How to find gaps in mathematics/theoretical physics/mathematical physics? I am interested to do independent research in physics though a purely mathematical/theoretical (pen and paper) approach with or without some programming. How to proceed further (with which methods) after finding a gap?(Undergraduate research and Publication)

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    It seems that you ran into the problem independent researchers have: you don't have colleagues to spar with or mentors who can help you with those steps. Commented Jun 24 at 7:33
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    Generic answer is to either get a PhD, or find someone in research to mentor you in how to do research (generally done by getting a PhD). Commented Jun 24 at 8:45
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    Could you narrow the question? As it is, the question is basically "how do I do research?", which is far too broad for us to cover here (if we could answer it in a couple of paragraphs, there would be no need for PhD programs).
    – cag51
    Commented Jun 24 at 15:43
  • @cag51 Actually I was asking about undergraduate research and publications. Commented Jun 28 at 16:39
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    @SayantikaBose That doesn't really narrow it down much with respect to the questions you've posed, research is research whether you're an undergraduate or not. Step 0, though, is to find a research advisor because these are all questions to ask your research advisor, and not limit yourself to this idea of "independent research"; having these questions is exactly the problem with trying to do this sort of thing independently, it's like saying you'd like to fly without wings and your only remaining question is how to go up and not down - that's the entire problem in the first place!
    – Bryan Krause
    Commented Jun 28 at 16:43

3 Answers 3


You can only be an independent researcher, i.e., a researcher without an affiliation with a research institution, if you are already a researcher. For this you should enrol in a PhD program to be trained as such. After that, you will be acquainted with the basic tools and methodologies to pursue new research directions and find the knowledge gaps to be filled. If you want to become a researcher independently, then you have a different question.

Even as independent researcher, I believe you should be part of the community. Getting inspired by others plays a big role on creativity and learning. It helps you look at problems from different perspectives and understand where you can expand the current knowledge.


You have asked two questions - how to find gaps and what to do when you find one.

If you know that a gap you have found is real (not just something known that you do not happen to know) and you have found a way to fill it then you write it up and submit it to an appropriate journal.

That said, it is unlikely that you can do "independent research in physics" without connections to current practitioners to share ideas with.


The sane answer is as already suggested get a PhD in the subject you want to do research in. Doing useful research is really hard. (Getting a job in doing it is even harder!).

But I know someone who took an unusual route into a PhD (at a prestigious institute) by first performing impressive original research that was a direct follow up of a well-known paper. The best way to do useful research and to be recognized for this despite having affiliations/degrees to vouch for you at least a little bit is to solve known open problems (preferably one where you have some hope of succeeding). These can often be found in conclusion/discussion sections of recent papers.

Note that you will likely be trying to solve problems that people with a much more appropriate background did not find easy to solve (or they would have done so). So this will probably be very very hard. (And you will probably at first not even understand any of the papers let alone the open problem and a good strategy for solving them.)

The story of the "independent researcher" I knew did not end that well. Their unexpected impressive result was not followed by more such results and they left their PhD without completing it or publishing much more additional original research.

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