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

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...

• What about something like Perelman's work on the Poincare / geometrization theorem, which he "published" only on arXiv? In some sense that is a minimum-rank journal. – Nate Eldredge Nov 6 '15 at 17:02
• Even more interesting would be self references along with an explanation of why a paper appeared in a lesser journal. – Bill Johnson Nov 6 '15 at 18:37
• The (of course inappropriate) converse, of unimportant papers in top journals, would also be interesting. – Peter Samuelson Nov 6 '15 at 23:34
• Surprised that the word "Tohoku" is not yet on this page, despite the fact that it's much earlier than OP's desired timeframe. – Steve Huntsman Nov 7 '15 at 0:41
• Putting this as a comment instead of an answer because it is quite old: Appel, Kenneth; Haken, Wolfgang (1977), "Every Planar Map is Four Colorable. I. Discharging", Illinois Journal of Mathematics 21(3): 429–490; Appel, Kenneth; Haken, Wolfgang; Koch, John (1977), "Every Planar Map is Four Colorable. II. Reducibility", Illinois Journal of Mathematics 21(3): 491–567 – Joel Reyes Noche Nov 8 '15 at 14:15

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.

• When I posted this, I had not yet seen the lower limit of 1995; so this example is too old... – Michael Stoll Nov 6 '15 at 18:29
• I'm not too fussed about the lower limit -- it was meant as a rough guideline. – gowers Nov 6 '15 at 20:35

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.

• I should add that some journals that are not particularly prestigious have a much more rigorous editing process than a few journals considered as "top" (I won't quote any, and it can depend on the time as the editors - fortunately- have a turnover). And some authors consider this as more important than the "average general ranking opinion", if it ever makes sense. – YCor Nov 7 '15 at 17:59
• I do not disagree much with your assessment of the reality but I am not on board with your reading of the question. To me the referenced discussion seems there to set the context. OP does not even take a position, but just recounts a suggestion that was made by somebody. The questions is intended to provide data for the discussion. Tangentially on: "This is why I added the big-list tag to the question." You did not. But it is there now. – user9072 Nov 7 '15 at 19:06
• Nice answer, and the reference to Caudine Forks was fun and instructive! – Lucia Nov 7 '15 at 19:42
• A discussion, which was rendered obsolete after an edit to the post, has been moved to tea: tea.mathoverflow.net/discussion/1636/… – Todd Trimble Nov 8 '15 at 19:23
• Once more Joël gives a brilliant answer to the type of question which generally sours my attitude towards this site. – Electric Penguin Nov 9 '15 at 18:03

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)

• Is it known if the simpler proof is (a part of) the reason for the less prestigious venue? – Boris Bukh Nov 7 '15 at 2:30
• From what I understand, during Soviet times it was more complicated for a person at the very beginning of his/her career to send a paper for publication in the West. The Georgian journal seemed like a faster alternative and, in the pre-Internet era, that was an important factor. – Liviu Nicolaescu Nov 7 '15 at 4:06
• @Nate Eldredge I will tell you of my experience in communist Romania. The situation in Soviet union was similar, if not worse.To send a paper to a capitalist'' journal you needed approval from communist authorities, the pretext being that of preserving state or economic secrets. The first paper I sent to Western math journal in the mid 80s needed a year worth of wait to get these approvals before I could even mail it. Behind the Iron Curtain we cared, but we had few options. – Liviu Nicolaescu Nov 8 '15 at 1:23
• @RobertIsrael I know Khimshiashvili personally. He told me that he got his PhD in Moscow and his adviser was Palamodov, Palamodov was plenary speaker at the 1966 ICM in Moscow. If you look at the list of Russian mathematicians who were plenary speakers in 1966 (Anosov, Arnold, Graev , Piatesky-Shapiuro,....)you see that Palamodov was highly regarded by his piers. – Liviu Nicolaescu Nov 9 '15 at 23:39
• one should understand that in the USSR publications were of secondary importance to presenting at prestigious seminars. One would present the work at Gerfand's seminar, gain approval of the important people, publish an extended abstract at Doklady, and never bother with writing all the details up to a real publication standard. – Dima Pasechnik Aug 14 '17 at 13:26

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.

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.

