48
$\begingroup$

This has been inspired by this MO question: Harmonic maps into compact Lie groups

Just for joking: which is your favourite never appeared forthcoming paper?

(do not hesitate to close this question if unappropriate)

$\endgroup$
9
  • 23
    $\begingroup$ I wonder if Bill Thurston is reading this. ;) $\endgroup$ Dec 6, 2010 at 20:17
  • 13
    $\begingroup$ @Nikita: Thurston explained his time-investment choices in a remarkable, penetrative essay, On Proof and Progress in Mathematics: arxiv.org/abs/math/9404236 . $\endgroup$ Dec 7, 2010 at 12:13
  • 7
    $\begingroup$ All of my papers never appeared! $\endgroup$ Dec 8, 2010 at 9:38
  • 2
    $\begingroup$ This question is starting to look a bit over-ripe. I'd vote to close if my vote weren't all-powerful. $\endgroup$
    – S. Carnahan
    Dec 19, 2010 at 8:35
  • 6
    $\begingroup$ I recalled Robert Thomason citing the various preprints of his paper "Algebraic K-theory and etale cohomology" as "to disappear" We are all glad that the paper finally appeared in Ann. Sci. Ecole Norm. Sup. (1985). $\endgroup$
    – F Zaldivar
    Mar 9, 2011 at 17:22

26 Answers 26

68
$\begingroup$

This doesn't exactly count as an unpublished forthcoming paper, but the supposed original proof of Fermat's Last Theorem that was "too large to fit in the margin" should probably be mentioned here.

$\endgroup$
83
$\begingroup$

EGA, Chapters 5 through 12

$\endgroup$
3
  • 3
    $\begingroup$ I can't believe this doesn't get more votes. $\endgroup$
    – AFK
    Jan 25, 2011 at 13:32
  • 16
    $\begingroup$ Well, the author is on vacation isn't he? :) $\endgroup$ Mar 18, 2011 at 12:37
  • 2
    $\begingroup$ Permanently, now... $\endgroup$
    – David Roberts
    Dec 11, 2019 at 23:58
41
$\begingroup$

Volumes 4 through 7 of The Art Of Computer Programming.

$\endgroup$
4
  • 6
    $\begingroup$ 4a is about to come out! $\endgroup$ Dec 7, 2010 at 4:57
  • 31
    $\begingroup$ According to Knuth, 4A was completed and sent to the printer today (December 6th, 2010) $\endgroup$ Dec 7, 2010 at 6:24
  • 1
    $\begingroup$ @Adrian: Were you at the same talk I was? $\endgroup$ Dec 18, 2010 at 23:20
  • 1
    $\begingroup$ I hope he doesn't have a lot of errors in it. :) $\endgroup$ Mar 9, 2011 at 12:14
39
$\begingroup$

The comment about stacks in the paper that first used them in an essential way probably belongs in this list:

"Full details on the basic properties and theorems for algebraic stacks will be given elsewhere." (Deligne-Mumford, The irreducibility of the space of curves of given genus, 1969.)

They don't quite say they will give the details in a paper, of course, so maybe it doesn't count.

$\endgroup$
1
  • 4
    $\begingroup$ I think it counts. Especially since the corresponding book is still forth-coming. $\endgroup$ Dec 7, 2010 at 6:45
37
$\begingroup$

Steven Krantz tells the following story, Mathematical Apochrypha, page 136:

My Ph.D. thesis was based in part on work of Walter Koppelman of the University of Pennsylvania. My source was a very brief research announcement that Koppelman had published in the Bulletin of the AMS. I could never find the promised subsequent paper that would fill in all the details, and I had to fill them in myself. I eventually went to my thesis advisor and asked him where the missing paper was. He said, "Oh, God. Don't you know?" And then he told me the sad story. There was a very unhappy graduate student at the University of Pennsylvania. He had had bad experiences with several thesis advisors (at least so he thought), the last being Koppelman. One day he went into the colloquium, shot the department chairman, shot Koppelman, and shot himself. Koppelman and the student died.

