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I'm planning to attend a top 25 school in the US for a Ph.D. in Mathematics. Are research collaborations with professors outside of the school generally encouraged? This could include short or long-term visits to other universities or just an online collaboration.

I understand that an answer to this question might be advisor-specific. Since I do not have an advisor yet, should I just email one of my potential supervisors (who I've been in contact with for a while now) and ask them? I'm not sure how such a question might be received.

Additionally, since many people reading this question on this website might have experience with math departments in the US (as a graduate student, professor, or otherwise) - it'd be nice to know if you have an answer to this question based off of your experience.

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    I'm not a mathematician but to me, one of the fundamental tenets of research is collaboration. I would find it weird if someone didn't want to collaborate with others, or if they tried to stop their student from doing so. Apr 7, 2023 at 9:07
  • I think major and specific university matters here. All the mathematicians I know are very reluctant about collaborations, and outright mock papers with more than one or two authors. On the other hand, collaboration is essential in most science fields.
    – Greg
    Apr 8, 2023 at 3:20
  • @Greg "All the mathematicians I know are very reluctant about collaborations" This is does not correspond at all to my experience as a mathematician (after having worked in three countries and now moving to a fourth). I wonder if there is simply some mismatch in how you think of collaboration and how mathematicians think of it, or if you are describing some very local culture (which you perhaps hint at when you say that the specific university matters). Sure, mathematical collaboration tends to be smaller in scale and tends not to be a team of people with very clear cut and distinct roles. Apr 8, 2023 at 15:15
  • @AdamPřenosil That was (as indicated) my personal experience, but I shared it exactly because I wanted to point out that local culture/major matters.
    – Greg
    Apr 10, 2023 at 12:47
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    @Greg Understood. I commented mainly so that the OP does not get the impression that mathematicians in general are reluctant to collaborate. Apr 10, 2023 at 13:54

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This is not something that would normally be university-level or department-level policy; it would be more about your particular advisor.

I don't think very many advisors would oppose the idea of collaboration altogether. Some might be proactive in helping you find collaborators, or connecting you with people in their own networks. Others might not do that, but would have no objection, in general, to you working with collaborators you found on your own.

There might be specific cases where a conflict could arise though. For one thing, your advisor's primary job is to help you write a thesis and graduate. So if at some point they think you're falling behind on your thesis work, and that the time you spend on your outside collaborations is interfering, they may advise you to reprioritize. In an extreme case, this could eventually come to the point of an ultimatum: "Either drop your outside projects and focus on your thesis, or else find yourself another advisor." Try to get someone else to help mediate before it gets to that point!

There is also the possibility that they don't approve of the specific work you are doing with the collaborators, or the specific people you are collaborating with. That also can lead to conflicts.

If outside collaborations are important to you (and they certainly can be very helpful), then this would be something to bring up in conversations with potential advisors, as you both try to determine whether it's a good fit. It could be something along the lines of "do your students usually work more individually, or directly with you, or with wider groups of collaborators?" Whatever they "usually" do likely has something to do with what the advisor encourages.

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Not in math, but I go to Georgia State. I have collaborators from other departments, and collaborators from other schools out of state.

So even if they don't explicitly encourage it, I'm encouraging it to you! Trust me, you'll learn so much if you can put yourself out there and meet others not in your immediate field!!! I was asked to review for a journal strictly because the editor knew of my work and we'd talked before (of course, I still know what I'm doing!).

So do it. Meet others with your interests. Sign up for overleaf! And have fun pursuing your interests with them.

Note: I'm a phd student who's already developed really specific interests. I can do my own work and write my own studies without needing my hand held. So, I can see why some people whose interests are still developing might not want to encouraging collaboration with others from elsewhere, since you're still learning what you like. But if you know what you like, go right ahead. Have fun. No reason not to.

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