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Living in France, I am sometimes asked about Cédric Villani, a very popular figure here. Will he come back to mathematics ? The question becomes more relevant with the coming parliament elections (he should not candidate, having split with the president's party).

My impression is that it would be difficult for him. Even after a two-weeks vacations, I find a bit difficult for me to think hard on a mathematical problem ; I just cannot imagine stopping a year long.

Are there examples of mathematicians who stopped mathematics for a while (at least several years) and then resume and achieved valuable results in their second career ?

Notice that the break may have various causes, such as nervous breakdown, imprisonment, war time, ... Of course, Jean Leray doesn't count, as he kept doing maths in an oflag (and what maths !).

Besides the case of women who stopped because of motherhood (I should have think of it from the beginning ; thanks to Fedor), let me mention that of chinese mathematicians who were sent to the countryside during Cultural Revolution (e.g. Hsiao Ling).

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    $\begingroup$ Of course. Many women make a mortherhood related break, and return succesfully. $\endgroup$
    – Fedor Petrov
    Commented Apr 22, 2022 at 15:33
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    $\begingroup$ As do men, related to fatherhood. Not as often as one may whish, though. $\endgroup$
    – leo monsaingeon
    Commented Apr 22, 2022 at 17:01
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    $\begingroup$ It's easy enough to give plenty of examples of people with 4-5 year gaps in their publication record (from e.g. being department chair, or having family crises) who then go on to do good work. But it's hard to know how little math they were doing -- maybe they had projects, but they moved slowly and they didn't do any writing. $\endgroup$
    – Andy Putman
    Commented Apr 22, 2022 at 18:07
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    $\begingroup$ The bar room question is whether mathematicians are wasting their time in public life or wasting their time in mathematics. $\endgroup$
    – JP McCarthy
    Commented Apr 22, 2022 at 18:23
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    $\begingroup$ Villani's case is obviously quite exceptional, given his talent. I'm sure he could easily return if he wanted to. At the very least, he probably has a bunch of unpublished results that he could write up. Could he return to his previous level, who knows... $\endgroup$
    – onefishtwofish
    Commented Apr 22, 2022 at 18:45

9 Answers 9

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Alice Roth became a mathematics teacher after her Ph.D. in 1938, and only returned to research after her retirement in 1971. Her 1976 paper on the "fusion lemma" is said to have "influenced a new generation of mathematicians worldwide".

Further listening: 8 minute portrait

Further reading: Alice in Switzerland: The life and mathematics of Alice Roth

Alice Roth remained at the Humboldtianum [high school] until her retirement in 1971. It appears that shortly before retirement she had begun her transition back to work in mathematics. After announcing her plans to return to research to friends and relatives, she was told by one of them that in his field of medicine it would be impossible to return after so long an absence. Surely, most mathematicians would agree that it is impossible in the field of mathematics as well.

And so Alice Roth would seem an unlikely candidate for success. Yet much had changed in the thirty years that she had been teaching. In particular, Roth's area of research – begun over thirty years earlier – had become fashionable. [...] At last Alice Roth had time on her side and was able to put her mathematical creativity to work. She was now "am chnobble" (pondering a problem) full-time, gave talks to other mathematicians at universities, and made good progress – at the cutting edge of contemporary mathematics.

Roth's past as well as future work was to have a strong and lasting influence on mathematicians working in this area. Her Swiss cheese set has been modified (to an entire variety of cheeses); the fusion lemma which appeared in her 1976 paper influenced a new generation of mathematicians worldwide.

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  • $\begingroup$ Alice Roth is mentioned in an answer to a related MO question. Another related MO question is Too old for advanced mathematics? $\endgroup$
    – Timothy Chow
    Commented Apr 23, 2022 at 0:55
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    $\begingroup$ What on earth does "ant chnobble" mean, in the quote? $\endgroup$
    – jogloran
    Commented Apr 23, 2022 at 22:12
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    $\begingroup$ @jogloran This was incorrectly spelled before, correct is "am chnobble", a swiss german version of "am knobeln" in german. $\endgroup$
    – user_1789
    Commented Apr 24, 2022 at 2:55
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I hesitate to posit myself as an example, but I was out of academia from 2001 to 2019, when I decided to become a stay-at-home dad while my wife became the breadwinner. (I won't go into the details of why I feel our decisions were the correct ones, but I'm satisfied they were.)