There's a report of the story in Observer-Reporter - Feb 12, 1970, page 23 of 32: https://news.google.com/newspapers?nid=2519&dat=19700212&id=WsddAAAAIBAJ&sjid=bV4NAAAAIBAJ&pg=906,1950274

$\endgroup$
2
  • 21
    $\begingroup$ I can confirm this story. My father was the graduate chairman at the time. He would have been at the talk, but had a headache that day and stayed home. The department chair (I don't remember exactly who, but I think it was Oscar Goldman) was wounded. $\endgroup$
    – Deane Yang
    Jan 25, 2011 at 3:09
  • 7
    $\begingroup$ tea.mathoverflow.net/discussion/918/… $\endgroup$ Jan 25, 2011 at 5:42
22
$\begingroup$

Dana Scott and Robert Solovay, "Boolean-valued models of set theory"

$\endgroup$
4
  • 2
    $\begingroup$ Absolutely — a classic of the literature! $\endgroup$ Dec 6, 2010 at 20:02
  • $\begingroup$ Scott did publish a paper - "A proof of the independence of the continuum hypothesis" (Mathematical Systems Theory, vol. 1, iss. 2, 1967) - on Boolean models and forcing, but the treatment was fairly low-level. I suspect that the intended content of the Scott/Solovay paper is closer to that of the paper "Boolean-valued set theory and forcing" (Synthese, vol. 33, no. 1, 1976) by Richard Mansfield and John Dawson, based off of notes from a seminar run by Dana Scott. $\endgroup$ Mar 9, 2013 at 22:31
  • 1
    $\begingroup$ @Noah: If I remember correctly this paper of Dana Scott presented Boolean-valued models in the context of second or third order arithmetic, concentrating on the particular Boolean extension obtained by adjoining a lot of random reals. (Or am I remembering a different paper from the one you cited.) I agree that the Dawson-Mansfield paper is a reasonable approximation to the nonexistent Scott-Solovay paper. A more detailed version would, I think, be Bell's book. $\endgroup$ Mar 10, 2013 at 2:18
  • $\begingroup$ @Andreas, yes, that's correct. I was just mentioning that paper because one could run across the date, title, and author, and suspect that it was basically the same as the promised Scott/Solovay, which it is not. $\endgroup$ Mar 10, 2013 at 2:49
22
$\begingroup$

Gromov's seminal "Pseudo holomorphic curves in symplectic manifolds" (1985) refers 10 or 15 times (for explanations of further applications that he only refers to or sketches briefly and for even "further discussion on $\overline{\partial}_\nu$ for non-regular curves") to his forthcoming "Pseudo holomorphic curves in symplectic manifolds, II", listed as "in press" by Springer.

It never appeared. Gromov wrote a few later papers on symplectic geometry, but never returned to holomorphic curves. The paper is the foundation of modern symplectic topology (Floer homology, quantum cohomology, Gromov-Witten theory, symplectic field theory, etc.)

$\endgroup$
20
$\begingroup$

Nobody can compete with Fermat, but papers confidently labelled with the roman numeral I and never followed by II might fit here. Of these my favorite is one by Tits, Normalisateurs de tores I in J. Algebra 4 (1966).

$\endgroup$
13
  • 19
    $\begingroup$ Here's a question: is there a paper labeled with roman numeral II for which part I never appeared? $\endgroup$ Dec 6, 2010 at 22:44
  • 7
    $\begingroup$ This isn't as dramatic as what you asked for, but you might be amused by looking at the authors of these papers front.math.ucdavis.edu/… $\endgroup$ Dec 7, 2010 at 3:32
  • 2
    $\begingroup$ @Victor Miller: One can ask even further questions. If there are I and III of something but not II? More generally, $n-1$ and $n+1$ but not $n$? $\endgroup$
    – zhoraster
    Dec 7, 2010 at 7:17
  • 12
    $\begingroup$ According to MathSciNet, Antony Wassermann has a series of papers on "Operator Algebras and Conformal Field Theory", with the first appearing in the 1994 ICM proceedings, the third appearing in Inventiones in 1998, and the second .... ? $\endgroup$
    – Yemon Choi
    Dec 7, 2010 at 17:48
  • 7
    $\begingroup$ Well, I got quite a few queries about where part I of "Applications of random sampling in computational geometry II," by Clarkson and Shor, was. (The answer is that it was called "New applications of random sampling ..." and was single-author Clarkson). $\endgroup$
    – Peter Shor
    Dec 8, 2010 at 20:44
18
$\begingroup$

I'm a fan of Peter May's book The Homotopical Foundation of Algebraic Topology (feel free to correct the title if I've got it wrong). It has been referred to by May in various places, and sounds really interesting! But it has never been written.

