I have recently read the following statistics in the book "The Survival of a Mathematician: From Tenure to Emeritus" by Steven G. Krantz, which seems a little odd:

It is a hard fact that more than 90% of American Ph.D. mathematicians never write a paper. Of those who do, most write just one paper based on the Ph.D. thesis and that’s it. Nothing more.

I have seen several new PhD's (graduated in Canada, US, or Europe) with no publications, but my estimate for the rate of such fellows was way more optimistic than the above quote. So, I would like to know:

How accurate is this statistic? Is it documented anywhere?

Are there similar statistics about Mathematics PhD's in other countries?

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    Does Krantz not give a reference? He should know better than that. Jul 26, 2014 at 14:40
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    Saying "hard fact" and giving no reference doesn't sound like a scientific argument.
    – Bitwise
    Jul 26, 2014 at 15:44
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    Incidentally, Krantz makes this same claim in his companion volume A Mathematician's Survival Guide: Graduate School and Early Career Development (page 133). No reference is given there either (though he again describes it as a "hard fact"). Vahid, if you don't contact him, I probably will. Jul 26, 2014 at 18:17
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    Just a comment: everyone here seems to be interpreting "hard fact" as meaning "solid fact" or "100% verifiable", but I think he means "hard-to-swallow fact".
    – Jeff
    Jul 26, 2014 at 18:26
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    @Jeff But people are disputing that it's even true. If it's not true, it's not any kind of fact! Jul 26, 2014 at 18:27

4 Answers 4


As much as I enjoy Krantz's work on the whole, this sentence strikes me as not really qualifying as "hard fact." On the other hand, I think part what may be throwing you off is that he says "Ph.D. mathematician" not "new Ph.D." So, he's including mathematicians who graduated long ago (one of the issues with "hard fact" status is that it's unclear how far back he's going. To the first Ph.D. awarded to an American?), at a time when mathematicians were under much less pressure to publish.

For new Ph.D.'s this number is surely false. 10% of the Ph.D. graduates of American Ph.D. programs (from 2010) is about 160. That's half the number that are employed immediately after graduating at PhD granting institutions in the US. I find it hard to believe that half of those people will never write any published papers, and I know for a fact that lots of PhD's who are employed at bachelor's institutions or go on to other kinds of work have at least one publication. The numbers above come from the 2010 AMS Annual survey.

  • Your answer is more convincing. But still I would like to know if there is any estimate for the above rate anywhere else?
    – user4511
    Jul 26, 2014 at 16:46
  • This might or might not help: could also be an exception: I know one American graduate student at a good institution without a single published paper, but with a long arXiv paper, landed a 3-year research postdoc at a research I US university. Jul 26, 2014 at 22:18
  • This is tiresome nit-picking given the general feeling that the claim is utter rot, but perhaps "American PhD mathematicians" != "PhD mathematicians from American universities". It seems unlikely to me either that all those people you know are publishing papers are foreign nationals, or that a large majority of US mathematicians are taking their PhDs overseas and never publishing. You just haven't considered those possibilities yet. Jul 27, 2014 at 10:26
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    @SteveJessop I don't see what nit you want to pick. I'm the drunk looking under the street light for his keys because the light is better there: new Ph.D.'s from US programs is something where I knew where to find (some of) the numbers, so that's what I gave as details. Part of my issue with the statement is precisely that "American Ph.D. mathematicians" is not especially clear. Is that people based in the US now? Those born in the US? Citizens? Jul 30, 2014 at 21:18
  • That said, I doubt there's any interpretation of "American Ph.D. mathematicians" that makes this statement true, and I am even more dubious that Krantz could possibly have data to back up his claim. Jul 30, 2014 at 21:19

I sent an email to Professor Krantz mentioning the present discussion and asking him whether his numbers are "supported by published or rigorously gathered data, or your own observations, or are simply meant rhetorically". Here is his response, posted here with his permission.

