What are some very important papers published in non-top journals?

Question

There has already been a question about important papers that were initially rejected. Many of the answers were very interesting. The question is here.

My concern in this question is slightly different. In the course of a discussion I am having, the question has come up of the extent to which the perceived quality of a journal is a good reflection of the quality of its papers. The suggestion has been made that because authors tend to submit their best work to the best journals, that makes it easy for those journals to select papers that are on average of a high standard, but it doesn't necessarily solve the reverse problem -- that they miss other papers that are also very important. (Note that the situation more generally in science is different, because there is a tendency for prestigious journals to value papers that make exciting claims, and not to check too hard that those claims are actually correct. So there one has errors of Type I and Type II, so to speak.)

I am therefore interested to know of examples of papers that are very important, but are published in middle-ranking journals. I am more interested in recent papers than in historical examples, since it is the current journal system that we are discussing.

Just in case it doesn't go without saying, please do not nominate a paper that you yourself have written...

Answer 1

One case in point may be

Frey, Gerhard: Links between stable elliptic curves and certain Diophantine equations, Ann. Univ. Sarav. Ser. Math. 1 (1986), no. 1.

This is the paper where Frey establishes the link between modularity and Fermat's Last Theorem.

Answer 2

The way the question is written seems a little weird to me. At first, a phenomenon is described and presented as a fact: many very important papers are published in journals much less well-ranked than we could expect. Then the OP notes that there is no obvious explanation for this fact. And finally he asks, not for an explanation, but for a list of examples corroborating the asserted fact. This is why I added the big-list tag to the question.

Rather than adding an item to the list, let me propose a simple explanation. Many mathematicians care much less about where or even whether they publish their paper than many think. And the proportion of those mathematicians who do not care is even more important among those who wrote a very important paper.

It is not hard to see why. Among the people who write important papers, let us consider three categories. A first consists of people which are very nerdy by standard judgment, who do mathematics for themselves or for a reason known only to themselves, and who do not care about money and their career -- from Casimir to Perelman the list is long and diverse. Those people have no strong incentive to publish, let alone in the best journals. A second category consists of people who are already famous. Actually many of the important papers are written by such mathematicians, I believe. Serre is a good example. Those mathematicians are in general already at the height of their career, have received enough money and honors, and know that their papers will be read wherever they are published. They have no strong incentive to publish in the best journals, except if they happen to be themselves on the editorial board of those journals. Finally, there is the category of people who just wrote their first very important paper. The system give them strong incentives to publish in the best journal, as that will help secure for them a good position and all its advantages. Yet even among them you can have some very self-conscious folks who, well-aware that they have written a very important paper, think they don't need to go under the Caudine Forks of a top journal, and others, at the opposite end, not too confident in themselves or in the system, who prefer to secure a quick publication in a medium-rank journal than to wait for the uncertain result of a review by a top journal.

Answer 3

In 1977 G. Khimshiashvili published in Comm. Acad. Sci Georgian SSR a very nice paper on the computation of the local degree of a degenerate map. You can find his proof in Chap. 5 of the first volume of the book on singularities by Arnold, Gusein-Zade and Varchenko. At about the same time D. Eisenbud and H. Levine proved the same result and published it in Annals of Math

The proofs are based on the same idea, local Grothendieck duality, but the concrete implementations are dramatically different. Whereas Eisenbud and Levine employ sophisticated techniques of commutative algebra in their proof, Khimshiasvilli's proof is elementary and geometric and can be read by anybody with basic knowledge of several variables complex analysis. (The form of local Grothendieck duality used in Khimshiavili's proof is described beautifully in Sec. 5.1 of Griffiths and Harris' book)

Answer 4

Grigori Perelman's proof of Thurston's geometrization conjecture (circa 2002-2003), and its corollary the Poincaré conjecture, was "published" only on arXiv, which in some sense is the journal of least possible rank.

• G. Perelman. The entropy formula for the Ricci flow and its geometric applications. https://arxiv.org/abs/math/0211159

• G. Perelman. Ricci flow with surgery on three-manifolds. https://arxiv.org/abs/math/0303109

• G. Perelman. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. https://arxiv.org/abs/math/0307245

Of course, Perelman specifically declined to submit his work to any traditional peer-reviewed journal, much less a top one; he also declined a Fields Medal and a Clay Millennium Prize.

