Least collaborative mathematician 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)?
 A: 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
A: 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
A: 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 $F_{12}=144=12^{2}$.  
A: 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
A: 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).
A: How about Marina Ratner. I believe she has had no collaborators.
A: Leopold Vietoris (1891-2002) wrote more than 70 papers, only one of them with a coauthor see
here.
A: I always like William Veech (57 papers) although it's unlikely, he will catch up. But his citation count is higher (after mathscinet).
A: 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.
A: 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.