• I initially mentioned this in a comment, and am posting an answer by request. This is peripheral to my area and I didn't follow the story particularly closely, so if there are inaccuracies here I hope people will correct them. I know it is also not entirely clear whether this meets the criteria, but I think it is in the spirit. – Nate Eldredge Nov 7 '15 at 0:07
• A publication in a better journal: B. Kleiner, J. Lott. Notes on Perelman's papers. Geom. Topol. 12 (2008), no. 5, 2587–2855. – ThiKu Nov 7 '15 at 1:49
• Still waiting for a vixra example. – Allen Knutson Nov 8 '15 at 2:04
• Maybe one of the readers of this post is encouraged to submit their solid work to vixra to beat the lower bound set by Nate's answer! – Suvrit Nov 9 '15 at 22:49
• I don't think that this is a reasonable example. The only reason why these papers have not been published properly is that Perelman didn't submit them anywhere. Annals or Acta would have accepted them. – M Mueger Nov 11 '15 at 21:46

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, ...)

• This hurts to read, on multiple levels. (Thank goodness though for Adv. Math.) – Todd Trimble Nov 7 '15 at 16:14
• Doron Zeiberger's opinion on that (see math.rutgers.edu/~zeilberg/Opinion81.html ) was an entertaining read: "Because You Snubbed Others You Were Snubbed, and Those Who Snubbed You Shall Be Snubbed". – Gejza Jenča Nov 9 '15 at 21:07
• @GejzaJenča "Entertaining" might be one word for it, for some people... For me, I found it way out of line, and it was one of the things that truly pained (actually, offended) me to read while I was following the second link. – Todd Trimble Nov 10 '15 at 2:31
• @ToddTrimble All Zeiberger's opinions are out of line; maybe even out of plane, space or $\mathbb R^4$. But sometimes he has a point :-) – Gejza Jenča Nov 10 '15 at 6:13
• This is an interesting story, but I strongly disagree with the assessment of Advances as a "non-top" journal. – Igor Rivin Nov 10 '15 at 11:06

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.

• The extreme length of the paper (by contemporaneous standards) was a factor in where this paper ended up, I believe. – Geoff Robinson Nov 8 '15 at 1:46
• Shouldn't there be a clearer reference to this article other than the authors' names? – PatrickT Nov 8 '15 at 9:29
• @GeoffRobinson The story I had heard (many years ago) was that the authors had promised the paper to an editor at the Pacific Journal for some reason... – Igor Rivin Nov 8 '15 at 10:45
• @PatrickT: This was the famous proof of the solvability of groups of odd order. I had not heard that story. The paper was a whole issue of that journal. I don't think John Thompson published any paper in the Annals, although he was definitely on the editorial board at some point. – Geoff Robinson Nov 8 '15 at 10:59
• Thompson's $N$-group papers(s) were arguably more fundamental than the odd order Theorem (he got the Fields medal for the $N$-group work, though Feit-Thompson had already received the Cole prize in algebra for the Odd Order Theorem)- they certainly provided a template for CFSG, though some refinements were necessary. For the record an $N$-group is a finite group in which every non-identity solvable subgroup has a solvable normalizer, and Thompson classified the simple $N$-groups, which include all minimal finite simple groups. – Geoff Robinson Nov 8 '15 at 15:27

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!

• There are other examples among Ruzsa's papers that I am surprised have not yet been mentioned. One example (the OP is familiar with) is Ruzsa's approach to constructing Sidon sequences that overcame a fundamental obstacle on a longstanding open problem: "I. Ruzsa, An infinite Sidon sequence, J. Number Theory 68 (1998)." Another is his Fourier analytic approach to Freiman's theorem which has been very influential in arithmetic combinatorics: "I. Ruzsa, Generalized arithmetical progressions and sumsets". Acta Mathematica Hungarica 65 (4): 379–388." – Mark Lewko Nov 8 '15 at 18:35
• @MarkLewko I think that until the OP and several others (I don't want to list the names, for fear of omitting someone) brought these results to bear on many other problems, this was not viewed as a central area. – Igor Rivin Nov 10 '15 at 11:10

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.

• Some time later Bourgain is said to have asked why this paper was not published in the Annals or something. After Chris and I proved this result, we would mention it in our travels. And David Preiss (who was then in England) heard about it. He was on the editorial board of the PAMS and invited us to submit it there. So we did. – Gerald Edgar Nov 7 '15 at 19:25
• Thanks for the info, Jerry. It would be a better story if you had submitted the paper to the Annals and had it rejected. :) – Bill Johnson Nov 7 '15 at 22:24
• The proof of the Erdos-Volkmann ring conjecture is only 2 pages, perfectly clear and understandable by any one who knows what is a Borel set. A very nice proof! – Joël Oct 12 '17 at 4:01

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.

