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This question already has an answer here:

What are the different unusual subjects in number theory? I am adviced sometimes to think before going into research in number theory as these subjects like number theory, algebraic geometry are highly old and most the works are done so that a people need a lot of prerequisites to go into that subject and the problems are tough. That's why I am bit nervous. Is it really true? I have come to know about different areas in number theory like ergodic number theory, probabilistic number theory, modular forms and I have studied elementary, algebraic as well as analytic number theory a bit and I love studying number theory. If the subject would be very terse in research then it would be very difficult to work with it. So I am worried. Please give me some advice.

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marked as duplicate by Mathmo123, Matthew Towers, TheSimpliFire, Arnaud Mortier, Arnaud D. Feb 12 '18 at 12:58

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ If you love it, dive into it. What's the problem? $\endgroup$ – Asaf Karagila Feb 12 '18 at 7:50
  • $\begingroup$ You should see the answers to the above linked question. Yes, modern number theory has a lot of prerequisites, more from other branches of mathematics (representation theory, geometry, topology) than from "old" number theory. Yes it's worth it. $\endgroup$ – Mathmo123 Feb 12 '18 at 9:32
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It would probably be best to talk to someone at a university who researches in number theory. There's many different area and aspects of research which would largely depend on a possible supervisor that you would have. They would also have possible projects that you could look into.

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Normally in my opinion in research there is nothing called number theory. We start with a subject called number theory and we develop tools to solve some problems.

Yes, it is true that to work in number theory we need to know a bit of stuffs but not a lot always. It depends on problems and possible projects of the supervisor.I would like to second @videlity that it depends on the present institutions and faculties.

E.g Representation theory and finite dimensional algebras are used in number theory, at the same time there is something called probabilistic number theory. Again some professors like Prof Alexandru Zaharescu works on Ramanujan Number theory, Prof G. Andrews works on Partition theory.

I hope it helps.

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