In fact, I am not sure that a proof of the geometrization conjecture has appeared in any "top" journal (i.e. Annals-level; though I may very well be wrong, as this isn't something I have followed closely). The most commonly cited paper I found was:

Cao, Huai-Dong; Zhu, Xi-Ping. A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006), no. 2, 165–492. MR 2233789

Also noted by ThiKu in comments:

B. Kleiner, J. Lott. Notes on Perelman's papers. Geom. Topol. 12 (2008), no. 5, 2587–2855.

There have been a number of books as well.

Answer 5

Friedrich Wehrung's A solution to Dilworth's congruence lattice problem in Advances in Mathematics, Volume 216, Issue 2, 20 December 2007, Pages 610–625. Dilworth’s half-century-old Congruence Lattice Problem was one of the most famous open problems in lattice theory.

The paper was sent to a more prestigious journal first, but the editors apparently managed to not just reject the paper, but to reject it on the basis that lattice theory lacked "interaction with other areas of mathematics". Makes me wonder whether universal algebra, non-classical logic, or Rota way combinatorics are missing interaction with other areas of mathematics too. (But I realized that the name lattice theory is most unfortunate, because is gives no indication at all what the subject is about, where it starts or where it ends, what it tries to achieve, which type of problems is solves successfully, ...)

Answer 6

The proof of the Gaussian correlation inequality by Thomas Royen was published in Far East Journal of Theoretical Statistics. This resolved a major conjecture at the interface of probability and convex geometry that remained open for more than 40 years. The proof went virtually unnoticed for almost 2 years, as reported in a Quanta magazine article, even though the preprint was available on the arXiv since 2014.

Answer 7

Feit and Thompson published their famous paper Solvability of Groups of odd order in the Pacific Journal, which is a better journal now than it was then. The proof takes up an entire issue of the journal (broken up in six chapters), and you can find it here.

Answer 8

Imre Ruzsa's paper "An application of graph theory to additive number theory" was published in Scientia Series A, Official journal of Universidad Técnica Federico Santa María 3 (1989), 97--109. It described what is now known as Plünnecke's inequalities (or Plünnecke--Ruzsa inequalities) in additive combinatorics.

The OP surely knows the importance of paper, having used the results many times. Nowadays, one of the first things a student of additive combinatorics learns is the content of this paper.

Anyone who tried to get a hold of this paper knows how obscure the journal was (it no longer exists). Back when I searched, there were fewer than five libraries in the United States that had a copy. Thanks to the interlibrary loan!

Answer 9

G. Edgar and C. Miller, Borel subrings of the reals. Proc. Amer. Math. Soc. 131 (2003), no. 4, 1121–1129

This paper proves the Erdos-Volkmann ring conjecture which had been open since at least 1960.

Around the same time (or perhaps a bit later) Bourgain independently found a different proof, using much more sophisticated machinery. Bourgain's paper appeared in GAFA.

One of the motivations for studying this problem was its connections to a host of related problems including the Kakeya conjecture, sum-product estimates, incidence estimates, and the Falconer conjecture. While Bourgain's proof appeared not to extend to finite fields, Bourgain, Katz and Tao were eventually able to apply ideas from the Edgar and Miller approach to finite fields. This lead to the first sum-product and Szemeredi-Trotter theorems in finite fields. These results, in turn, have had a revolutionary impact on additive combinatorics, computer science and harmonic analysis.

In my view, this paper's role in this story has been a bit overlooked. In any event, notwithstanding the subsequent developments, the paper did solve a 43 year old problem which Erdos had worked on.

Answer 10

Here is what naturally came to my mind, before I saw the date constraint. I will add it nonetheless, as it is a fine example of a truly significant paper published in a rather curious choice of journal.

Atle Selberg, Bemerkninger om et multipelt integral (translating from the Norwegian: Remarks on a multiple integral). Norsk matematisk tidsskrift B. 26 (1944), pages 71-78.

It was, as far as I know, the only paper that Selberg published in Norwegian. In his Collected Papers Selberg comments:

This paper was published with some hesitation, and in Norwegian, since I was rather doubtful that the results were new. The journal is one which is read by mathematics-teachers in the gymnasium, and the proof was written out in detail so it should be understandable to someone who knew a little bit of analytic functions and analytic continuation. In a different form I had used the formula given here in my paper Uber einen Satz von A. Gelfond. (Selberg, Collected Papers, vol. 1, p. 212.)

