research process – How to find gaps in mathematics/theoretical physics/mathematical physics ? How to proceed after you found them?


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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