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A young colleague of mine got Ph.D. in mathematics in a field A. He spent one year elsewhere at a postdoc. Then he got a tenure track position at his alma mater. Meantime he realized that he better likes to work in a different field B. However he does not have enough background in the field B, and he needs to learn quite a few advanced courses which do not exist in his department. After two years of having the tenure track position he is thinking to go for a postdoc to such a place where the field B is well represented.

What are his chances to find such a postdoc, in particular is such a plan realistic at all?

As a partial explanation of his change of interests is that he used methods close to the field B to solve a long standing problem from the field A. However he is not considered to be an expert in the field B and has no publications in B.

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    I do not understand why he needs to be a postdoc. As a tenure track researcher he can shift his interest toward the new field, if it is inside mathematics.
    – Greg
    Jun 28, 2023 at 13:48
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    The problem is that in essentially all departments where he can get a job as an expert in the field A the field B is not represented. Thus he has to learn the field B in isolation. This is hard.
    – MKO
    Jun 28, 2023 at 14:51
  • @cheery.beach7701 that is presumably why it was posted as a comment, not an answer. Jun 29, 2023 at 12:04
  • Oops. Thanks. I moved it to where I intended it to be, under an answer. Thanks again
    – Cheery
    Jun 29, 2023 at 12:06
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    Are sabbaticals an option? Sep 9, 2023 at 9:06

4 Answers 4

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It is not uncommon for people to switch fields of mathematics. But you should really ask your colleague, why he thinks this cannot be done in-situ.

One reason to go would be to learn about field B. But at the level we are talking about, he should be perfectly capable to study a topic at a faster speed from textbooks and lecture notes, especially if he already understands some of the ideas. I am also one of the people who would like nothing more than to forever be a student, but I still realise that this clearly is not the best use of my time.

The other reason to go would be to work with people in field B. You say that he is no expert in that, but nowhere does it say that this is required. The only things you need is to know someone and have an interesting problem to work on. Both can be achieved by simply going to some conferences of B, presenting his results as "how B can be applied to A" and then talk with people there about what else is possible, leading first maybe to a few more works in A+B, allowing him to understanding B better and then go to also work in B without A at some point.

All this can be done while staying at his current position, painting him as expert in A and B, with a possibility to even start introducing classes on B at his alma mater, right in time for his tenure review. In contrast, if he leaves, he will just be another postdoc in B, in a sea of younger, more accomplished people.

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    Or perhaps there is a summer school in B, or spend a summer visiting a university that has a strong B program...
    – Jon Custer
    Jun 28, 2023 at 13:09
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    The statements in this answer are all true, but the question was explicitly "What are his chances to find such a postdoc, in particular is such a plan realistic at all?", and not "how can he get into field B"
    – Cheery
    Jun 29, 2023 at 12:05
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    @cheery.beach7701 You are completely right, but to me the question seemed a bit like an XY-problem. But maybe that are just my reflexes from running into similar issues with students asking about the wrong thing too often.
    – mlk
    Jun 29, 2023 at 12:37
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    Mostly agreed with this answer, but I don’t think “textbook and lecture notes” are usually sufficient — in fields I know, that can get you to the level of (say) a beginning graduate student, but getting up to current research is difficult without some direct contact with people in the field. Summer schools or visits, as @JonCuster suggests, or more generally conferences in the target field, are the kind of thing that can help to bridge this gap.
    – PLL
    Jun 29, 2023 at 14:03
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Not unheard of, but near zero chances of working out.

People who land a tenure track position are, by definition, top candidates and thus more likely to land a second tenure track position. I know of a tenured Biologist who got a second PhD in the humanities and then applied and landed a tenure track position at a humanities department at another university! Talk about switching fields. So switching between math fields does not sound that dramatic in that context. Knowing nothing else about your friend, I would say that his chances are better than average (but that's not enough, read on.)

You asked about the chances of this plan working: close to zero. Too few positions, too many good candidates out there, and the black mark of having left a tenure track position after only two years because of a change of heart. He probably has a better chance of working in field B by staying in his current job and learning what he can from there.