$\endgroup$
5
  • 3
    $\begingroup$ I recently emailed him about this and he said that he was commissioned to do this well before I was born, but it will never be written. :) $\endgroup$ Dec 8, 2010 at 16:16
  • $\begingroup$ Too bad. His article in Peter Hilton's birthday volume is sort of a preview for the book. It's called The Dual Whitehead Theorems, I believe. $\endgroup$
    – Dan Ramras
    Dec 8, 2010 at 17:08
  • $\begingroup$ There is also Concise 2 that is in the works and hidden somewhere on his website. $\endgroup$ Jan 25, 2011 at 5:11
  • $\begingroup$ That's exciting! $\endgroup$
    – Dan Ramras
    Jan 25, 2011 at 18:56
  • 1
    $\begingroup$ Concise 2 = 'More concise algebraic topology': math.uchicago.edu/~may/TEAK/KateBookFinal.pdf $\endgroup$
    – David Roberts
    Dec 11, 2019 at 23:59
18
$\begingroup$

How about "The classification of finite quasithin groups" by G. Mason from 1980? The classification of finite simple groups was announced when G. Mason was still working on this important case and he then abandoned the work. This hole in the classification was closed finally in 2004 by M. Aschbacher and S. D. Smith.

$\endgroup$
17
$\begingroup$

The sequel to Kontsevich's "Deformation quantization of Poisson manifolds, I" has never appeared.

$\endgroup$
14
$\begingroup$

Deligne's construction of the Galois representations attached to modular eigenforms (he did give a sketch in a Bourbaki talk though).

$\endgroup$
6
  • 1
    $\begingroup$ And indeed, to this day, I don't think there is a published reference for this result. $\endgroup$
    – Olivier
    Dec 7, 2010 at 15:32
  • $\begingroup$ It's been quite a while since I looked at it, but I recall Tony Scholl's article "Motive for modular forms" filling in some of the details of Deligne's construction. $\endgroup$
    – Ramsey
    Jan 25, 2011 at 2:13
  • 2
    $\begingroup$ Of course, I should seek greater pluralism in my motifs. $\endgroup$
    – Ramsey
    Jan 25, 2011 at 2:30
  • 1
    $\begingroup$ Dear Nick, You are correct re. Scholl's article. Dear Laurent, My memory is that Langlands's article in LNM 349 (vol. II of Antwerp) gives the construction (and quite a bit more). Best wishes, Matt $\endgroup$
    – Emerton
    Jan 25, 2011 at 7:03
  • 2
    $\begingroup$ @Chandan: Kevin Buzzard has explained elsewhere on MO that Brian Conrad's book "achieved infinite length." $\endgroup$ Mar 9, 2011 at 22:20
13
$\begingroup$

The books Classical Banach Spaces III and Classical Banach Spaces IV by Joram Lindenstrauss and Lior Tzafriri never appeared (after having been promised in various places of volumes I and II).

As written by Albrecht Pietsch in his book History of Banach Spaces and Linear Operators, the reason the later volumes never appeared was that "the development was too vigorous. Thus, in order to finish this project, a complete rewriting would have been necessary". Even still, the influence of volumes I and II in Banach space theory has been exceedingly nontrivial; indeed, Pietsch also writes: "The two-volume treatise of Lindenstrauss/Tzafriri on Classical Banach Spaces has become the most important reference of the modern period".

