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The recent question about the most prolific collaboration interested me. How about this question in the opposite direction, then: can anyone beat, amongst contemporary mathematicians, the example of Christopher Hooley, who has written 91 papers and has yet to coauthor a single one (at least if one discounts an obituary written in 1986)?

Ricardo Andrade
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Ben Green
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    Quite hard to sharpen anything of Hooley's. – Charles Matthews Jun 21 '10 at 13:23
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    Aha, so an interesting isolated point does exist! But doesn't he have an appendix by Nick Katz in (at least?) one of his papers? That tarnishes the perfect record a bit, so it justifies mentioning the example of Harish-Chandra who co-authored only one paper (with Borel) if one ignores his physics stuff. – Boyarsky Jun 21 '10 at 13:39
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    Point taken. One might also note the Hooley-Wooley theorem, though that's not (of course) the result of a joint paper. – Ben Green Jun 21 '10 at 14:58
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    There's a Hooley-Wooley theorem? The world is a slightly better place than I had realized. – Pete L. Clark Jun 21 '10 at 16:17
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    Great question! There is a huge career incentive to have joint papers because each author gets credit for the paper. It's a lot of work to write solely authored papers, work that isn't properly accounted in the career structure of mathematics. I'm not against joint papers, there are certainly good reasons to have joint papers, but the bad reason is a real problem. Besides just counting papers, you could also look at very long papers such as those by Gromov, or of course harder measures of significance or originality. – Greg Kuperberg Jun 21 '10 at 16:27
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    There's also Hooley, Crelle 328 (1981), 161--207, which depends crucially on Milne, Crelle 328 (1981), 208--220. Maybe I should have insisted on a joint paper.... – JS Milne Jun 21 '10 at 16:49
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    Pete: I think that the Hooley-Wooley theorem, which has to do with sums of cubes, is named thus in Mel Nathanson's book "Additive Number Theory,I: the classical bases", though I do not have a copy to hand. There are other subtle gems in there too (for example the notion of "The Anglo-Michigan school" in connection with the Hardy-Littlewood method). – Ben Green Jun 21 '10 at 17:30
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    Dear Greg, Your position "the bad reason is a real problem" is a very strong one, which I've not heard advocated before. Do you have a sense of how widely it is held? Could you elaborate on it? (This is probably not the correct forum for doing so, but I am very curious about this, since my view on collaboration (which, I should say, I've not subjected to much critical examination) has always been that it is basically a positive thing for the mathematical community.) – Emerton Jun 21 '10 at 17:45
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    Are we restricting ourselves to contemporary mathematicians or are we allowed to include mathematicians like Carl Ludwig Siegel who I believe did not have a joint paper – Mohan Ramachandran Jun 21 '10 at 18:14
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    Emerton (Matt): Let me say it carefully. I have absolutely nothing against material collaboration, which I agree is entirely a good thing. What bothers me is when X looks more active than Y and is more likely to get hired, because (say) X has 15 papers with 3 or 4 authors, while Y merely has 8 solely authored papers. We all know that it's stupid to just count papers. But the fact is that letters of recommendation and hiring decisions are inherently biased, and these biased arguments are presented to relative outsiders (such as deans) who can only make snap judgments. – Greg Kuperberg Jun 21 '10 at 19:36
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    Emerton (Matt) 2: So my advice to anyone worried about employment is that you should write joint papers for both good reasons and cynical reasons. Yes, you should admire and emulate Feit-Thompson, Hardy-Littlewood, Atiyah-Singer, etc. But you should also write joint papers just because it's easier and it works in your favor. If given a choice between a thank you in the acknowledgments and coauthorship, your decision might rationally depend on whether you have tenure. – Greg Kuperberg Jun 21 '10 at 19:52
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    Dear Greg, Thanks for your thoughtful elaboration on your remark. – Emerton Jun 22 '10 at 20:13
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    Regarding Greg's point, I wonder whether it really is easier to write joint papers? After all, in many cases it involves much more time and back-and-forth between the authors. – Joel David Hamkins Apr 20 '12 at 07:29
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    I have seen members of promotion and tenure committees discount work that was coauthored for dumb reasons. X was at University A for a postdoc and after having left coauthored papers with Y who is currently at University A. This was interpreted as X still working with her/his postdoc mentor, which was not the case. This is really frustrating. When people coauthor things with their advisor, they might get less credit. I think it matters who you coauthor things with. – Sean Tilson Apr 20 '12 at 15:57
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    After sitting on tons of selection and promotion committees, I have many times seen young researchers' ability doubted if their only papers are jointly with someone senior, especially if it was their PhD advisor. Sole author papers serve to establish personal credentials. Conversely, good advisors will not try to get their name on all their student's work. Later in a career, joint papers are lovely. – Brendan McKay Aug 15 '13 at 23:22
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    This question really troubles me. It's like asking for the name of the smallest iceberg. – Christian Blatter Jun 21 '10 at 17:50
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    I've not read the integrality of Opera Omnia (who did ?), but I don't remenber having seen anything written in collaboration. Nevertheless, Euler could be a candidate for the most collaborative mathematician, since he wrote thousands of letters. – few_reps May 15 '15 at 12:28
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    @JoelDavidHamkins You are probably right in that writing joint papers is perhaps more convoluted (In my personal experience, by clashes in style and $\LaTeX$ formatting... I know, I am a neurotic!). But I think that this issue is greatly compensated by the collaborative pooling of ideas, among other things (I am very glad whenever my colleagues finds a typo or a subtle mathematical mistake in my writings). – Matemáticos Chibchas Oct 14 '20 at 13:52

