Publishing papers that became classics before they were submitted

Question

Sometimes the following happens: a result is proven, but the author never submits a paper for publication. In some cases, a preprint appears. In some cases, the proof is so short that it can be presented at a conference or lecture series, and the community is convinced. Maybe it later becomes incorporated in the work of others, book or lecture notes expositions appear, other work generalizes or improves upon it etc. The result is widely accepted, and the community gives due credit.

Now assume that some years later, the author decides to submit the paper to a prestigious journal. How should the editor treat it, depending on the circumstances listed above, importance of the result, etc.? The two obvious extreme points of view are "reject, since the result is not new" and "treat the paper as proving a new result with a somewhat delayed submission", but there's a whole spectrum in between, e.g., "what was good for Annals 20 years ago is not anymore, but OK for a lesser journal".

I would be especially interested in precedents that are publicly known or can be shared publicly.

Answer 1

Such things frequently happened to papers of William Thurston. His opus magnum "Geometry and topology of 3-manifolds" existed as a preprint for several decades, until a part of it was published as a book, but the whole is still unpublished.

His preprint on Combinatorics and dynamics of rational maps was never published in a definite form, even as a preprint. There are papers of other authors which give an exposition of his results. This text revolutionized the subject. In the preface to "On the geometry and dynamics of homeomorphisms of surfaces, Bull. AMS 19 (1988), he wrote:

This article was widely circulated as a preprint, about 12 years ago. At that time the Bulletin did not accept research announcements, and after a couple of attempts to publish it, I gave up, and the preprint did not find a home.

Same applies to many other papers of Thurston. Some of them were published with decades of delay, others never published. He partially explained this situation is his article On proof and progress in mathematics, BAMS 30 (1994). Roughly speaking, he thought that formal publication in a journal was not the best way to spread important ideas.

Edit. Another example is G. Perelman's proof of the Thurston Geometrization conjecture, which the author never submitted to a journal despite a million dollars prize promised. But Perelman at least published his complete text in the arXiv, which Thurston did not care to do.

Edit 2. Another example is the "Esquisse d'un programme" by Grothendieck. This was not even a preprint, but a kind of job application. It made a very substantial influence, and was developed by many people.

Edit 3. Stockholm lectures of Paul Painleve (1895) despite their enormous influence during the last 125 years, exist only as a (hand-written!) preprint.

Answer 2

This happened in my career. In 1984 I published two preprints, joint with M. Lyubich, in Russian and two short announcements based on these preprints (also in Russian). These had a substantial following. In the early 1990s we wrote a paper and submitted it to a journal. The paper was rejected on the grounds that "this is a survey of the well-known results". (Which was essentially true: by that time the results were already well-known since many people read and used our preprints). So we submitted the paper to another journal, and in 1992 the paper was published. It is my most cited paper.

The situation is quite common in the subject of holomorphic dynamics. In 1982 Douady and Hubbard published a large preprint (>200 pages) "Etude dynamique des polynomes complexes" and announced the main results in a CR note. They wanted to write a book, but this plan never materialized. This preprint established the foundation of the study of Mandelbrot set.

Answer 3

There are countless examples, especially if one includes the publication of the Nachlass of a deceased mathematician. Let me mention just one example that I have been looking forward to. The book Integration in Finite Terms: Fundamental Sources (probably not the best hyperlink, but I don't think it has a DOI yet) is slated to be published soon. When I requested more information from one of the editors, Michael Singer, he provided me with a sneak peek at an early draft of the Preface. After explaining that the book contains four items, the first two of which are reprints (of a paper by Rosenlicht and a book by Ritt, both entitled Integration in Finite Terms), the Preface goes on to say:

The third is a revised version of Robert Risch’s unpublished On the integration of elementary functions which are built up using algebraic operations. This latter paper reduced the problem of finding elementary antiderivatives of elementary functions to a problem in arithmetic algebraic geometry: the problem of determining if a point on the jacobian of a curve is of finite order. Risch presented a solution of this latter problem in [Ris70] in the context of deciding the elementary integrability of an algebraic function in [Ris70]. The present paper includes the complete proof. The commentary of Clemens G. Raab discusses the impact of this paper and further developments. The final paper is the unpublished thesis of Barry M. Trager Integration of Algebraic Functions. This latter paper provided practical algorithms for performing the integration in finite terms of algebraic functions after the theoretical results of Risch. It is followed by the commentary of Barry Trager, who gives further insight into the methods of this thesis as well as subsequent developments.

