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I am a 2nd year math PhD student. If one specializes in pure math (say dynamical systems with no particular real-world application in mind), how difficult can it be to transition into industry after the PhD? What are measures one can take to make this a smooth transition? I am not particularly interested in applied math at the moment, but I'm not too optimistic about the future of the pure mathematician (unless he/she solves some Millennium Prize Problem!!). I would like to think that I have the option of switching from academia to industry if I had to. I am haunted by words of one of my undergrad math professors: "No one should major in pure math. You major in applied math and you continue to study pure math if you're interested in it."

I have a M.A. in math, and my thesis was concerned with estimating the fractal dimension of sets arising in dynamical systems. My ideal profession with a PhD in math would be to teach and to do research. My research need not be limited to pure math.

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    Dynamical Systems have a lot of real-world applications. Do pay attention to real-world applications -- even if you don't spend any time analyzing them, those applications are quite helpful when it comes time to prove that your work is important. – Ben Voigt Sep 9 '15 at 2:45
  • Related: What are the potential pitfalls of having a PhD? (Also related: many of the questions in the sidebar) – ff524 Sep 9 '15 at 2:47
  • BTW the reference chapter (yeah, it's that long) of Haddad's book contains a lot of practical applications, beyond the many already used in the text -- even if your work has no known direct practical applications, at least you can demonstrate that you're contributing to an area with many. – Ben Voigt Sep 9 '15 at 2:50
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    If you think there's nothing for pure mathematicians to do except solve Millennium Problems, you have a huge misconception about where pure mathematics fits into the world. You absolutely must address that before taking your PhD plans any further because you can't possibly make an informed choice about your future, otherwise. Also, I think the advice that haunts you is really, really terrible advice. – David Richerby Sep 9 '15 at 8:18
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A lot of PhDs in theoretical mathematics end up "in industry" of one part or another. Many times this is not by choice, which is sad, but it also means the learning curve is not too steep. There is a reputation, reasonably well-deserved, that a PhD in mathematics teaches you how to think and solve problems in a rather fundamental and robust way, and that all other skills can be overlaid on top of that. Certainly I've seen PhDs in "purely theoretical" mathematics with no programming skills, actuarial or statistical knowledge, etc. be hired by industry. In fact many of these people get on-the-job training in the first year of their job...while they are getting well paid.

Well, but the job market is pretty tight all around these days, as perhaps you've heard. If being totally clueless outside of theoretical mathematics can land you an industrial job, being less than totally clueless will be even better. I advise PhD students that as soon as they have real thought of a non-academic post-PhD career they should explore this in a positive way, including mentioning it to their advisor so that aspects of their program of study can be adjusted. For instance, in my PhD program you need to take two exams in foreign languages, but one of these can be replaced by a computer project. Although I think the computer requirement would serve many would-be academics better as well, if you think you may go into industry, then reading in a third language is obviously not going to be as marketable as computer skills.

While you're in a PhD program in mathematics, talk to the students and faculty who have connections and experience in industry. (Realize that your thesis advisor may not be such a person. For instance I have zero industrial experience. I do not pretend to give advice in this area -- well, not specific advice, anyway! -- but I try to find other people who can.) Don't be shy or embarrassed about this. It's your life and you get to do what you want to do.

My feeling is that solidifying basic industrially applicable skills -- e.g. programming and even lower-level tech-savviness like spreadsheets, learning how to share and transfer files, etc. -- and supplementing with coursework and other training (e.g. taking actuarial exams; taking one solid course in statistics or financial mathematics) is a better bet and easier to do in your spare time than trying to change your thesis topic to something more applied. As above, my feeling is that most industrial jobs don't care what you did your thesis on, and having done it on something rarefied and inapplicable is actually fine with them as long as you have, or can make them confident that you can learn, the skills you will need on the job. But again, talk to people other than the academic lifers like me!

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    Its reassuring to know that even PhD graduates still get some training on the job. – John_dydx Sep 9 '15 at 20:47
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This question is likely to be closed in the end because it depends to a great extent on the exact details of your personal situation, and there simply isn't enough information available to us to know how things might work out for you.

You're certainly smart to be planning for the possibility of transitioning out of academia into a career in industry. The current academic job market can be extremely difficult for new PhD's and it's impossible to accurately predict whether the market will improve or get worse by the time you complete your PhD. Your own marketability in the academic job market will also depend on how successful in research you are as graduate student and post-doc. Finally, getting a tenure track job is to some extent a matter of dumb luck- many well qualified applicants fail to find a tenure track position while similarly qualified applicants do succeed. It's unreasonable to believe that this is all the result of a meritocracy.

What really matters in finding work in industry are your skills and experiences. There's certainly some value in having completed a PhD in mathematics, but when it comes time to interview for a job in industry, the most relevant sections of your resume are going to describe skills that you have (e.g. computer skills, communication skills, ability to collaborate with others, and ability to solve problems creatively) and relevant experiences that demonstrate what you have done.

As you go through your PhD you should take time to develop those skills that would be useful in both academia and industry and you should consider carefully whether you want to take time to develop skills that would be of more value in industry even if doing so might take time away from developing your academic career.

Here are some options to consider:

  1. Switching to a more applied area of mathematics.

  2. Earning an additional certificate or master's degree in a more applied area such as high performance computing, data science, or software engineering.

  3. Taking time off to work in an industrial internship.

Ultimately, it's your life, and you'll have to decide what's most important to you. It would be foolish to simply give up on the career that you've dreamed of, but it would be equally foolish to not have backup plans.

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You need to make a decision as to what the alternate career will be. This will depend a lot on your own aptitudes and interests.

Certainly, there are many roles that can make good use of a mathematician: both in terms of how they think and what they can actually do.

I would think that many of the latter involve being able to perform mathematical computations of some kind. In other words, programming.

So if you haven't already, consider making an effort to learn some computer science, software engineering and programming skills.

Note that these are not the same. Mathematicians who refuse to learn the difference are often terrible programmers. Those who do learn it are often great engineers.

Doing this:

  • May tell you that its not for you; better to know sooner than later
  • Can be very useful whether or not you continue as an academic mathematician
  • You may find you really enjoy it, and become the focus of a career

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