10 Answers10

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Lucien Godeaux wrote more than 600 papers and not one of them is a joint paper. He cowrote a textbook in projective geometry. Mathscinet records only 15 citations to all these papers! But there is something called Godeaux surfaces which is mentioned in the literature. This is about the weirdest example I know.

http://www.ams.org/mathscinet/search/author.html?mrauthid=241534

Felipe Voloch
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    How did he have so many papers with so few citations? Were they very rote papers? – Greg Kuperberg Jun 21 '10 at 18:16
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    I never read any of his papers, so I am not sure. They seem to be about specific classes of algebraic varieties with obscure properties and perhaps only he cared about them. – Felipe Voloch Jun 21 '10 at 18:32
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    This is extraordinary! It looks like he kept the Belgian journals in business single-handed..... – Ben Green Jun 21 '10 at 18:35
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    It's apparently even more impressive than that! The article MR1321036 is a biography of Godeaux. I don't have access to the article, but according to the review he lived from 1887-1975, wrote 1072 articles and 41 books and "courses" (I guess those are unpublished course notes?), but only has been cited or referred to in 17 papers. – Andy Putman Jun 21 '10 at 18:35
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    His wikipedia page: http://en.wikipedia.org/wiki/Lucien_Godeaux – Ben Green Jun 21 '10 at 18:36
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    I can't help but feel that this record is somehow pathological if he had so few citations. To have someone work so hard and yet attract so little attention is bizarre. I would be interested in a more complete explanation of how it happened. – Greg Kuperberg Jun 21 '10 at 19:06
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    Greg, MathSciNet only lists citations after about 1997. For example, they list only 16 citations from references for Weil's Foundations of Algebraic Geometry, the earliest of which is 1997. – JS Milne Jun 21 '10 at 19:27
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    Greg, there are well-known results of Godeaux in birational geometry of surfaces. On the other hand, since you are so worried about citations, check out author="Riemann, B*" on MathSciNet. You may be in for a shock! – Victor Protsak Jun 22 '10 at 00:15
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    Godeaux's sole coauthor has no other publications in Math Reviews - Godeaux has no Erd"os number. – David Roberts Jun 22 '10 at 00:35
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    Here's a way to get mathscinet to give an idea of Godeaux's influence: searching for papers with "Godeaux" in the title gives 34 hits, and searching for papers with "Godeaux" anywhere gives 856, so subtracting his 682 papers gives 174 papers with "Godeaux" in one of the mathscinet searchable fields. –  Jun 22 '10 at 08:52
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    I guess all the would-be co-authors got tired of waiting for Godeaux. – Gerry Myerson Aug 16 '13 at 00:35
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    En attendant Godeaux ... – Denis Serre May 12 '15 at 08:07
  • I wonder if he also has most pages as single author... I see several 5-7-pages papers om MathSciNet. – Per Alexandersson May 12 '15 at 13:52
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Until well into the 20th century, collaboration was more the exception than the rule among mathematicians. As an example, define the Betti number as the distance to Enrico Betti in the collaboration graph. Well, it seems that your Betti number is infinite (unless you are Enrico Betti): indeed, according to the link below, Betti is an isolated point in the collaboration graph: http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath&idno=AAN8909

Alain Valette
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How about Marina Ratner. I believe she has had no collaborators.