Edited to add from a very useful comment: Changing the field is not the issue, abandoning the position is the problem. Whenever someone leaves unexpectedly, teaching load has to be redistributed, a new hiring committee convened, etc. In other words, lots of additional work for precisely the people doing the hiring. One of the many criteria for hiring is "is this person sticking around, or are we going to have to do this thing again in two years?"

Someone wins the lottery every day, but that still doesn't mean it's a good idea to play the lottery.

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  • Thank you. Why it is a black mark to leave a tenure track position because of a change of heart?
    – MKO
    Jun 28, 2023 at 11:02
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    @MKO I would say the main point is that changes of heart are seen as not statistically independent. Anyone hiring him will ask, what guarantees that he will not become bored of B as well and leave again?
    – mlk
    Jun 28, 2023 at 11:20
  • @mlk: Well, the guy made a significant contribution to the field A and proved himself to be a serious person. He wants to move to other field. May be one day he will want to change the field again. But of cause nobody can guarantee that he will be equally successful.
    – MKO
    Jun 28, 2023 at 12:33
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    @MKO Changing the field is not the issue, abandoning the position is the problem. Whenever someone leaves unexpectedly, teaching load has to be redistributed, a new hiring committee convened, etc. In other words, lots of additional work for precisely the people doing the hiring.
    – mlk
    Jun 28, 2023 at 13:53
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    @mlk do you mind if I add that to the answer?
    – Cheery
    Jun 28, 2023 at 14:01
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This is a very risky plan

Your colleague has already beaten the odds by getting a tenure track position, and there is no guarantee that they will be so fortunate if they decide to start over. We all like to think that our success is due solely to our own talent and hard work, but chance plays more of a role than we usually want to admit. Leaving a tenure track position for a postdoc means taking another spin on the wheel of fortune and accepting the new result, even if it's not as good as what you've already got.

Beyond that, I would expect your colleague not to be a top candidate for the postdocs. Presumably there are students graduating every year who have done their PhDs in field B, so why would someone hire your colleague with no relevant experience instead of one of them?

Furthermore, your colleague is now overqualified for a postdoc position. Often people are reluctant to hire overqualified candidates because they are concerned that they will quickly become unhappy in the junior position because of its lower pay, lack of autonomy, and lesser prestige. Maybe your colleague would be an exception, but the prospective supervisor has no way of knowing for sure. Hiring someone with appropriate qualifications will be seen as a safer choice.

Finally, after all of that, even if your colleague manages to get a position in field B, and even if it goes well, then what? We all know what the academic job market is like. Would you really advise someone to face that again?

There is nothing stopping your colleague from pursuing work in field B, especially once they get tenure. It will involve some reaching out and making connections, as well as some self-study, but they don't have to do it all at once. They can still be productive in field A while training up in field B. People do it all the time; you don't have to go back to apprenticeship every time you want to do something new.

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I agree that this is a low percentage plan, but I wanted to point out something I didn't find in the other answers: postdocs in mathematics don't take courses (though at least in the United States they usually teach them). The people who take courses are students. Postdocs in mathematical field X are hired for....their expertise in some aspect of mathematical field X. The only way I see this working is if the person's expertise and work in the field they did train in is of great interest to someone working in their new field who wants to collaborate in some mixture of the two fields.

Let me also say that the way I think of a PhD in mathematics is not as the end of your studies in mathematics but the point at which you can direct your own further studies in mathematics. I know plenty of tenure track mathematicians who have shifted from one field of mathematics to another; they all did this while retaining their tenure track job. Some of them switched from pure mathematics to applied mathematics. One switched from mainstream pure mathematics to mathematical logic. One switched from mainstream pure mathematics to mathematics education. And so forth. So if I'm being honest, even your colleague's proposed move somewhat undercuts the perception of his mathematical maturity and competence. On the other hand, that he solved a longstanding open problem in his field of initial expertise certainly helps the perception of his competence, so if people have enough faith in his abilities maybe he can make this work. But in general this seems very unlikely to succeed.

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