The OP also asks what an editor should do in such situations. Although MO usually frowns upon opinion-based questions, I will offer an opinion anyway. The mathematical community should do more than it currently does to encourage the publication of, or at least the wide distribution of, such material. As a community, we often encourage people to read the masters, and we also take some pride in the "democratic" nature of our subject, meaning that mathematics is open to all. Well, it's not open to all if some of the writings of the masters are available only to a privileged inner circle. Publication of important and highly influential unpublished material does not solve all such problems but it is a step in the right direction. Currently I think we place too much emphasis on novelty. I like what Harold Edwards said in his book Riemann's Zeta Function about Siegel's monumental effort to study Riemann's Nachlass and present his findings to the mathematical public.

One wonders whether anyone else would ever have unearthed this treasure if Siegel had not. It is indeed fortunate that Siegel's concept of scholarship derived from the older tradition of respect for the past rather than the contemporary style of novelty.

Answer 4

Here are two examples of work by John Tate. The first is his PhD thesis:

• Tate, J. Fourier Analysis in Number Fields and Hecke's Zeta-Functions. Thesis (Ph.D.)–Princeton University. 1950

It was hugely influential, but was not published until Tate allowed it to be published in a conference proceedings 15 years later:

• Tate, J. Fourier analysis in number fields, and Hecke's zeta-functions. Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), 305–347, Thompson, Washington, D.C., 1967.

The second is Tate's construction of a $p$-adic uniformization for elliptic curves with non-integral $j$-invariant, which appeared in a letter that was widely circulated. I don't have my copy handy, but it certainly predates exposition of the material by, for example, Alain Robert in 1973 (Elliptic curves. Lecture Notes in Mathematics, Vol. 326. Springer-Verlag, Berlin-New York, 1973). This, too, had a tremendous influence, and a number of people published expositions of the material (with credit to Tate), but the original version was published under Tate's name only in 1995:

• A review of non-Archimedean elliptic functions. Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), 162–184, Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995.

Answer 5

G.A.Margulis announced his super -rigidity and arithmeticity in an ICM talk (which he could not attend). At the next ICM where he received the Fields medal, this was one of the major cited works. He later gave a different proof in an appendix to a Russian translation of M.S Raghunathan's book on discrete subgroups of Lie groups. Later an English translation of this appendix was published in the Inventiones.

Here is a link to the review https://mathscinet.ams.org/mathscinet-getitem?mr=739627

Answer 6

Two other recent examples are Vaughan Jones's 1999 arXiv preprint "Planar algebras. I", [Zbl 07402062] (https://zbmath.org/07402062) or Ragnar-Olaf Buchweitz's 1986 habilitation "Maximal Cohen-Macaulay modules and Tate cohomology" Zbl 07498869, both published posthumously only in 2021 after making a huge impact on the respective fields. In both cases, it seems obvious that the editorial intention was to make a published version available without curtailing their significance.

Side note: As we all know, there are way more examples of unpublished classics around. Actually, a few years ago (when we did some analysis in Bannister, Adam; Teschke, Olaf, An update on time lag in mathematical references, preprint relevance, and subject specifics, Eur. Math. Soc. Newsl. 106, 37-39 (2017). Zbl 1384.01099 of citation delay and publication status in zbMATH), I half-jokingly suggested to a Springer editor to found a journal which accepts only unpublished math classics on the suggestion of an expert board (both examples above would have been among the top 100 most likely candidates) which would become immediately a top impact factor math journal. (Imho, it deserves a honourable mention that the answer included "Fortunately, for math journals, we are not yet slaves of impact factors".)

Answer 7

There are many examples in homotopy theory, and I list a few below (maybe others can add more). I think this is because the field has historically been very friendly (safe to share unpublished results without fear of being scooped) and small enough that conferences were a good way to get ideas out so folks could start using them right away. The arguments are also generally very technical and difficult to write, which delays things further.

Examples:

1. Jacob Lurie has written thousands of pages about infinity categories and higher algebraic geometry, and it has largely been taken up by the community. But only his first book (Higher Topos Theory) has been published as far as I'm aware. His second book Higher Algebra has been cited 1053 times according to Google scholar and has not yet been published. And he has more books, continuing to revolutionize the field.

2. Bousfield localization. This has become an indispensable tool in the field. It allows you to formally add more weak equivalences to your theory (e.g., enlarging from weak homotopy equivalences to rational equivalences). In 1973, Frank Adams presented how to do it at a conference in Chicago (you can still find his lecture notes if you search hard enough on Google). Pete Bousfield was in the audience and famously gave Adams a really hard time about the set-theory. It turns out Pete was right and work was needed! Doug Ravenel was aware of Adams' ideas, and used the localization ideas to carry out new computations. He wrote the paper (now a classic) "Localization with Respect to Certain Periodic Homology Theories" and folks in the field started using it. That paper was finally published in 1984 and includes the line "This paper supersedes a preprint of the same title which I had planned to publish along with [41] in the proceedings of the 1977 Evanston conference." Meanwhile, Bousfield published papers in 1975, 1977, 1978, and 1979 working out the localization theory. Then he published another, in 1996! For the latter, the ideas were out there being used by others (as he points out in the introduction).