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.

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 Tohoku paper. The journal became famous because of the paper.

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

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

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.

• One of the rare disagreements between Joram and me was over this. We wanted a paper in this volume dedicated to Kakutani and Joram said that we should publish the paper there. We knew that the lemma was neat and potentially useful since it eliminated the "curse of dimensionality" in certain high dimensional pattern recognition problems and I was worried that putting it in a proceedings volume would bury it. Joram said, "If the lemma is useful, people will find it." As usual, Joram was right, but he did take the trouble to tell Nati Linial about the lemma, and Nati named and publicized it. – Bill Johnson Nov 8 '15 at 3:30

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.

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

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.

• Israel Journal is very strong. – Igor Rivin Nov 10 '15 at 11:12
• Israel Journal is top journal – user21574 Nov 10 '15 at 22:56
• @HassanJolany since I published there myself, I'm happy to agree. Still, this is an unusually strong paper even for such a journal. – Dan Romik Nov 10 '15 at 23:32
• I did not have any first-hand memory on the matter (in spite of being the editor of IJM as well as working with Oded Schramm at that time) but I asked Itai Benjamini who told me that Oded decided to submit the paper to IJM, as a tribute to Israeli mathematics, and especially to the HUJI math department that largely runs IJM where Oded himself studied, and especially to Joram Lindenstrauss who was a major moving force behind IJM and had much influence on Oded himself. Of course, we were very happy to get the paper. – Gil Kalai May 9 '16 at 10:41
• @user21574 define "top journal". I doubt that Israel Journal is at the level of Annals (though if I had to split all the journals into several numerical grades, it would be in the second grade, right after Annals, Inventiones, JAMS, PMIHES) – user140765 May 31 '19 at 10:38

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.

• The associative property seems to hold in the case of non-(top journal) and (non-top) journal. Could you explain why it fails? – PyRulez Nov 6 '15 at 21:38
• @PyRulez: Some things are not journals. – Douglas Zare Nov 6 '15 at 21:49

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).

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

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

1. 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;

2. 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.

• I should add that, according to some stories I heard, that the paper was originally submitted to a much more prestigious journal than JAustMS. – Yemon Choi Nov 6 '15 at 21:39
• Why 'sadly'? (or why 'sadly topical'?) – David Roberts Nov 9 '15 at 4:36
• Because Charles Read died in August 2015. – Gareth McCaughan Nov 9 '15 at 12:53
• Thanks, @GarethMcCaughan; I wasn't aware of him or his work. – David Roberts Nov 10 '15 at 4:14
• @WadimZudilin relative to the significance of the result. (I have a paper in JAuMS, of which I'm quite proud) – Yemon Choi Aug 14 '17 at 14:09

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) http://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)

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.

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.

• Most papers of Selberg fit the bill! For example, the Selberg integral paper is in Norwegian in a journal for high school teachers. (Ah I see this is also Dimitrov's answer.) – Lucia Oct 16 '17 at 16:55

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.

• My impression has always been that Journal of Algebra was a top journal in algebra at least through 1990s (with first Graham Higman and later Walter Feit as the editor-in-chief). – Victor Protsak Apr 20 '17 at 14:43

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.

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.

• How is Mathematische Annalen not a top journal? Or is your point that the KN paper could have been sent somewhere even more "prestigious"? – Yemon Choi Nov 9 '15 at 16:16
• If a paper is published in Math. Ann. when it could have waltzed into Annals, Acta or JAMS, then it counts as an example for my purposes. – gowers Nov 9 '15 at 17:14
• I think what @gowers means is that "math. ann." does not commute. – Vidit Nanda Nov 9 '15 at 21:03

For Applied Mathematics, a good example would be R.E. Kalman's "A New Approach to Linear Filtering and Prediction Problems" in the Transactions of the ASME--Journal of Basic Engineering, 1960. A pdf version of this paper, posted with permission of the ASME, may be found at https://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf.

Wikipedia notes:

Kálmán's ideas on filtering were initially met with vast skepticism, so much so that he was forced to do the first publication of his results in mechanical engineering, rather than in electrical engineering or systems engineering.

