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This is a bit of a meta question I guess but I was wondering to what extent does a career mathematician need to use multiple areas of math in their profession?

Example, is it possible to exclusively work in analysis or have most of the analytic tools been exhausted and everything is moving to a more algebra feel?

As a background to the question, I am exiting undergrad and trying to decide what to do, I learned I like analysis but I have a hard time caring about the other topics and I loathe algebra. I'm trying to decide if career wise if I should continue.

Undergrad101
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  • It is wiser to talk about this with some other senior members of your department, then to rely on the answers you get here. Why don't you talk to some people doing research level analysis to see what they know about other areas of mathematics? – Sebastian Goette Nov 09 '15 at 17:34
  • "Why don't you talk to some people doing research level analysis to see what they know about other areas of mathematics? " That was my intention here.... – Undergrad101 Nov 09 '15 at 17:37
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    Well, this is not precisely a place to talk about something… Put differently: Your question is much too broad, one needs more detail about you and finally, all answers would be only helpful to you and nobody else. – Dirk Nov 09 '15 at 17:50
  • The question isn't broad nor is it specific to me. In other words it asks to what extent does a career mathematician in analysis need to be interdisciplinary? – Undergrad101 Nov 09 '15 at 17:55
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    If the need to learn a piece of algebra in the course of reading papers or conducting some research in analysis is a deal-breaker for you, then I'd guess that a career in academic mathematics is not a safe bet for you. You can substitute any area of math for "algebra" here. Generally, I believe that choosing a career path in mathematics based on what you want to avoid is ill-advised and a little strange. Your question reminds me of another discussion: http://mathoverflow.net/questions/165405/category-theory-free-areas-of-pure-math-category-theory-loaded-areas-of-app – Todd Trimble Nov 09 '15 at 18:14
  • (Keep in mind too that you will probably have to pass qualifying exams to enter a PhD program, and usually this involves an algebra portion.) – Todd Trimble Nov 09 '15 at 18:16
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    @ToddTrimble I agree with the general thrust of your comments, but the one about quals is not universal outside North America. (Doesn't apply in the UK, for instance) – Yemon Choi Nov 09 '15 at 18:27
  • @YemonChoi Oh, okay; thanks. I might have known that before but forgot. – Todd Trimble Nov 09 '15 at 18:28
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    Pursue? Yes. Succeed? Not likely. Even if you just limit yourself to looking at analysis papers on the ArXiv, you will see many of them reaching out to other disciplines to borrow from or lend to. There is room for purely analytical solutions to classical problems, but I would be surprised if you had more than 2 analysts out of the thirty or so on MathOverflow who might read and answer your question and suggest to stay narrow and avoid all other realms. I'm often reevaluating my knowledge deficiencies to decide what to repair. Gerhard "Remember To Make It Fun" Paseman, 2015.11.09. – Gerhard Paseman Nov 09 '15 at 18:38
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    Let me add, for the benefit of the OP, that one may grow to like or appreciate different things after one finishes a first degree. "Analysis" and "algebra" are not these monolithic opposites that they sometimes appear to be in students' minds. If there is some algebra you find opaque or hard to follow, there may be other parts which are more to your taste – Yemon Choi Nov 09 '15 at 18:54
  • The short answer is "yes". One can make a career in mathematics by pursuing just one narrow area. Examples are abundant. – Alexandre Eremenko Nov 09 '15 at 21:48
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    academia.stackexchange.com? – Fan Zheng Nov 10 '15 at 01:22

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