The Selberg integral identity proved in this paper is a generalization of Euler's Beta integral. Selberg discovered it in an early work on a Polya-Hardy-Fukasawa-Gelfond problem concerning integer-valued entire functions with slow growth. As he indicates in the quoted passage, Selberg was hesitant as to whether the formula was worth a separate paper, so he wrote this pedagogical article addressed to high school teachers. It lay for over thirty years in obscurity until Bombieri encountered its complex version in his study of Chebyshev methods in prime number theory; asking Selberg for an opinion, he was immediately referred to the 1944 Norwegian paper. Since then, the Selberg integral has been recognized to have a profound significance for random matrix theory and the Riemann zeta function, as attested by the title of this extremely interesting and informative Bulletin article:

Peter Forrester, Ole Warnaar: The importance of the Selberg integral, Bull. AMS, vol. 45, no. 4 (2008), pp. 389-534.

Answer 11

I am a little late and this paper might be a bit too old to qualify but the quintessential example of this is Grothendieck's 1957 Tohoku paper. The journal became famous because of the paper.

Grothendieck, A. "Sur quelques points d’algèbre homologique, I", Tôhoku Mathematical Journal, (1957) 9(2): 119–221 (dio).

Edit: Just saw Steve Huntsman's comment to the main question but I'll leave my answer here for reference.

Answer 12

On page 168 of Steven G. Krantz's Mathematical Apocrypha (ISBN 0-88385-539-9), we read this:

Marshall Stone was one of the most eminent mathematicians of the twentieth century. He played a seminal role in building up the University of Chicago Mathematics Department in the 1940's and early 1950's. He had a long a distinguished career, and in his later life was a statesman for modern mathematics. A few years ago a big conference was held at the University of Chicago to remember and to honor Stone's many contributions. It was aptly entitled "The Stone Age".

One of Marshall Stone's claims to fame is the "Stone-Weierstrass theorem", a deep and an important generalization of the Weierstrass approximation theorem. This is the sort of result that could have been published in the Annals of Mathematics. But Stone sent it to Mathematics Magazine (his article, "The generalized Weierstrass approximation theorem", appeared in two parts in volume 21 (1948) of Mathematics Magazine: the first part can be found in the March-April issue (pp. 167-184) of the aforementioned volume of the magazine and the second part in the May-June issue (pp. 237-254)) because he had promised them a paper to help them get off to a good start. And that is where this blockbuster paper appears.

You can find additional information regarding this story in this article:

G. L. Alexanderson & P. Ross, Twentieth-century gems from MATHEMATICS MAGAZINE. Mathematics Magazine Vol. 78, No. 2 (Apr., 2005), pp. 110-123.

Answer 13

Somewhat before the cut-off date, but it seems quite fitting otherwise:

Johnson, William B.; Lindenstrauss, Joram "Extensions of Lipschitz mappings into a Hilbert space". Contemporary Mathematics 26. Providence, RI: American Mathematical Society. pp. 189–206, 1984.

This is the paper with the famous lemma, yet it is "only" in a conference proceedings.

Answer 14

Oded Schramm, Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118 (2000), 221--288.

This paper introduces the Schramm-Loewner Evolution (SLE), an amazing family of stochastic processes with deep connections to complex analysis and statistical physics.

Answer 15

If one is prepared to go back to 1987, there is

M. Gromov 'Hyperbolic Groups'. In Essays in group theory, S. Gersten (ed), MSRI publications vol 8.

Though this is more a case of an important paper in a non-(top journal) than a (non-top) journal.

Answer 16

I originally mentioned this one in comments, but realised while checking that I had misremembered the journal. So I've deleted the comment and am taking the opportunity to post it here as an answer for extra visibility, even though it goes against the original question's exact wording:

"I am more interested in recent papers than in historical examples, since it is the current journal system that we are discussing."

Anyway. The first paper that came to my mind when I saw the original question is Le Résumé:

A. Grothendieck, Résumé de la théorie metrique des produits tensoriels topologiques. Boll. Soc. Mat. Sao Paulo 8 (1956), 1–79

Answer 17

Kontsevich published his 1997 seminal preprint "Deformation quantization of Poisson manifolds" in Letters in Mathematical Physics... in 2003.

Letters in Mathematical Physics is a good journal, but it is not a top-journal (especially if one considers the impact of this paper: it solved the most important conjecture in the area and opened the road for a lot of new developments).

Answer 18

The pioneering paper of Selberg introducing the first trace formula, which opened the path to many developments, throwing a wide new light on number theory issues and still widely used as a central tool in the Langlands program:

Selberg A., Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.), 20 (1956), 47-87.

