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I have heard that, in mathematics, there might be several difficulties in changing one's field once one has a tenured position. I am wondering what those difficulties are. Is it possible at all?

Let me mention two difficulties I heard about.

  1. Obviously, one has to learn a new area of math on a professional level, which is not easy.

  2. These days, there is a strong pressure to get grants and, hence, to publish regularly. If one does not yet have a reputation of a serious expert in the new field it will be difficult to get a grant. This pressure is weaker if one has a tenure, but it still exists.

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    Actually, tenure is exactly what gives you the freedom to do this. It isn't a constraint. It is tough if you are on the tenure track, but not yet tenured.
    – Buffy
    Commented Dec 5, 2020 at 19:26
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    You don't need grants to publish in mathematics.
    – Alexander Woo
    Commented Dec 5, 2020 at 19:38

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I found changing fields after tenure to be not much of a problem as a tenured mathematics professor. The threat of losing some funding for a while is a serious issue if one has an expensive lab. If one is doing theory, then grant funding is not so critical. A sabbatical is a great time to study up on a new field.

I should add I am talking about moving to fields that have some connection with the old. If there is no overlap in people or background theory, then this might be more challenging.

The greatest difficulty is the bruising of the ego. The new field may not be open to your ideas, and you are essentially heading in as if you are a graduate student without an advisor to make the introductions. You need to realize that it might be years before you get invited to the right conferences or get referees who really read your papers.

It can take a few years to really switch fields, but if one has tenure and a decent sabbatical program, it can be worth the effort. One can keep some side projects in the old area to keep some papers coming in and to get excuses to meet your old friends at conferences at exotic locales (someday). Coauthors are great for this.

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  • Thanks very much. Perhaps it is another question, but I am wondering whether it is realistic to go for sabbatical to collaborate with people from different field. I thought that one normally visits people from the same field interested in a collaboration.
    – user132441
    Commented Dec 6, 2020 at 16:49
  • @user132441 Perhaps a new question is in order, on how sabbaticals work in practice, perhaps focused on math and in a specific part of the world. As is the case for grant applications, there are written rules, unwritten rules, and always some paperwork.
    – Terry Loring
    Commented Dec 6, 2020 at 17:51
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This can be a tough situation. If you're in a research position with pressure to publish, it can be very difficult, unless you have some background in the new field or fall in with a research group that can help you get up to speed. Tenure will offer some protection, but it will be a lot of work (most likely).

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    But it's a tough situation because of the mathematics, not because of the tenure. Insight in one math subfield doesn't necessarily imply insight in others.
    – Buffy
    Commented Dec 5, 2020 at 19:27
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    @Buffy - Right. I had insight in summability theory, where I started, and am now returning. I had insight in algebra as well, but not enough, and only the basic background, so my transition was successful on a lower level, but I could never seem to push deeper. There are other areas of mathematics where I have absolutely no idea what's really going on (and not for lack of trying).
    – Chris Leary
    Commented Dec 5, 2020 at 19:34

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