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How much should a mathematician confine themselves to a particular area if they are to be successful? My main discipline is PDE however, I have a heart for computer science too. I am wondering if I should work to get my knowledge in the ladder area up or continue what I am doing. My plan is to do research in PDE as a career, but is there possibly room for Computer Science in my research?

I guess, if I were to do both, the question boils down to if there exists such an occupation in which I could do both. Any other way, coding and computer science would be mere hobbies which I am fine with however, less satisfies with.

This question can be generalized to the cases of others too, though: What is more important, getting insights in your main discipline, or strengthening your knowledge in weaker, less familiar areas of mathematics that may be somewhat unaffiliated with what you already know?

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    I think you should do both : Concentrate on what you really want, but also study other subjects because it is always possible that you discover useful links that can help you to understand the important subject even better. – Peter Feb 22 '18 at 21:53
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    I'm a numerical analyst. For my late research theme I have to know ètale cohomology. Judge by yourself – Exodd Feb 22 '18 at 21:54
  • @Peter That is true although, I can’t see how computer science and PDE go hand in hand. –  Feb 22 '18 at 21:56
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    As to the question in your title, I think the study walls should be sufficient. I see no need for ropes or any other constraints. It's probably a good idea to lock the door on the outside and bar the windows. $\ddot{\smile}$ – Rob Arthan Feb 22 '18 at 21:56
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    @majormaki, since often in practical situations PDEs are solved numerically, "theoretical" results about stability, continuity in parameters, and so on are very important to avoid producing misleading garbage. – paul garrett Feb 22 '18 at 23:07
  • @majormaki . And the "mulligan" problem: Whether a sequence of iterations that converges actually converges to a solution. – DanielWainfleet Feb 22 '18 at 23:37

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A (most likely useless) tremendously vague and incomplete answer.

  • Have clear concrete short-term goals (depending on your definition of success). Work hard on these goals. This will: clarify what is your potential, your weaknesses, your motivation; speed up your capability of judging different career options/topics; force you to broaden your knowledge with purpose; meet professionals;...(many other benefits)

  • Keep an eye around you.

  • Make sure you're having fun.

Rgkpdx
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