Answer 19

Not sure this counts as a top paper, but certainly the journal is not one would expect given the very serious content, and the authors:

M.F.Atiyah and GB. Segal, Twisted K -theory. Ukrainian Math. Bull. 1 (2004) https://arxiv.org/abs/math/0407054

I'm having trouble even finding the journal online... (AustMS/ARC ranking was B, for those keeping score at home - note that these rankings are no longer updated or current, and are officially deprecated by the Australian Research Council)

Answer 20

I like mentioning the following paper (in italian):

E. De Giorgi: “Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari.” Memorie dell’Accademia delle Scienze di Torino. Parte Prima, Classe di Scienze Fisiche, Matematiche e Naturali (3)3 (1957): 25–43.

This was the last step in the solution of the 19th Hilbert's Problem.

Answer 21

A sadly topical example that comes to mind is

C. J. Read, Relative amenability and the non-amenability of $B(l^1)$. J. Aust. Math. Soc. 80 (2006), no. 3, 317–333. MR 2236040

In this paper, which circulated as a preprint before final acceptance, Read introduced a novel approach to the old problem of showing that $B(E)$ is non-amenable for reasonable Banach spaces $E$. This question had been raised in the 1972 paper of Johnson that introduced amenability for Banach algebras, but to my knowledge the state of play before Read's work was as follows:

1. $B(\ell_2)$ was known to be non-amenable by the mid-to-late 1970s, but this relied intrinsically on ${\rm C}^*$-algebra and von Neumann algebra theory applied to the Calkin algebra. (Alternatively, use amenability implies nuclearity.)

2. For pairs of Banach spaces where $K(E,F)=0\neq K(F,E)$, $B(E\oplus F)/K(E\oplus F)$ has a kind of "upper-triangular structure" (possibly "lower-triangular structure") which is Kryptonite to hopes of amenability. Since amenability passes to quotients, $B(E\oplus F)$ can't be amenable. Cases where we can apply this are $E=\ell_p$ and $B=\ell_q$ for $\infty>p>q\geq 1$.

3. No infinite-dimensional $E$ was known for which $B(E)$ is amenable.

4. For $E=c_0$ or $E=\ell_p$ where $p \in [1,2) \cup (2,\infty]$ no one knew if $B(E)$ is amenable.

Read's paper proved, with customary originality, that $B(\ell_1)$ is not amenable, and his method applied to some other sums of $\ell_p^n$ if I recall correctly. His proof used random hypergraphs as a technical tool: in between the preprint and publication, Pisier (Springer LNM 1850, 2004) showed that one can replace the random hypergraphs with suitable expanders, and then Ozawa (IMRN, 2004) offered an improved argument using configurations from Property (T) groups which handled both $B(\ell_1)$ and $B(\ell_2)$ but not any other $\ell_p$. While I haven't spoken to either Pisier or Ozawa about this work, I had the impression that Read's original result was a breakthrough that spurred people to find improvements.

As a coda, I note that

5. non-amenability of $B(\ell_p)$ for all $1\leq p\leq\infty$ was finally established by Runde (JAMS, 2010), building crucially on estimates established in Ozawa's paper;

6. the space of Argyros and Haydon which solved the "scalar plus compact" problem (Acta Math, 2011) provided the first known example of an infinite-dimensional $E$ for which $B(E)$ is amenable (for, since $E$ is a predual of $\ell_1$, it is relatively easy to deduce that ${\mathbb C} I + K(E)$ is amenable using known techniques). However as far as I know there is no connection between the Argyros-Haydon work and the negative results I've mentioned elsewhere in this answer.

Answer 22

This example predates the 1995 cutoff by quite a bit, but I think it's a nice story people might enjoy. It's from the Ralph P Boas Jr chapter in Albers, Alexanderson, and Reid, More Mathematical People, pp 29-30:

One day I went into the [Cambridge University] mathematical library, glanced at the shelf of new journals, but saw nothing of interest. [Frank] Smithies came in and asked, "Anything interesting today?" "No," I replied in a disgusted tone of voice, "only the Proceedings of the Lund Physiographical Society." Frank went over and picked it up. It turned out to contain Thorin's famous paper on the Riesz convexity theorem and caused a sensation in Cambridge. I now distrust people who want to disregard minor journals.

[I think this is about this and the paper is G. O. Thorin, An extension of a convexity theorem due to M. Riesz, Kungl. Fysiografiska Sällskapets i Lund Förhandlingar (Proceedings of the Royal Physiographic Society at Lund), vol. 8 (1938), no. 14.]

