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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.

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What exactly do you mean by 'working as a mathematician'? From your post you are currently writing your PhD thesis in a computer science department. You can definitely write a very math heavy thesis, especially if your advisor supports it. You can also submit papers to mathematical journals, provided the topics of your articles are suitable. Journals care for the content of your papers not your academic credentials. You can also collaborate with mathematicians, do joint projects and write joint mathematical papers.

Once you have your PhD thesis you can apply for postdoc or lecturer positions in math departments. If you research fits to their needs a computer science PhD will be just as good as a math PhD. It might be a little less obvious why you would be a good fit for a position but if you can argue that you are they wouldn't exclude you because of a PhD with a different title.

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  • Thank you. Actually I mean what you mentioned (which I forgot to cover). The publication in math journal and working with other mathematicians, etc. that you provided.
    – Saksit Suwanteerankul
    Commented Mar 12, 2022 at 14:18
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The professor seems okay with the choice.

This is very important, but I think there is an equally important issue you need to pay close attention to. To successfully do a PhD in a topic X, especially at the level that would position you to pursue an academic career, it is really really important to have an advisor who is not just “okay” with your choice but who actually has the knowledge and expertise in topic X so that they are able to guide you towards good research problems and successfully completing work on them.

So, if you want to specialize in analytic number theory (even if it’s mainly computational aspects of number theory), and your advisor is not an expert in this subject, and you don’t have anyone else aside from your advisor who does have that expertise and who is able to mentor you in a way that involves a significant time commitment (for example as a co-adviser), then your plan is not a good plan.

Summary: yes you can be a mathematician with a specialty in analytic number theory, and whether your formal PhD is in computer science or math is in a sense immaterial. But what is a lot more critical is if you have access to a mentor/advisor who has the knowledge to train you in this specialty. If you don’t, then even if you were in a math graduate program I would advise you to rethink your plan.

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  • Actually, during the discussion he seemed interesting about the topic and a sketch proof. Your point is my primary concern indeed, as it is CS department so there might not be so many experts in the field. There was a mathematician who taught at the university before, in the math department in the field I interested but he left to other university and other country.
    – Saksit Suwanteerankul
    Commented Mar 13, 2022 at 2:14
  • Though I am not sure if he had students teahing there or even I can access to them. May be I need to contact the professor together with my advisor if this is possible.
    – Saksit Suwanteerankul
    Commented Mar 13, 2022 at 2:15
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Actually, anyone can "work as" a mathematician. You don't need any degree at all. You can also publish as degrees aren't required for that. But if you want to get paid for that work then you need to get hired into an appropriate position and while CS overlaps with math, the overlap is actually quite small.

Unless your CS education, generally, was unusual in some way then there are probably vast parts of mathematics that you don't have any experience with. This makes it less likely that you have general insight into math, though it isn't impossible.

If you only want to work in those parts of math that are covered by the overlap, then getting hired for a CS position will serve about as well as any other, and you can, as an intelligent person, expand your understanding of the rest of math - which is a vast landscape. People do change fields and some are competent experts in more than one.

Going the other way is a bit easier, actually, since a deep understanding of math gives an equally deep understanding of some important parts of CS, such as, say algorithmics and computability. Much of the rest can be learned.

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  • So, I'm not sure I understand you correctly but maybe you suggest me to get hired in the CS position and then expand my understanding of math myself? I do agree with your point about anyone can work as a mathematician, even without degree. I think I can learn math more by myself, but the lack of professional network and decent collaborations or disscussions may be the big obstacles.
    – Saksit Suwanteerankul
    Commented Mar 12, 2022 at 16:35
  • So, I suppose that it is okay to work in CS department with the publications on the small overlaps with math together with even unapplicable pure maths (maybe with some collaborations) that you recommended?
    – Saksit Suwanteerankul
    Commented Mar 12, 2022 at 16:36
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    I recommend you get the job you can. I think CS is more likely to have a home for you. Note that the market at the moment is especially tight and you are competing with a lot of highly trained mathematicians for any math position. Just don't neglect applying for CS openings.
    – Buffy
    Commented Mar 12, 2022 at 16:37
  • Note that the "small overlaps" aren't unimportant.
    – Buffy
    Commented Mar 12, 2022 at 16:38
  • Thank you. I didn't treat it as unimportant. Actually, they are very meaningful to me and I really want to work on these (and other pure ones as I mentioned).
    – Saksit Suwanteerankul
    Commented Mar 12, 2022 at 16:43

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