For a few years I didn't do a whole lot of mathematics, but it's never left me entirely. I began to get slightly more involved around 2004, especially after seeing some of my earlier work talked about. The n-Category Café, MathOverflow, and the nLab became important to me during the years 2006-2019; they kind of kept me going, as I carved out time to do mathematics. I didn't do research in the sense of writing papers (at least not much), but these activities nevertheless helped me keep some of my tools sharpened and to continue learning mathematics.

In every such case, whether it be Villani or myself or anyone, I think it's possible to return to mathematics research, if the sirens keep calling and the mind is still fit for it. In such cases, it's mostly a matter of desire. And, of course, time.

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    $\begingroup$ And so what happened in 2019? Did you start back as a professional mathematical researcher? $\endgroup$
    – cdiggins
    Commented Apr 25, 2022 at 17:37
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    $\begingroup$ I started teaching again, and being part of an institution makes certain aspects of doing research a lot easier (I found). $\endgroup$
    – Todd Trimble
    Commented Apr 25, 2022 at 17:40
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According to wikipedia article on Yitang Zhang, he had a long pause from 1991 to 1999, after obtaining his phd. During this period he had multiple jobs outside academia. In 1999, he obtained a position as a lecturer at the University of New Hampshire, with only one publication in 2001 until his important work on bounded gaps between primes, published in 2014 in Annals of mathematics.

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    $\begingroup$ Did he really "leave" mathematics? The story that I heard is that he keeps thinking his mathematics during his "multiple jobs". By the way, it was not a deliberate pause, but that he failed to find a job in academia. $\endgroup$
    – Z. M
    Commented Apr 22, 2022 at 21:13
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    $\begingroup$ I don't think he left mathematics. He published a fine paper in 2001 (it's in a prestigious journal, Duke, but I know nothing about number theory so I can't comment on the work), and surely he didn't start the work in 1999! $\endgroup$
    – xuq01
    Commented Apr 23, 2022 at 21:16
  • $\begingroup$ @Z.M I never said he left mathematics, and the OP didn't asked anything about leaving math. $\endgroup$
    – efs
    Commented Apr 23, 2022 at 23:19
  • $\begingroup$ @Z.M It's not clear what OP means by "stopped mathematics". Doing something other than being a professor, or possibly industry researcher, certainly doesn't mean you had to stop thinking about these things altogether. You can have a hobby. Possibly for years you could give up on re-entering mathematics but never actually stop thinking about it and working on it. I find it hard to imagine to the contrary, in fact, which would make it hard to find any answer to OPs question by requiring the person to have ceased all substantive thought on research entirely. $\endgroup$
    – zibadawa timmy
    Commented Apr 24, 2022 at 11:33
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It is hard, but definitely possible with the right motivation. The Gaussian correlation conjecture was a major open problem in Probability and convexity, until it was solved by https://en.wikipedia.org/wiki/Thomas_Royen, a retired statistician.

And a very different example: If you search for the publications of James Simons at Mathscinet (which are arranged in reverse chronological order), you will find the following two adjacent publications, with only one 1992 interview noted in the intervening 23 years:

[1] Simons, James; Sullivan, Dennis Axiomatic characterization of ordinary differential cohomology. J. Topol. 1 (2008), no. 1, 45–56.

[2] Cheeger, Jeff; Simons, James Differential characters and geometric invariants. Geometry and topology (College Park, Md., 1983/84), 50–80, Lecture Notes in Math., 1167, Springer, Berlin, 1985. (Reviewer: P. Molino)

The 2008 paper was followed by a number of other significant joint papers by Simons and Sullivan.

