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I'm in mathematics, and have recently gotten an opportunity to do applied/industrial research for a strong research institute in my country. As of now I have two MSc degrees in math and engineering respectively, and I also legally qualify as an Engineer. I have a passion for math, but also physics, computer science, and engineering. Thus I have very wide interests and want to continue to do research and interconnect these topics.

I fear that if I choose to go into research (my country's rough equivalent to the latter part of a PhD) I will not have the opportunity to conduct research in different topics, but rather have to specialize myself in a subarea of a math field.

At a research institute I will not be able to do pure math, but I'll have a very good pay and I'll at least get to do some applied/industrial math and publish in those areas. I will also be able to get a doctorate (latter part of PhD) via the research institute, but again it will be in applied math.

Right now I'm thinking of trying it out, and switch back if I don't like it as much, relying on my publications and teaching experience to get in somewhere.

Going fully into academia doesn't seem a good idea if I want to have varying research areas, but at least I'll get to choose my specialization. Going into industrial research I will have a varying job, good pay, but not as much intellectual stimulus and I can't choose my projects. How can one approach this, and what can I do to make either of these a better choice?

  • There are PhD programs and postdocs at the intersection of physics, mathematics, and scientific computation. – Jake Dec 6 '19 at 22:47
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    Unfortunately there are not too many jobs in the world where people will pay you to work on exactly what you want to... – Nate Eldredge Dec 6 '19 at 23:21
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    Hmmm. Why do you think that going into industrial research gives you a "varying job"? You have much less control their over what you do. You will have a manager who sets the research agenda. Yes, it may vary, but by their rules and needs, not yours. – Buffy Dec 7 '19 at 1:27
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    Agreed with @Buffy - the only way you are likely to have a "varying job" in industry is if you change jobs frequently, which may or may not be a good option for you, and the extent to which you fail to specialize may make it harder to go further in that career type. – Bryan Krause Dec 7 '19 at 2:19
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    @Buffy, the research institute performs both their own research and contacted research, which means that they get new problems pretty frequently. Within these problems you often get much freedom to model, build, and explore your own solutions, given that you get responsibility for a project, which they said they considered for me. In this case. – Seal Dec 7 '19 at 9:34
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My best advice, though it might not suit everyone, is to pick something, anything, that you are willing to work very hard at for a decade or so and become an expert in that field as an academic (my choice). At that point you can probably get tenure and with tenure you can set your own research agenda, more or less. But your ideal academic job may or may not be in your current country of choice.

In some academic jobs you can set the research agenda completely yourself, though you may need to convince people that you are contributing to the mission of the institution. But if you are a mathematician who made the grade in, say, topology, no-one will be likely to tell you that you need to keep doing topology, and few will tell you that you can't branch out into applied fields, or even quite different fields for at least part of the time.

And, in fact, many academics do change their interests over time, even if they stay fairly close to the core field they started in.

But an industrial job, now-a-days, comes with many restrictions on what you can do and many requirements on what you must do. The days of old in, for example, Sun Microsystems or Bell Labs, are over. People in the successors of those places generally can't just think deep thoughts and try to build something interesting. But even in those old style labs, the people permitted to do that were few and had already risen through hard work in the lesser jobs for some decades that left them at the top of the heap. There are surely exceptions, but I think very rare.

But the bottom line, is that if you want to be a polymath, then you need to work very hard to build a reputation that lets you have the freedom to do what you want. It is just more accessible in academia, I think.

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    Relevant PhDComics: phdcomics.com/comics/archive.php?comicid=2031 – Bryan Krause Dec 7 '19 at 2:24
  • I'll try it out then, and if I don't like it I switch. This far I believe that academia suits me better, and I have done original research before and I really enjoyed it. – Seal Dec 8 '19 at 16:47
  • Buffy hit around this point but I want to make this clear: becoming an expert in a given field doesn't mean ignoring every other field. Some of the most successful researchers are deep in one area and broad across multiple, much like a T-Square. The book Range by David Epstein is a good read if you want some examples of how people with broad interests were able to be productive. – kjacks21 Dec 9 '19 at 19:33
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IF you have any bent for business or just "seeing how things work in the real world" (can be interesting, to have to define problems, run interviews, etc.), you might consider industrial engineering. It can be very consultative.

There is some math in terms of queuing theory (OR) and statistics. Some physics in terms of whatever you are looking at (root cause analysis).

IF that works for you, depends on how much you still want really high powered math/physics. Because IE is not. But the actual problems and problem solving are pretty interesting and non-trivial.

  • I have already gotten a position at an institute/company that does industrial mathematics, and my job will be to construct more efficient numerical models for physics simulations used in various industries. To me, this could be interesting as they have given me large freedom to design it, mostly due to these methods currently being nonexistent. I will have great power to steer what I will use and if I need to research some new methods. If I turn out dislike it after the current proposed project is done, I can just leave and apply for academia again. – Seal Dec 7 '19 at 9:57
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  1. Do not get a PhD if you do not want to specialize. A PhD is a specialist's degree.
  2. Your specialty could be a methodology. If that methodology is applicable to many areas, you can have wide research interests but a focused expertise in that methodology.

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