# 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. 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. Nov 6 '15 at 18:37
• The (of course inappropriate) converse, of unimportant papers in top journals, would also be interesting. 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. 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 Nov 8 '15 at 14:15

Shelah's paper A partition theorem, Sci. Math. Jpn., 56(2), 413–438, is such an example.

In this paper Shelah proves a theorem which is equivalent to the main result of the paper Set-polynomials and polynomial extension of the Hales-Jewett theorem which is published in Annals of Mathematics (see Hindman's review of Shelah's paper in Mathscinet), but Shelah's proof has one more advantage; it gives primitive recursive bounds, in particular it answers a question asked by Gowers in his paper Some unsolved problems in additive/combinatorial number theory (see Theorem 5 of the paper on page 5 and the remarks after it).

• In fact, I believe many of Shelah's paper could be published in top journals. Aug 14 '17 at 13:02
• It is published where? Aug 20 '17 at 8:28
• @მამუკაჯიბლაძე Scientiae Mathematicae Japonicae Aug 20 '17 at 10:22
• Another fact is that Shelah's paper contains an infinite dimensional Ramsey theorem (conclusion 3.1 part 2) in $ZFC$ which is proved with creature forcing Aug 20 '17 at 10:29

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? 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. 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". Nov 6 '15 at 23:51
• I think the OP should post these as three separate answers. (I have similar opinions to @LasseRempe-Gillen) Nov 7 '15 at 0:58

Gabriel, Peter Unzerlegbare Darstellungen. I.
Manuscripta Math. 6 (1972), 71–103; correction, ibid. 6 (1972), 309.

where Gabriel introduced representations of quivers and classified quivers of finite representation type.

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.

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.

The paper

Avraham N. Trahtman: The Road Coloring Problem. Israel Journal of Mathematics, Vol. 172, 51–60, 2009

of

R.L. Adler, B. Weiss. Similarity of automorphisms of the torus, Memoirs of the Amer. Math. Soc. 98, Providence, RI, 1970

This was a notorious problem in automata theory that was motivated by symbolic dynamics and had partial results from people like J Friedman and MP Schutzenberger before Trahtman solved it. Moreover, his solution has ideas that have been used in a number of papers.

Many important results in Fair cake-cutting were published in the American Mathematical Monthly.

An early example is: Dubins and Spanier, 1961.

A more recent example is: Su, 1999.

Edit: See the comments for a discussion of this journal, which while not primarily mathematical, is definitely a top journal.

Atiyah and Bott's article on Yang-Mills theory has been cited over 700 times, according to MathSciNet. The reference is

• Atiyah, M. F.; Bott, R. The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523–615. doi:10.1098/rsta.1983.0017.

A personal anecdote: When I was a graduate student, there was a meeting at the American Institute of Mathematics that had gathered together an impressive cadre of mathematicians whose work was heavily influenced by this paper. This was back when AIM was housed in the Fry's Electronics store, a low-slung building in a Palo Alto strip-mall. AIM had a policy against interlopers, but I got permission to join for the day so that I could talk to Bill Goldman. During a conversation, someone incorrectly claimed that the main cohomological results in the Atiyah-Bott paper were rational, not integral. Like a wild west saloon at the appearance of an extra ace, four or five of us dug into our backpacks simultaneously to produce our well-worn copies of the paper, and the matter was quickly put to rest.

• That's hardly a non-top journal - it's just not so well-known for mathematics. Oct 4 at 5:38
• Maybe I should think of it like Proceedings of the National Academy of Sciences in the US? It seems like the journal ended in 1990 so maybe my lack of familiarity with it (apart from this paper) is more about my age and nationality than the journal... Oct 4 at 16:31
• Roughly. The journal is very much still going royalsocietypublishing.org/journal/rsta - and the Philosophical Transactions started being published in 1665, it's pretty much the original journal. Oct 4 at 23:04
• I'm glad to have learned more about this journal! MathSciNet lists it as having ended publication in 1990, maybe due to a change in ISSN. Strange. (Recent mathematical articles in this journal are indexed.) Oct 20 at 20:37
• Yes, I had to dig a little to get the proper journal history: mathscinet.ams.org/mathscinet/search/journal/… the usual search feature doesn't immediately turn up the current version. Confusing as there is the very similarly titled mathscinet.ams.org/mathscinet/search/journal/… Oct 21 at 2:06

Kazimierz Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódz. Mat. 559 (Rozprawy Nauk. 114), Łódź 1989, pp. 1-75.

This is a habilitation thesis of my supervisor. The journal is rather less-known, nevertheless this important dissertation is very-well known and widely quoted in a field of multifunctions of convex-type.