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I finished my PhD in probability a few years ago and left to go work in the industry as software engineer in operating systems and databases. I sometimes ponder whether I can go back to doing research, perhaps on a part-time basis, if I somehow transform my character to have more self-discipline. When I was an undergraduate student, I really loved mathematics. Even now, on my spare time, I frequently go over my old courses and, as Terrence Tao puts it, learn and re-learn old materials. Each time it brings me great pleasure and newer insight.

What I have trouble with is actually spending time solving research problem. With absolutely no intention of offending mathematicians, I find that most of the open problems in mathematics don't hold that much interest to me because I find them too narrow. I really had a tough time with the proofs in my PhD thesis because they are hard and I couldn't sustain consistent work each day. I prefer discovering new connections and asking my own questions, such as pondering on the connection between complex analysis and probability or asking "what if I remove this assumption" and see if I can derive new theorems. Even then, I usually can only do that for one day or two. I simply cannot do it day after day like a professional researcher. I would go back to my old habit of debugging and writing programs which I can do for 8 hours a day five days a week no problem.

Thank you for reading so far. My overall question is, how do I determine if my lack of success in research mathematics is due to lack of interest in research or lack of self-discipline? Can I just use something like the pomodoro technique and build up my tolerance for prolonged mathematics research?

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First of all, you completed a Ph.D. in mathematics-- I would hardly call that a "lack of success."

Secondly, I'm a big advocate for getting paid to do what you're good at. And from an economic point of view, that's the best thing you can do for society. If you want to tinker with math problems in your spare time or build up self-discipline and concentration skills, by all means, go for it. Such things will sharpen your skills in every aspect of life. But humans are pretty straightforward creatures: we tend to pursue and get better at what we're interested in, and we flounder when put in career paths that just don't match our personalities. You're not a lazy or unintelligent person for not wanting to do math research. You already tried the path when getting your Ph.D. If it didn't fulfill you then, it's definitely not going to if you try to force yourself back into it.

  • Thank you so much for your feedback. It is very useful. – Shuheng Zheng May 24 at 21:30
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The term and the field research is very broad. Roughly I would distinguish

  • fundamental research

  • applied research

  • interdisciplinary research

and in my opinion identifying which one you fit more could be a first step or looking into applied mathematics research.

Reasons you might not like working in both:

  • you work pretty much most of time alone in lab/office, apart from conferences but are a very social and communicative guy (social gap)

  • you don't see an (immediate) use of your results for society (purpose gap)

  • to much theoretical/mathematical background necessary (with PhD can probably be ruled out, maybe IQ gap to be easily competitve and successful)

  • you don't have the right personality and have to force yourself to do research day by day (personality gap)

There is the option to do a personality test (Myers–Briggs Type Indicator). I'm not sure how relieable it is to identify your personality and how other types fit into research, but I made the test and was characterized as INTJ:

INTJ: The Scientist. INTJ (introverted, intuitive, thinking, judging) is an acronym that represents one of the 16 personality types described by the Myers-Briggs Type Indicator. People with INTJ personalities are highly analytical, creative and logical.

While I would suggest to you to make a personality test, I would also suggest to rethink and remember your university time, from beginning to end and what courses/topics you really liked and if you see there a chance of research at an university or institute. Applied and interdiscplinary research profits a lot from scientists with fundamental research AND industry experience and is by far much bigger and more researchers are working in it than in purely fundamental research.

An article of timeshighereducation also suggests that many top-scientists didn't have best grades and I see this as a confirmation that many of above factors have to match for a personality (not necessarily being INTJ) fitting a distinct position in research like it is known for people with autism-syndrome to be only productive in a suited working environment or fulfilling special tasks.

To tell a personal anecdote, I started studying physics because of an strong interest in particle/astrophysics like many other physics students. To my experience most of such motivated students later don't even write a master nor a PhD thesis about such topics due to breaking up studies, too theoretical/mathematical necessary background, vanishing interest, other exciting fields in physics at the local university, better job chances in there or not seeing themselves in hardcore fundamental research and the ivory-tower their rest of life (my case). I do now applied physics as post-doc and love it. I did all astrophysics courses but decided in the master thesis to switch to condensed matter physics (I want to see faster results usable for society and I'm more the lab/communicative/team guy) and still read out of interest also news on astrophysics.

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    Definitely anecdotal: I've taken different versions of Meyer-Briggs the past 10 years, and I've gotten the same result every time. I like that you brought it up, and I think it's one of the better tools for helping people figure out their strengths and career options. – artificial_moonlet May 24 at 12:12
  • @artificial_moonlet I just made it recently after PhD and wondered what have been my result/category before attending university :-) Not sure if this can change drastically. So I would like to know or find a test that also show disposition for other Meyer-Briggs categories in % and how much I'm INTJ and/or INFP,... – user48953094 May 24 at 12:18
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    Thanks for such a thorough answer. I like how you broke down the gap into four dimensions. Although in some ways, the social gap is a type of personality gap. I probably have an IQ gap compared to the really good mathematicians who usually performed nationally on math competitions at a young age. I also scored ENTJ on my MBTI with a strong E. Although I would never fit into a marketing, management , or sales job. But being an engineer is a lot more team-oriented. – Shuheng Zheng May 24 at 21:28

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