This paper (plus two slightly later papers of his) won the AMS Steele prize in 1986.

• From the original question: "I am more interested in recent papers than in historical examples, since it is the current journal system that we are discussing." – Yemon Choi Nov 6 '15 at 18:33
• Google Scholar reports 20,932 citations: scholar.google.com/…. – jeq Dec 10 '15 at 16:10
• Corrected link to Wikipedia quote: en.wikipedia.org/wiki/Rudolf_E._K%C3%A1lm%C3%A1n. – jeq Jun 8 '16 at 19:04
• I thought Kalman filtering was discovered by Gauss... – Igor Rivin Apr 20 '17 at 18:14
• Google Scholar now reports 25,000 citations scholar.google.com/… (a 20% increase in the last year and a half, for whatever reason) and a slightly different search scholar.google.com/scholar?cites=5225957811069312144 gives 34,000 citations. – jeq Apr 26 '17 at 20:09

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

• Does GAFA not count as a "top journal"? It may not quite be on a par with Annals/Acta/Inventiones/JAMS in terms of reputation, but I would think it is generally held in pretty high esteem. – Lasse Rempe-Gillen Nov 6 '15 at 23:47
• I took his approval to apply more to the Doc. Math. paper given in the same answer. I have trouble thinking of GAFA or Adv. Math. as "middle-ranking journals" as stated in the question. And if it becomes "papers that are good enough to have appeared (e.g.) in the Annals but were published instead in another very high-quality, but not quite-as-good journal" then it just seems to become extremely broad to me. No disrespect at all to the fantastic papers cited, of course! – Lasse Rempe-Gillen Nov 7 '15 at 1:08
• First, there is a also "approval by omission." OP commented on that post, would they have a problem with the Advances paper they ought to have said so. Second, Documenta Mathematica is arguably also a very good journal; possibly not yet as widely known as it is still somewhat recent and not advertised much (I think). Finally, what precise criterion do you propose for the journals? If one is not very restrictive with 'top' it becomes quite opinion based what is very high quality (for example depending on subject and location) – user9072 Nov 7 '15 at 10:46
• Well, this may apply also to the first and second proofs of Szemeredi's theorem. – Gil Kalai Nov 7 '15 at 20:14
• If @gowers feels this fits the list then I (and I'm sure many readers) am really curious - what was the reasoning behind the journal choice for this one? – Emilio Pisanty Nov 7 '15 at 23:04

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.]

Varadarajan, V. S. "Groups of automorphisms of Borel spaces." Trans. Amer. Math. Soc. 109 1963 191–220. (Proof of ergodic decomposition for general group actions.)

Goncharov, A. B. "Geometry of configurations, polylogarithms, and motivic cohomology." Adv. Math. 114 (1995), no. 2, 197–318. (Expression of $\zeta_F(3)$ and the Borel regulator in terms of trilogarithms.)

Agol, Ian "The virtual Haken conjecture. With an appendix by Agol, Daniel Groves, and Jason Manning." Doc. Math. 18 (2013), 1045–1087. (Proof of the virtual fibering theorem.)

• Doc. Math.? Adv. Math.? Not top journals? – darij grinberg Nov 6 '15 at 19:25
• I am hardly an expert on these papers, but given the OP's criterion that "the journal should be lower ranking than one would have expected" I do not find anything weird about placing the third paper in this category. The paper solved one of the major open problems in 3-manifold topology. According to the arXiv it has already been cited 113 times for instance. So one would expect that it could have been published in a far more "prestigious" journal. – user1073 Nov 6 '15 at 19:47
• Agreed -- I think it is an excellent example, though I'd guess that it isn't an example that was "missed" by a top journal -- more that the authors probably (and correctly) didn't think that where they submitted it to would make any difference to the prestige they got from the paper. – gowers Nov 6 '15 at 20:38
• To quote the OP, "I am therefore interested to know of examples of papers that are very important, but are published in middle-ranking journals." I have to admit that I have trouble classing Adv. Math. as a "middle-ranking journal". – Lasse Rempe-Gillen Nov 6 '15 at 23:51
• I think the OP should post these as three separate answers. (I have similar opinions to @LasseRempe-Gillen) – Yemon Choi Nov 7 '15 at 0:58

L. A. Santalo, Un invariante afin para los cuerpos convexos del espacio des n dimensiones, Portugaliae Math. 8 (1949), 155–161.

The Blaschke-Santalo inequality.