# 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
• Let's go for a paper published since 1995. And to avoid having to devise an absolute scale, I'll ask merely that the journal should be lower ranking than one would have expected, given the great importance of the paper. – gowers Nov 6 '15 at 18:09
• 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

Shelah's paper "A partition theorem" 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. – Mohammad Golshani Aug 14 '17 at 13:02
• It is published where? – მამუკა ჯიბლაძე Aug 20 '17 at 8:28
• @მამუკაჯიბლაძე Scientiae Mathematicae Japonicae – Mohammad Golshani 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 – Mohammad Golshani Aug 20 '17 at 10:29

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.

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.

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):

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:

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.

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 (!)

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.

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.