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I have a BS in math and a BS in computer science. I attempted to get into a math PhD program right out of undergrad, but I was not prepared for the GRE subject test, so my applications did not go well. I had to find a job while I thought up a new plan, and I have now been accepted to computer science PhD programs.

My ultimate goal is to be a professor and spend my life researching math topics in computer science, or just math. I have a couple questions about getting to that point. Should I get a PhD in math after getting one in computer science? I read that math PhDs find faculty positions much more easily than any other kind of PhD. Should I pursue a postdoc position at some point? I don't want to be a "permadoc," as I've heard them called. I also read that computer science PhDs often go to the private sector, but I don't think I'm interested in that. What advice do you have to help me get where I want to be?

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    I wonder where you've read that "math PhD's find faculty positions much more easily than any other kind of PhD." I'm not aware of any evidence that supports this statement.
    – Brian Borchers
    Feb 8, 2018 at 4:44
  • I read a few articles on the topic. This one had the most evidence I could find: sciencemag.org/careers/2013/07/want-be-professor-choose-math
    – Pareod
    Feb 8, 2018 at 5:39
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    I read the article you cited in your comment and it uses statistical data out of context. The availability (by percentage) of postdocs, of non-faculty career options, etc. is vastly different for the fields that were considered.
    – Dave L Renfro
    Feb 8, 2018 at 11:16
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    The article misses quite a few important differences between faculty roles in mathematics and other science and engineering disciplines. For example, many new PhD's in mathematics spend several years in temporary positions (e.g. "Visiting Assistant Professor") that are not called postdocs but are very similar in effect.
    – Brian Borchers
    Feb 8, 2018 at 17:01
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    Another important point is that in the US, the majority of faculty positions are teaching oriented positions with little time for research. The typical faculty member is teaching 3-4 sections a semester of precalculus to calculus at a community college or regional comprehensive university rather than teaching a 1+2 load and doing lots of research at a flagship state university.
    – Brian Borchers
    Feb 8, 2018 at 17:33

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My ultimate goal is to be a professor and spend my life researching math topics in computer science, or just math.

Not really. That is, it seems you are not seriously committed to any kind of research, you just like the idea of you being a professor. That is not good enough of a motivation. Don't presume to become a professional life-long researcher before you've done some significant research first. And you won't get such research done before you find a particular research subject (or a few subjects) which fascinates you, which is important to you enough emotionally that you want to spend a large chunk of your life exploring it.

When you tell us that you "want to research X. Or maybe Y"." - what I hear is: "I'm not particularly attached to any research problems."

So - your question is premature right now.

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There are several points to consider:

  • There are far more PhDs who want to be professors than actual open positions, so most people won't make it. Just take it as a fact of life, and don't be frustrated when being rejected somwhere. It also means that there is no universal career guideline that is guaranteed to work.

  • While a PhD is a compulsory badge for you, earning another PhD in most cases won't add add much to your CV, so if you have enough flexibility in choosing a research topic in your current program, stick to it.

  • During your PhD studies do you best to build up your own research profile. Find a problem you like, achieve progress, publish in the best journal/conference that is ready to accept your work.

  • It is almost equally important to build up your network. When you have a chance to meet colleagues from your domain, do it, and keep connections. If you can collaborate with someone outside your university, take this chance.

People will judge your CV on the basis of its objective merits (whether your research results are good enough according to some reasonable criteria) and your "fitness" for the particular institution/group. Thus I don't think you should focus or general presumptions that there are higher chances to be hired in a field A rather than field B: it all depends on your personal achievements and your target institution profile.

Personal connections do matter, employing someone you know is a safer bet, of course. In general, be ready to more across countries, and accept postdoc positions — no matter how you look at them, it's better to be a postdoc than to have no job or go to industry (if you wish to stay in academia).

As you spend more time inside this system (as a PhD student / paper writer / conference attendee), you'll gain more understanding of your personal goals, I believe. It's quite natural that your current picture of the future is vague, but it will clear up as you go.

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