3. Jeff Smith is an amazing homotopy theorist who regularly does great mathematics and then never publishes it. Instead, he presents it at conferences and others eventually work it out. For example, he invented combinatorial model categories. Tibor Beke and Clark Barwick wrote down what Smith had in mind, in Sheafifiable homotopy model categories and On left and right model categories and left and right Bousfield localizations. He invented symmetric spectra, solving a hard problem that had been open for 20 years (this was written up by Hovey, Shipley, and Smith later). He also came up with the idea to use Delta-generated spaces in homotopy theory, and several authors have worked out aspects of that story. And he came up with a concept of ideals of ring spectra that Hovey put into paper form (and I did a follow-up but that's beside the point). Most of Smith's ideas are instant classics ("widely accepted and the community gives due credit" as the OP says) but this way of doing things does make publishing difficult.

4. Goodwillie calculus, aka Functor Calculus. It's now a whole branch of homotopy theory. As pointed out in the comments to the OP's question, it was introduced in the early 1980s but Goodwillie's three papers took twenty years to be finished. In the meanwhile, dozens of other papers were written and published using the ideas. The first was published in 1990, the second in 1991, and the third in 2003. However, there are papers as early as 1985 using the theory (e.g., "Contributions to the study of continuous functors" by Char)

I'll add more examples if I think of them. I am sure Mike Hopkins has done things that were immediately taken up and used by the community and then took years to be published.

Your second question was how should the editor treat it when the paper is finally submitted for publication. I would argue that your second extreme "treat the paper as proving a new result with a somewhat delayed submission" is the right answer. As well, the fact that the ideas have been widely accepted and used should count in favor of the submission. People have all sorts of reasons for delaying writing things up. Maybe the author had some trauma in their personal life (death of a spouse, etc), for example. Do we really want to be part of a publishing machine that says "if you don't write it up fast enough, you don't get credit"? I think it's better to have a warmer, more human approach, that understands that sometimes delays happen. We as a community can be intentional about making it a friendlier process, even as academic jobs become more demanding and stressful.

Answer 8

When I was a student at Berkeley, George Bergman handed me his preprint "On diagram-chasing in double complexes" from 1973, that introduced me to the "Salamander lemma". The ideas are beautiful. Eventually Anton Geraschenko blogged about the preprint here. I think this gave enough impetus for George to update the paper and get it published in 2012 in Theory and Applications of Categories.

He has an even more famous preprint "On Jacobson radicals of graded rings" that is extensively cited. It hasn't yet been formally published. However, you can find a list of George's unpublished notes here.

Answer 9

Reprints in Theory and Applications of Categories is a journal for

articles or other works from the body of important literature in Category Theory and closely related subjects which has never been published in journal form, or which has been published in journals whose narrow circulation makes access very difficult.

They have published a number of unpublished PhD theses and as well as reprints of old articles that are hard to find. They have a page explaining their policies.

They are connected to, but distinct from, the journal "Theory and Applications of Categories" mentioned in Pace Nielsen's answer.

Answer 10

Another example in holomorphic dynamics: The paper

Gromov, Mikhaïl On the entropy of holomorphic maps. Enseign. Math., II. Sér. 49, No. 3-4, 217-235 (2003)

is basically the 1977 SUNY preprint (still available from the author's website). Since the beginning it has inspired a lot of research and earned multiple citations. Here is the editors' note appended at the end of the published paper, in my translation from the French (it may need some correction, as I am not as proficient in French as in English, and neither language is my native one):

The preceding article was written in 1976 and has circulated in the form of a SUNY preprint since 1977. We published it "as is", with the exception of the last remark of $\S 4$, adding three references and correcting a small number of misprints. Serge Cantat, whom we thank, kindly agreed to prepare on this occassion a short text to point the reader to some of the numerous works influenced by the article by Mikhaïl Gromov.

Cantat's text, about half a page long, follows the note.

Answer 11

There were several important unpublished results floating around representation theory for years, including the Langlands classification irreducible admissible representations of real algebraic groups and "Schmid's Thesis". Mimeographed copies of the Langlands paper could be obtained from the IAS. Schmid's thesis was available from University Microfilms (what is now ProQuest). Eventually, Paul Sally and David Vogan assembled five such papers and arranged to have them published by the AMS as a book. This was particularly handy because they were re-typeset in TeX, rather than the old typewriter format with handwritten mathematics. So, in this case, the editors decided to treat the papers as something other than a journal article. See MathSciNet entry for "Representation theory and harmonic analysis on semisimple Lie groups", edited by Paul J. Sally, Jr. and David A. Vogan, Jr. (1989)