Summary: he does not appear to have data at hand to support those numbers, but he believes they are accurate.

Dear Nate,

Your question is a good one.

Certainly my statement is well supported by my own personal observation---after forty years in the business. But I have seen sources even recently that say pretty much the same thing. I'm sorry that I can't say what those sources are.

You can think about the matter this way. The vast majority of academic jobs in this country are at what we call comprehensive schools. And those are places where teaching is the thing.
Generally speaking, people don't do much research there. They have to publish a paper or two to get tenure, and those papers tend to be fairly close to the thesis. But then that's about it.

A lot of other people get jobs at the National Security Agency, or Los Alamos, or another government think tank. Generally speaking, publishing is not the thing there either. Sometimes people publish in special classfied government journals.

Other people get jobs at Microsoft or Hewlett-Packard or what have you. And publishing is not the thing there either.

Those of us who are lucky enough to be in math departments at true research universities are definitely in the small minority.

I believe that, at the time I wrote those words, I consulted some people at the American Mathematical Society and they had data to support what I was saying.

Feel free to quote me to others if you wish.


Steve Krantz

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    Thank you Nate for communicating with Prof. Krantz and sharing his response. To support his point of view, I think it is safe to assume that most PhD's with a few publications (and closely related to their theses) have written those papers under the influence of their supervisors, and consequently after graduation and getting a non-research jobs they are not able or not willing to write independent papers. And I think it is not an issue seen only in US.
    – user4511
    Aug 5, 2014 at 17:19
  • How do we know this is a legitimate response an not invented by you? Dec 16, 2017 at 0:53
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    @Santropedro: You don't. There is nothing I could post here that would prove that it is authentic. You'll simply have to decide whether you want to take my word for it or not. Dec 16, 2017 at 23:35

There have been several papers analyzing the data from the Mathematical Reviews database (MathSciNet). One of them is Patterns of Collaboration in Mathematical Research, Jerrold W. Grossman, SIAM News 35, 2002. That paper gives a distribution of number of papers by author. It confirms that 42% of authors in the database have 1 paper.

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    Grossman also has similar 2005 Notices article. Apparently from 2002 to 2005, the number of authors with 1 paper went up to 43%, but it still seems unlikely that Krantz's statement "most write just one paper based on the Ph.D. thesis and that’s it" was true at any point in recent history. By the way, for most institutions, Ph.D. theses are not listed as an author publication in the MR database.
    – Kimball
    Jul 28, 2014 at 15:21

To test Krantz's assertion for recent Ph.D.s from U.S. universities, one can use statistical sampling. The American Mathematical Society published a list of 2013-2014 doctoral degrees in mathematics from U.S. institutions. Selecting random names from this list and checking the obvious places for papers should give a good estimate for what percentage have written at least one paper by a year and a half after graduating.

Unfortunately, I don't see a good way to sample uniformly from this list, without some counting or approximations. Instead, I flipped through it and grabbed ten names from near the centers of the pages, about three pages apart (in a 31-page document). This isn't a particularly careful sampling technique, and it presumably introduced some bias, but it should suffice to detect anything occurring 90% of the time.

For each of the ten people I selected, I looked for mathematics papers on Google Scholar, the arXiv, a home page, or MathSciNet. I did not count the dissertation itself, and I was prepared to exclude anything that appeared to be undergraduate research but this turned out not to be an issue. The results were as follows:

  1. Six people had publications in journals.

  2. Two more had papers they described as accepted by journals.

  3. One listed a conference publication. Web searches make it clear that this paper exists (and it has been cited by another paper with disjoint authors), but I could not find a copy online.

  4. For the remaining person, I found no evidence of any papers.

I was surprised at how high the percentage of people with publications was, and perhaps it indicates that my sample was not so representative. However, it appears that even people working in teaching-only jobs or outside academia are likely to write at least one paper.

If anyone carries out a more careful study of this issue, I would love to see the results.

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