I want to ask if it is possible to be a mathematician (while also being a computer scientist reseaching in a mathematical related field).
I really love mathematics, specifically analytic number theory. For example I would like to create algorithms to solve problems in number theory and I already talked with my professor who supervises my PhD (which is in computer science field) about this. The professor seems okay with the choice. I would like to ask if it is possible or even okay to be both a mathematician and a computer scientist in this sense.
The mathematics part that I would like to go deep into are mathematical theorems about number theory. That may include finding large primes (from the use of an analytic approach) in computer part, and also maybe the study of the proof or the calculation to verify the elementary theorem involving Riemann's hypothesis.(This one is what interests me the most)
I need to further study about mathematical theory that may not have any application in the real world (even in computing). So I am not sure if it is a good choice to start and if it is possible to be such a person by attending a PhD in computer science as I mentioned.