Mohan Ramachandran
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    That is true! She only has 31 papers, but some of these have had an enormous influence on modern mathematics. – Ben Green Jun 21 '10 at 17:52
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    Wiles has 21 research papers. Emil Artin's collected works fill a small book. The "quantity" metric is not so meaningful. – BCnrd Jun 21 '10 at 17:59
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    BCnrd: Selberg would be another example of this (and also, almost, an example for my main question) – Ben Green Jun 21 '10 at 18:25
  • Another interesting question, who was the most influential without having co-authors? Of course this might be too subjective to be discussed here... – Helge Jun 21 '10 at 18:36
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    As Gauss said about Dirichlet's output, "One does not weigh jewels on a grocer’s scales”. – KConrad Jun 21 '10 at 18:38
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    That is an awesome quote from Gauss. I would be interested in a reliable citation. – Greg Kuperberg Jun 21 '10 at 19:20
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    By the way, Laurent Lafforgue has a whopping 10 ordinary journal papers in Math Reviews, in addition to an erratum and two ICM Proceedings. Not to mention that only one of his 10 papers is joint. – Greg Kuperberg Jun 21 '10 at 22:43
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    A bunch of Lafforgue's "orginal journal papers" are actually research announcements. Of course, one of them is a 241 page paper in Inventiones and another a 329 page Astérisque volume... – Andy Putman Jun 21 '10 at 23:05
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    I also just noticed that the only joint paper I can find by Lafforgue (the one w/ M Florence entitled "Galois theory and arithmetic") is actually a historical survey... – Andy Putman Jun 21 '10 at 23:08
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    So how many actual research papers does he have, not counting surveys, talks, announcements, etc.? Is Lafforgue the most laconic of the Fields Medalists? – Greg Kuperberg Jun 21 '10 at 23:29
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    The nine papers are: 4 CR announcements, Asterisque vol 243, one in Journal AMS, one in Inventiones, his ICM 2002 talk and the historical survey with Florence. SO one could say he only has three actual research papers (admittedly totalling 605 pages...) – David Roberts Jun 22 '10 at 00:18
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    Greg, re the quote from Gauss: it is apparently in a letter from Gauss to Humboldt in 1845, which may be found in Briefwechsel zwischen Alexander von Humboldt und Carl Friedrich Gauss (edited by K.R. Biermann), p.88. Unfortunately, this book in not in our library, so I can't verify this immediately. – John Stillwell Jun 22 '10 at 01:39
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    @Greg: http://books.google.com/books?id=tqaWlHIsZXAC&pg=PA18#v=onepage&q&f=false – Kevin H. Lin Jun 22 '10 at 22:07
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    With some creative Googling I found the original quote. Gauss nominated Dirichlet for some distinction, and he defended his thin publication recrord with the statement, "Aber sie sind Juwele, und Juwele wägt man nicht mit der Krämerwaage." In current American English, you could translate it as: "But they are gems, and you wouldn't weigh gems on a grocery scale." – Greg Kuperberg Jun 23 '10 at 23:43
  • @quid: Thanks quid. Didn't notice it. – C.S. Aug 15 '13 at 15:52
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Leopold Vietoris (1891-2002) wrote more than 70 papers, only one of them with a coauthor see here.

Péter Komjáth
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    The last of his papers appearing in 1994. I wonder how many other mathematicians have published after their 100th birthday? –  Jun 21 '10 at 19:16
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    Stephen, sometimes people publish even after they are dead. For example, Robert Remak died in 1942 and his last paper appeared in 1954. Several decades old manuscripts find their way to print, too. – Victor Protsak Jun 22 '10 at 00:21
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    Is Euler still posting his papers on the arxiv? – Boyarsky Jun 22 '10 at 01:26
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    Victor, Boyarsky,

    Good point; it looks to me like it's plausible that Vietoris' last publication was a manuscript he'd had sitting around for a long time (it was part III of a series in which I and II appeared in the 50s). On the other hand, he published a few other things in the mid 80s. In the absence of definitive proof I prefer to believe that he was mathematically active past 100! (And please don't spoil my fun if you know otherwise...)

