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I think it is an important question, which frequently appears in discussions. Do you know any surveys which approach it? What are the reasons for people with completed PhD in mathematics to quit it? Definitely, there are many reasons, but how many of them would like to do research in math, but switch to something else because of uncertainty in the future?

Anyway, what are your expectations of such a survey? I heard many estimates, from 0% to 50%.

By quitting mathematics I mean, that a person stops doing research. So, switching to finance, programming, only teaching without active research means "quitting mathematics" in most cases.

I don't know, we can define "doing mathematics" by writing at least one research article in five years or so. Or working on research positions in academia or Microsoft Research and similar. Any surveys are welcome, in any country and time period.

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    $\begingroup$ @Alephnull The OP is asking about people who have completed a PhD and then leave mathematics $\endgroup$ – Yemon Choi Apr 1 '17 at 20:39
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    $\begingroup$ Could you give some guidelines for what kinds of survey data you are interested in (e.g. which time period, which countries)? I am conerned that this question will just attract anecdotes and "extrapolation from limited experience" $\endgroup$ – Yemon Choi Apr 1 '17 at 20:41
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    $\begingroup$ This seems like a better fit for academia.stackexchange.com $\endgroup$ – Gabriel C. Drummond-Cole Apr 1 '17 at 21:04
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    $\begingroup$ @paulgarrett yes, thank you. I definitely mean "research" mathematics. $\endgroup$ – Nikita Kalinin Apr 1 '17 at 21:05
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    $\begingroup$ @DouglasZare, Yes I can. People can quit academia for money: if you have a family and a postdoc without certain future, you can go to industry. Sure, it is a combination of reasons. One may ask: what is the first reason, what is the second... Or ask in percentage: 10% money 30%prestige, 50% working conditions... Definitely, it should be a work of sociologists. It seems that nothing like that was done. $\endgroup$ – Nikita Kalinin Apr 1 '17 at 22:03
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The question asks for data on why people leave research mathematics. I don't have any, so in a sense I can't really answer the question. What I have is personal experience and a reasonable number of anecdotes: I had a pretty good postdoc but I didn't even apply for tenure track positions, and a surprisingly large number of my colleagues made similar choices.

Granting the subjective nature of my experience, I would emphasize that all parameters in the naive expected payoff computation come into play, not just the probability of success:

$$\mathbb{E}(\text{Stay in math}) = \mathbb{P}(\text{Tenure}) \text{Payoff}(\text{Research}) + (1 - \mathbb{P}(\text{Tenure})) \text{Payoff}(\text{Non-Research Job})$$

My generation of math PhD's had the harrowing experience of being one of several hundred or even upwards of a thousand applicants for one or two postdocs, and it doesn't get much better for tenure track jobs. Moreover public investment in research and postsecondary education appears more likely to decrease than increase, at least in the US. So the probabilities are quite discouraging.

But what I want to emphasize is that the payoff for non-research jobs is quite high these days, and this is just as important for many people. I and a solid majority of my colleagues who left research mathematics did so not for finance but for data science. Engineering advances have left businesses in all industries with literally more data than they know what to do with, and for the time being they are convinced that it is worthwhile to hire people with strong mathematical and scientific credentials to help sort it out.

Unlike mathematical research where it is typical to spend years working on something that only a handful of people can appreciate, a data scientist can have an impact which is recognizable to people outside of math or science in 6-12 months. And a lot of beautiful ideas are involved - information theory, functional analysis, convex geometry, graph theory, and even a dash of topology all arise nontrivially. The fact that there are many more openings than people to fill them is icing on the cake.

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    $\begingroup$ Very useful, good, answer. Hopefully people can think about these realities/opportunities without being upset that "classical fantasies" are not real. (Hint: they never were.) $\endgroup$ – paul garrett Apr 2 '17 at 0:30
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    $\begingroup$ the payoff for non-research jobs is quite high these days - this depends on your objective function.... $\endgroup$ – David Roberts Apr 2 '17 at 1:56
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    $\begingroup$ @DavidRoberts I suppose my point is that industry jobs can accommodate a broader range of objective functions than they used to. For folks interested in particular areas probability theory, dynamical systems, and graph theory (among other disciplines) you can work on essentially the same problems in industry or academia. But it is true that the range of subjects is still not as extensive. (This also does not address lifestyle factors, such as getting summers off.) $\endgroup$ – Paul Siegel Apr 2 '17 at 8:55
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    $\begingroup$ This is a nice answer, but the picture you paint of "being one of several hundred applicants for 1-2 postdocs" is somewhat misleading, because hopefully everyone applies to more than one department! If there are 600 applicants and 130 departments, each of which has 1-2 postdoc positions, one's chances at each job may be low; but overall there are enough positions for a third of the applicants. $\endgroup$ – Tom Church Apr 4 '17 at 1:41
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This is more of a suggestion than an answer, but perhaps the following objectively measurable statistic would come close to addressing the question:

The number of people in the final year of their current position who applied to at least (say) five academic positions but received no offers from academic institutions.

The first part of this description indicates some kind of desire for an academic position, while the latter part suggests an involuntary exit from the academic world. Note that "final year" could be the final year of a Ph.D., a postdoc, or a tenure track.

Of course this does not exactly match the original question, for several reasons.

  1. It does not capture those who were (in Nikita's terminology) "afraid" that they would not get an academic position and therefore elected not to apply.

  2. It does not distinguish between "academic position" and "position in which one does mathematical research," neither of which implies the other.

  3. It does not allow for the possibility that someone works at a non-academic position for some time and then returns to an academic position later.

But it seems close. I don't know that anyone has conducted a survey that tries to measure exactly this number, but perhaps some group that already conducts related surveys could be persuaded to add this to their existing questionnaires.

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From the AMS (American Math Society) "Report on the 2014–2015 New Doctoral Recipients" (PDF download):


PhDMath
Figure from the August 2016 Notices of the AMS, p.755.


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    $\begingroup$ thank you, but this speaks nothing about why did they do this and what happens then. Many people quit research mathematics after 1 or 2 postdocs $\endgroup$ – Nikita Kalinin Apr 1 '17 at 21:40
  • $\begingroup$ @NikitaKalinin, I do not have stats at hand, but it has been apparent for some years that there are simply not as many tenure-track jobs as people working in postdocs. One either finds that one has no further up-scale academic job, or anticipates that situation and looks elsewhere. $\endgroup$ – paul garrett Apr 1 '17 at 21:43
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    $\begingroup$ @NikitaKalinin: The precise question you ask is surely not addressed in any survey or annually collected data. So one must infer as much as possible from what data is available. $\endgroup$ – Joseph O'Rourke Apr 1 '17 at 21:43
  • $\begingroup$ @paulgarrett Sure. There are also possibilities to move to another country. etc. So you think that if x is the number of people who have done at least one postdoc, then the answer is (x-#tenures)/x ? $\endgroup$ – Nikita Kalinin Apr 1 '17 at 21:58
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    $\begingroup$ @NikitaKalinin, it is surely somewhat larger than (x-tenures)/x: quite a few people do wait to find themselves unemployed on a schedule beyond their control, but pre-emptively create a more secure situation. Two-body issues, issues of not wanting to endure geographic randomness, needing to have security for kids, cohabiting with partner (!), and such. Quite a few of my PhD students have made choices for such external reasons, ... not at all that they didn't like math or wouldn't have wanted to "go for it" if conditions were otherwise. The old monastic model is no longer relevant. $\endgroup$ – paul garrett Apr 1 '17 at 22:06

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