Answer 23

Alastair King's "Moduli of representations of finite-dimensional algebras" (1994) is foundational for everything that has happened in quiver moduli, wall crossing formulae, and various other stability phenomena in the last 20 years; it has 201 citations in MathSciNet. It was published in Quart. J. Math. Oxford Ser. which isn't bad, but I don't think is nearly as prestigious as one would expect in retrospect.

I would guess that the reason it didn't get into a better journal is that none of the proofs are very difficult once one knows what one should prove.

Answer 24

My expertise lies very far from algebra so I am a little hesitant to post this, but my first thought on seeing the question was

J. Tits, Free subgroups in linear groups, Journal of Algebra 20 (1972) 250–270

which has been cited almost eight hundred times according to Google Scholar, and effectively has its own page on Wikipedia. I'm not personally in a position to comment on the standing of Journal of Algebra in the 1970s, but it's not something I think of as being an elite journal today.

Answer 25

Eberhard Hopf's paper on what is now called the Hopf bifurcation appeared in the Proceedings of the Saxon Academy of Sciences in 1942. This is about as obscure as it gets. Of course the war may well have been part of the reason.

Answer 26

There are several very important papers in quantum computing that appear only on arXiv and have not been published at all. Here are some examples (the last one seems to appear in some obscure proceedings though, but I could not find it online):

• Quantum computation by adiabatic evolution (2000) by Farhi, Goldstone, Gutmann and Sipser (797 citations)
• Quantum measurements and the Abelian Stabilizer Problem (1995) by Kitaev (643 citations)
• The Heisenberg representation of quantum computers (1998) by Gottesman (365 citations)

These papers introduce the following important ideas: adiabatic quantum algorithm (an alternative to the standard circuit-based model of quantum computing), the hidden subgroup problem (a wider class of problems amenable to the same techniques as used in Shor's algorithm for factoring), and how Pauli matrices can be used to track quantum evolution (this is useful in quantum error correction and measurement-based computation).

In terms of important published papers, probably the best example is this:

• Quantum cryptography: Public key distribution and coin tossing (1984) by Bennett and Brassard (6946 citations)

It originally appeared in the proceedings of the International Conference on Computers, Systems & Signal Processing in Bangalore, India. It introduces the so-called BB84 protocol for quantum key distribution. On its 20th anniversary, it was re-published in the journal Theoretical Computer Science.

Answer 27

There are at least three famous examples of groundbreaking works, connected to probability theory, that were published in proceedings or non top journals.

1 ) Paul Malliavin: Stochastic calculus of variation and hypoelliptic operators. Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976), pp. 195–263, Wiley, New York-Chichester-Brisbane, 1978.

The paper gave a probabilistic proof of Hormander's theorem and led the foundations of the nowadays called Malliavin calculus.

2) Bakry, D.; Émery, Michel Diffusions hypercontractives. (French) [Hypercontractive diffusions] Séminaire de probabilités, XIX, 1983/84, 177–206, Lecture Notes in Math., 1123, Springer, Berlin, 1985.

The paper is now cited around 450 times on mathscinet and even cited in Perelman's first preprint. The paper led the foundations of the $\Gamma_2$-calculus and of its ramifications to many different areas of mathematics. I actually had the occasion to discuss this with D. Bakry. He told me that he certainly knew that the paper was good, but he did not want to bother with referees and that since the paper is interesting, it will anyhow attract the attention of the worthy mathematicians.

3) Lyons, Terry J. Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998), no. 2, 215–310

The paper essentially builds the rough paths theory. This theory is at the source of the theory of regularity structures for which Martin Hairer was awarded the Fields medal. As far as I know, the paper was actually first submitted to Annals of Math., but a famous probabilist rejected it on the basis that it would have no applications (!)

Answer 28

Gowers, A new proof of Szemerédi's theorem, GAFA, 2001.

Answer 29

My favorite example is Kronheimer and Nakajima's paper " Yang-Mills instantons on ALE gravitational instantons." Math. Ann. 288 (1990), no. 2, 263–307. Here moduli spaces of instantons are shown to be certain quiver varieties, beginning a much deeper understanding of both.

Answer 30

Another old but in retrospect tremendously influential paper:

Edward N. Lorenz (1963). "Deterministic Nonperiodic Flow". Journal of the Atmospheric Sciences. 20 (2): 130–141.

This introduced the butterfly effect (gave a simple example of a chaotic ODE), more or less.