     –  Jun 23 '10 at 09:43
  • There were some articles on Vietoris' longevity that mentioned his later publications. One had "Nestor of Mathematicians" in the title, others were obituaries when he died as Austria's oldest centenarian. The most recent work mentioned was on a relatively concrete question in plane geometry and he seemed to be active well into his 90's. An interesting item the articles did not discuss was his political position, if any, as a prominent academic during World War II. – T.. Jun 30 '10 at 01:39
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    My basic AT instructor told us about how Vietoris was winning skiing competitions well into the end of his life, he was the only person in his age group. – Sean Tilson Jul 27 '10 at 01:05
  • Shock! -- Leopold Vietoris is not listed in the Biographies Index of The MacTutor History. – Włodzimierz Holsztyński Aug 16 '13 at 03:34
  • Dirk Struik published some articles when he was over 100, although they weren't mathematical research papers. For example, "Multiculturalism and the history of mathematics" was published in Monthly Review, a socialist magazine, when he was 100. – Timothy Chow Jun 21 '20 at 01:03
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I always like William Veech (57 papers) although it's unlikely, he will catch up. But his citation count is higher (after mathscinet).

Helge
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I think amongst the Field medal laureates, Atle Selberg would be a good candidate: He wrote 48 articles, and only one is a collaboration (with S. Chowla), see this link.

Dominic van der Zypen
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Here is what Zentralblatt (which now includes Jahrbuch der Mathematik) says about Godeaux, Lucien.

https://zbmath.org/authors/?s=0&c=100&q=Godeaux%2C+L Author-ID: godeaux.lucien Published as: Godeaux, L.; Godeaux, Lucien Documents indexed: 1213 Publications since 1906, including 28 Books Co-Authors 1 Brocard, H. 1 Errera, Alfred 1 Mineur, Adolphe 1 Plakhowo, N. 1 Rozet, Octave

And about Vietoris, Leopold

Author-ID: vietoris.leopold Published as: Vietoris, Leopold; Vietoris, L. Documents indexed: 80 Publications since 1916, including 1 Book Co-Authors 1 Tietze, Heinrich

Peter Michor
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I have just noticed that MathSciNet lists a total of 81 publications for John H. E. Cohn: among them, there is only one paper written jointly (viz.: J. H. E. Cohn; L. J. Mordell, On sums of four cubes of polynomials. J. London Math. Soc. (2) 5 (1972), 74–78.). Fibonacci-numbers enthusiasts will surely recognize the name because it was J. H. E. Cohn the individual who proved around 1964 that the largest perfect square in the Fibonacci sequence is $F_{12}=144=12^{2}$; Y. Bugeaud, M. Mignotte, and S. Siksek would establish some forty-odd years laters that, in point of fact, the only non trivial perfect powers in the Fibonacci sequence are $F_{6}=8=2^{3}$ and $F_{12}=144=12^{2}$.

Community
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José Hdz. Stgo.
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Wilfrid Norman Bailey (1893--1961), a British mathematician primarily known for Bailey's lemma (Bailey pairs, Bailey chains) in the theory of basic hypergeometric series, has authored 75 papers and one book. Only one of his papers is joint, with John Macnaghten Whittaker (the son of famous Whittaker from Whittaker--Watson --- notice the order of authors); it is one page long and places Bailey second on the authors' list! More about him can be found in my semi-historical review "Hypergeometric heritage of W.N. Bailey. With an appendix: Bailey's letters to F. Dyson" (http://arxiv.org/abs/1611.08806, published version https://doi.org/10.4310/ICCM.2019.v7.n2.a4).

Wadim Zudilin
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I've checked the complete list of works of Isaac Newton and it does not look as if he ever had a co-author for a single one of his works (I didn't check the entire thing though as it includes over 1500 items).

I think this meets the criteria in terms of highest number of most significant works produced by one single author and no collaborations with anyone.

Hollis Williams
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