part-time, especially completely divorced from other mathematicians and the state of the art. Math isn't something you can do half-heartedly. I can certainly read math journals, lurk on message boards like this one, and so on--- but that's not the same as doing original research. $\endgroup$
    – anomaly
    Sep 10, 2015 at 19:12

2 Answers 2

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There is an abundance of research at Aerospace firms, Trading Houses and Hedge Funds, Private Labs (such as Bell Labs), and lots of others that have R&D divisions that use mathematicians, physicists, and engineers, all of whom focus on applied mathematics research.

Trading Houses and Hedge Funds absolutely do have research groups. Goldman Sachs (suggested read on Emanuel Derman, the prominent particle physicist who became famous at GS and in the financial derivatives industry) and Morgan Stanley are only two examples of successful I-Banks that have huge research budgets in the areas of quantitative research for derivative products and algorithmic trading.

And before turning away from "applied math," the money can be phenomenally good - would you be more interested working at Goldman if your annual bonus was $\$500$K or more? I've known fresh PhD's to enter with a base salary at $\$100$K+, plus a first year bonus that is equal to a 1 or 2 multiple of the base. And that is 1st year!

Finally, while a career in R&D might not be ideal, it can offer both exciting challenges different from those of a career in pure mathematics, along with financial compensation that would be difficult to match as a university professor.

On a personal note, I was a professor who left academics a long time ago. I have worked at both leading financial institutions and trading houses and did compromise the intellectual freedom for the financial security. It is a decision one makes and should be without future regret.

I wish you the sincere best in whatever path you choose. And remember, after you make your first $\$10$ million or so, you can always return to academics. And in the interim, use your spare time to stay current in the research literature and have as much fun with math as you can!

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You can always become a professor: get good pay, get grants from industry, and continue your focused research that you say keeps you excited in hopes of advancing your field, at least that's what your application will say.

Companies are intersted in one thing: making money. Pure theoratical math rarely, if ever, can be used in a away to attain money. Thats why most jobs you find are in applied math (modelling, optimization, applied statistics or machine learning, applied number theory in security, etc). A company can use applied math and apply it to a product, then sell that for money. What do you imagine a company can sell with pure theory? And who will buy it?

Even big companies like Google, Intel, and Microsoft only suppory the kind of research that's likely to advance one of their products so they can make more money. I can assure you their executive couldn't be less enthusiastic about abstractness.

That's why it's important, when applying for a job, to think of what both sides want. A university, on the other hand, will be delighted to have someone doing pure theoratical work with no immediate or obvious way to derive money from it. And you get to be around like minded individuals who care as deeply about theory as you, whereas in industry, people might ridicule you for being too abstract. So being a full time professor is an option to seriously consider before leaving academia.

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    $\begingroup$ Thanks for your comment. Becoming a professor and remaining in academia is indeed exactly what I want, but I got screwed over by my department and so wound up in industry. (It was certainly never my intention to do so, and I hate it.) I do realize that companies are purely profit-driven and aren't rushing to fund research into, say, surgery theory. Still, is there really nothing more abstract or deep available there? This is probably more a matter of finding the least-bad option rather than something I genuinely want. $\endgroup$
    – anomaly
    Aug 13, 2015 at 4:22
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    $\begingroup$ Uh, have you seen the kind of research that goes on at industry labs? Microsoft Research has an entire lab devoted to quantum computing (research.microsoft.com/en-US/labs/stationq/default.aspx), and I can assure you that Windows is not going to be running on a topological quantum computer any time soon (technologyreview.com/featuredstory/531606/…). It also has a complexity theory group; if you have any clue how Microsoft plans to make bank off proving that $\operatorname{VP} \neq \operatorname{VNP}$, I'd love to hear it. [cont...] $\endgroup$
    – Vectornaut
    Aug 13, 2015 at 5:11
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    $\begingroup$ [...] Microsoft's venture into computer Go seems more plausibly profitable (research.microsoft.com/en-us/projects/go/default.aspx): winnings from Go tournaments could be a valuable source of revenue! Microsoft researchers have published a computer-checked proof of the Four-Color Theorem (maa.org/external_archive/devlin/devlin_01_05.html), shown that a certain theoretical model of heart tissue is Turing complete (research.microsoft.com/apps/pubs/default.aspx?id=79271), [cont...] $\endgroup$
    – Vectornaut
    Aug 13, 2015 at 5:14
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    $\begingroup$ [...] and developed a tool for "discovering whether a formula can be rewritten into a Boolean combination of monadic predicates" (research.microsoft.com/apps/pubs/default.aspx?id=205099). That doesn't sound like the work of people who couldn't be less enthusiastic about abstractness. $\endgroup$
    – Vectornaut
    Aug 13, 2015 at 5:14
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    $\begingroup$ @Vectornaut: Although Microsoft Research does do genuine abstract research (in fact, I've spoken with a topology professor there who was working on quantum computing), it's a small group and not really representative of what's available in industry. There are very few companies that have that level of funding, long-term planning, or even interest in more abstract or ambitious long-term research. I'd probably be happy at Microsoft Research; but if I had the bona fides to join a bona-fide research group, I'd just go into academia like I had intended. $\endgroup$
    – anomaly
    Aug 13, 2015 at 5:14

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