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)?

15$\begingroup$ Quite hard to sharpen anything of Hooley's. $\endgroup$ – Charles Matthews Jun 21 '10 at 13:23

117$\begingroup$ There's a HooleyWooley theorem? The world is a slightly better place than I had realized. $\endgroup$ – Pete L. Clark Jun 21 '10 at 16:17

18$\begingroup$ 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. $\endgroup$ – Greg Kuperberg Jun 21 '10 at 16:27

31$\begingroup$ There's also Hooley, Crelle 328 (1981), 161207, which depends crucially on Milne, Crelle 328 (1981), 208220. Maybe I should have insisted on a joint paper.... $\endgroup$ – JS Milne Jun 21 '10 at 16:49

16$\begingroup$ 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 FeitThompson, HardyLittlewood, AtiyahSinger, 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. $\endgroup$ – Greg Kuperberg Jun 21 '10 at 19:52
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

24$\begingroup$ This is extraordinary! It looks like he kept the Belgian journals in business singlehanded..... $\endgroup$ – Ben Green Jun 21 '10 at 18:35

33$\begingroup$ 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. $\endgroup$ – JS Milne Jun 21 '10 at 19:27

22$\begingroup$ Greg, there are wellknown 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! $\endgroup$ – Victor Protsak Jun 22 '10 at 0:15

16$\begingroup$ 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. $\endgroup$ – GS Jun 22 '10 at 8:52

101$\begingroup$ I guess all the wouldbe coauthors got tired of waiting for Godeaux. $\endgroup$ – Gerry Myerson Aug 16 '13 at 0:35
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/textidx?c=umhistmath&idno=AAN8909

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Leopold Vietoris (18912002) wrote more than 70 papers, only one of them with a coauthor see here.

16$\begingroup$ The last of his papers appearing in 1994. I wonder how many other mathematicians have published after their 100th birthday? $\endgroup$ – GS Jun 21 '10 at 19:16

6$\begingroup$ 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. $\endgroup$ – Victor Protsak Jun 22 '10 at 0:21

29$\begingroup$ Is Euler still posting his papers on the arxiv? $\endgroup$ – Boyarsky Jun 22 '10 at 1:26

2$\begingroup$ 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...) $\endgroup$ – GS Jun 23 '10 at 9:43

14$\begingroup$ 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. $\endgroup$ – Sean Tilson Jul 27 '10 at 1:05
How about Marina Ratner. I believe she has had no collaborators.

25$\begingroup$ Wiles has 21 research papers. Emil Artin's collected works fill a small book. The "quantity" metric is not so meaningful. $\endgroup$ – BCnrd Jun 21 '10 at 17:59

81$\begingroup$ As Gauss said about Dirichlet's output, "One does not weigh jewels on a grocer’s scales”. $\endgroup$ – KConrad Jun 21 '10 at 18:38

12$\begingroup$ That is an awesome quote from Gauss. I would be interested in a reliable citation. $\endgroup$ – Greg Kuperberg Jun 21 '10 at 19:20

14$\begingroup$ 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. $\endgroup$ – John Stillwell Jun 22 '10 at 1:39

33$\begingroup$ 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." $\endgroup$ – Greg Kuperberg Jun 23 '10 at 23:43
I always like William Veech (57 papers) although it's unlikely, he will catch up. But his citation count is higher (after mathscinet).

3$\begingroup$ An excellent example. Like Hooley, he's being resisting collaboration for 50odd years.... $\endgroup$ – Ben Green Jun 21 '10 at 15:00
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.
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 AuthorID: godeaux.lucien Published as: Godeaux, L.; Godeaux, Lucien Documents indexed: 1213 Publications since 1906, including 28 Books CoAuthors 1 Brocard, H. 1 Errera, Alfred 1 Mineur, Adolphe 1 Plakhowo, N. 1 Rozet, Octave
And about Vietoris, Leopold
AuthorID: vietoris.leopold Published as: Vietoris, Leopold; Vietoris, L. Documents indexed: 80 Publications since 1916, including 1 Book CoAuthors 1 Tietze, Heinrich
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.). Fibonaccinumbers 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 fortyodd years laters that, in point of fact, the only non trivial perfect powers in the Fibonacci sequence are $F_{6}=8=2^{3}$ and $F_{12}=144=12^{2}$.
Wilfrid Norman Bailey (18931961), 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 WhittakerWatson  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 semihistorical 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).
I've checked the complete list of works of Isaac Newton and it does not look as if he ever had a coauthor 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.

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1$\begingroup$ @YCor: Pythagoras presumably only authored stone tablets rather than papers :p $\endgroup$ – AlexArvanitakis Oct 14 at 13:30