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  • $\begingroup$ This reminds me of the following, which I heard from a colleague, some years back (details may not be quite accurate): How much do you think is the average net worth of top mathematicians? Of course, “top” is subjective; let’s draw an arbitrary line, say, mathematicians with 3 papers in Annals. And net worth is a crude figure, of course, but, very roughly… well, to start with, is it over a billion dollars, say? Surely no, you say. But no — turns out it’s over a billion! Maths must be a pretty lucrative career… The explanation here is Jim Simons. $\endgroup$
    – Peter LeFanu Lumsdaine
    Commented Apr 22, 2022 at 19:13
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    $\begingroup$ I was focusing on Mathematical work, but since you mention this: How many mathematicians have at least 3 papers in the Annals? $\endgroup$
    – Yuval Peres
    Commented Apr 22, 2022 at 19:32
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    $\begingroup$ I think that joke doesn't quite work. If you look at mathscinet's entry for the Annals, it lists 100 authors with 8 or more papers in it. I am not good enough with scripting to count authors with at least 3 papers, but it must be a substantial number. Since Simon's net worth (according to wikipedia) is $25.2 billion, the average must be well under one billion. See here: mathscinet.ams.org/mathscinet/search/journal/… $\endgroup$
    – Andy Putman
    Commented Apr 22, 2022 at 20:45
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    $\begingroup$ @AndyPutman I did not look through all that list, but a quick look at the authors with 20+ publications in Annals reveals that almost all of them are long dead. I did not look further down. $\endgroup$
    – Vladimir Dotsenko
    Commented Apr 23, 2022 at 19:44
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    $\begingroup$ @GHfromMO, per Wikipedia, "Net worth is the value of all the non-financial and financial assets owned by an individual or institution minus the value of all its outstanding liabilities." $\endgroup$
    – LSpice
    Commented Apr 26, 2022 at 1:48
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Grothendieck is indeed a very good example.

After leaving the mathematical community partly because :

In the month of November, 1969, I discovered that the Institut des Hautes Études Scientifiques, where I have been a professor essentially since its founding, had been receiving subventions from the Ministère des Armées for three years. Already as a young researcher, I found it extremely regrettable how few qualms the majority of scientist had in agreeing to collaborate in one form or another with military institutions. My motivations back then were essentially of a moral nature, and thus not very likely to be taken seriously. Today they acquire a new force and dimension, given the danger of destruction of the human species threatened by the proliferation of military institutions and of the means of mass destruction that they posses. I have explained my thoughts on these problems, which are much more important than the advancement of any of the sciences (mathematics included), in more detail in other places.
SGA 1, Intro

He devoted himself first to ecology then education, Meditation, Buddhism,...

Then in 1981 one of his major passions (the other being women and meditation) reawake in the form of a vast mathematical reflection with "La Longue Marche à Travers la Théorie de Galois", after this he would not refuse this passion for mathematics anymore (Pursuing stacks, Récoltes et Semailes, Dérivateurs, Esquisse...).

The "Esquisse d'un programme" is a research program submitted to CNRS in 1984.

In those last years, Grothendieck would do mathematics as "a spiritual adventure".

My personal view of the question and this answer is that those pauses are connected to the form we come back, maybe with long pause mathematics as a sport (trying to finish first something) is certainly very hard, but long pauses are healthy for a more wise vision and deeper perspective.

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To answer the question about Villani, he has come back to mathematics in september 2022 with a Chair in Analysis jointly at IHES and Université de Lyon.

Source : https://www.ihes.fr/cedric-villani-rejoint-ihes/

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  • $\begingroup$ His prestige will always guarantee him a position. He is still involved in politics, nonetheless. $\endgroup$
    – Beni Bogosel
    Commented Jan 31 at 11:41
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Not really relevant but I did a part-time Maths PhD, starting at age 48 having done a first degree in Physics and spent my whole career in computing. I wasn't very good but it made a change from programming & teaching. I'd always wondered whether I could have been a mathematician and now (maybe) I know.

It took seven years after which I took early retirement!

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Not a pure mathematics example, but a famous example in the sciences is Nettie Stevens, a US geneticist who discovered sex chromosomes.

Born in 1861, she taught at a high school for many years before returning to further education and obtaining her Master's degree in Biology in 1900 and her PhD in 1903. She continued as Reader in experimental morphology for a year and worked at Bryn Mawr as an Associate in experimental morphology, publishing 38 articles (some of them of major significance in the field). She tragically died of breast cancer aged 50 in 1912.

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Perhaps not as well known is the story of Wei-Liang Chow, see e.g. https://mathshistory.st-andrews.ac.uk/Biographies/Chow/

According to Chern, it was certainly difficult for anyone to come back to research after years of hiatus. (Chern himself was cut off from latest research in Europe/America for several years.)

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    $\begingroup$ There's a difference, though, between being cut off from the latest research (which means that your own research will fall out of sync with the latest trends—maybe not such a bad thing!—may duplicate existing work, …), and not doing research at all. $\endgroup$
    – LSpice
    Commented Apr 24, 2022 at 16:48

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