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I'm a fairly new student in pure math, in my second year of studying analysis. In my first year, I took courses on basic real analysis using Rudin, and this year, I'm taking classes on measure theory (using Folland) and probability theory (using Durrett and Breiman).

Both years, I have/have been struggling to do well in the courses: I struggle mightily in getting proofs started and finishing them as well as coming up with examples/counterexamples.

I really enjoy pure math, but when it comes to actually solving problems/taking exams, I do rather poorly and really discourages me in pursuing the discipline. Could it just be that I'm just not cut out for pure math?

I'd appreciate any advice or comment. Thanks!

Shaun
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Mog
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    Twice in my master's program, I ended up in a class where no one made an A and I genuinely questioned whether or not I was cut out for mathematics, as they were leveling courses.

    The point is that you shouldn't let one class be the be-all-end-all of your mathematical career. Life goes on, and you learn to live with what you're given. That said, putting in the work into learning pure math is no small task on its own. Ask for feedback from your professors and see if there's any guidance they can provide on what you did wrong or how you could've improved your answer to maximize your score.

     – Decaf-Math Sep 17 '18 at 21:35
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    Read this by Terry Tao. – Shaun Sep 17 '18 at 21:37
  • Why did people downvote? – Olba12 Sep 17 '18 at 21:42
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    Maybe you should try other branches of Mathematics which suits better your "brain". Anyway IMHO if you enjoy it you will spend a lot of time on it and eventually become good at it. Do not let bad grades discourage you. Doing proofs is a matter of time, competence and creativity. Try to study more than the book suggested by the prof. (a more advanced or general text) in order to get a picture of what is going on. – Overflowian Sep 17 '18 at 21:43
  • Thank you guys for the advice and the recommendation. I guess my worry is that since I'm struggling in rather elementary level of mathematics, I cannot help but ask myself if I simply lack the 'reasonable amount of talent' as Tao puts it. – Mog Sep 17 '18 at 22:20

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For me the overriding question here is: Do you enjoy the work (the intellectual struggle) and have you proven you're in the top strata of your cohort (classmates, students at the same level in other schools...)? Note that only those who persist and struggle, no matter what their intellectual gifts, ever really succeed. (Good Will Hunting is mostly fiction.) Look honestly into your future and see if you have a career ahead of you.

David G. Stork
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  • I do enjoy the work, and in terms of proving myself in comparison to my cohort, I'd done very well in every class prior to the analysis courses, but since taking on analysis, my performance has been subpar. As such, I guess I'm beginning to question if I'm really cut out for this despite some of the successes I've had previously in other courses. – Mog Sep 17 '18 at 22:22
  • Might it be that you're a visual learner--great for geometry, trigonometry, much of calculus... but not for analysis and number theory? – David G. Stork Sep 17 '18 at 23:14
  • I never really thought of myself that way, though I did extremely well in organic chemistry as well which may be an evidence that I'm a visual learner... I managed to do ok in abstract algebra as well though, for some reason I just struggle with analysis mightily it seems. – Mog Sep 17 '18 at 23:35