$\endgroup$
9
  • 1
    $\begingroup$ Weren't there actual proofs of results stated in I & II that were meant to appear in III & IV? $\endgroup$
    – Yemon Choi
    Dec 7, 2010 at 3:24
  • 1
    $\begingroup$ @Yemon: At least one such case occurs in the proof that $\ell_\infty$ is prime (Vol. I, p.57). Another instance occurs on p.106. $\endgroup$ Dec 7, 2010 at 3:48
  • 2
    $\begingroup$ Although this is off-topic, this thread has reminded me of the fact that the papers Complementably universal Banach spaces and Complementably universal Banach spaces II by Johnson and Szankowski appeared in print some 33 years apart. I wonder if there is a bigger gap between a paper and its sequel? $\endgroup$ Dec 7, 2010 at 5:11
  • 1
    $\begingroup$ If books are allowed, there will be a ton of examples. Because it is much more difficult to put an end mark to a book than to an article. Let me give two items. The book on semi-groups by Benilan, Crandall and Pazy, the book on analytic geometry by Demailly. $\endgroup$ Dec 7, 2010 at 6:28
  • 2
    $\begingroup$ Phil, at our present pace, the gap between parts II and III will be longer. $\endgroup$ Jan 25, 2011 at 8:10
11
$\begingroup$

Jeff Smith's book on combinatorial model categories.

$\endgroup$
1
  • 5
    $\begingroup$ or his paper on ideals in ring spectra. $\endgroup$ Dec 19, 2010 at 4:12
9
$\begingroup$

Here is a gap in a famous series of papers.

G.H. Hardy, and J.E Littlewood Some problems in Partitio Numerorum, VII

Their series of papers "Partitio Numerorum" is quite influential in the development of the Hardy-Littlewood circle method.

Some comments on the missing part are on page 253 in a paper by R.C. Vaughan, Hardy's legacy to number theory, Journal of the Australian Mathematical Society (Series A) (1998), 65: 238-266. Cambridge University Press

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4937088

$\endgroup$
9
$\begingroup$

Kervaire, Milnor: Groups of homotopy spheres II.

In the introduction to part I, they write:

"More detailed information about these groups will be given in Part II. For example, for $n = 1, 2, 3, \ldots, 18$, it will be shown that the order of the group $\theta_n$ is respectively:" (a table follows). Similar remarks are scattered throughout the text.

The details have been written down by other people and it must be said that part I contains the much more complicated arguments.

$\endgroup$
1
  • 3
    $\begingroup$ In some sense, the sequel appeared; namely, Levine's paper "Lectures on groups of homotopy spheres" contains what he assumed would be the content of Kervaire-Milnor II. $\endgroup$ Mar 9, 2011 at 19:47
8
$\begingroup$

The Igusa-Waldhausen paper (roughly) entitled,

The expansion space model for $Q(X_+)$

which is supposed to give a very different proof of the splitting $A(X) = Q(X_+) \times \text{Wh}^{\text{diff}}(X)$ that is based on a description of $Q(X_+)$ as the moduli space of finite relative cell complexes over $X$.

$\endgroup$
1
  • 11
    $\begingroup$ At one point they were joking that each of them hesitated to put his name on the paper because he did not fully understand the other author's contribution, and that perhaps one way out of this impasse would be to publish it anonymously. $\endgroup$ Mar 9, 2011 at 12:26
8
$\begingroup$

There is a result by Oesterle, that proves that you can find the first non residue quadratic modulo a prime in no more than $70\log(p)^2$ step assuming the GRH, this result was then improved by Bach who replaced the constant $70$ by $2$. The result of Oesterle was never published and when I asked him why, he told me because the laptop containing the proof was stolen from his car. However I think he exposed his proof to the mathematical community, so it is widely recognized.

$\endgroup$
8
$\begingroup$
  • S. Gel'fand, Yu. Manin, Methods of homological algebra, first appeared in Russian as Методы гомологической алгебры. Введение в теорию когомологий и производные категории. Т. 1 (that is VOLUME 1). Volume 2 has never appeared in Russian and also has been given up and the Springer Western edition does not cite Russian original, has many typing errors in formulas which Russian original does not have and it scraped off the tome 1 from the title.

  • M. Demazure, P. Gabriel, Groupes algebriques, tome 1, Mason and Cie, Paris 1970 -- later tomes/volumes never appeared

  • Z. Semadeni, Banach Spaces of Continuous Functions, Polish Scientific Publishers, Warzawa, 1971, second volume never appeared from the Polish Sci. Publ. There is however a different book with a similar title in Springer in 1982, Schauder bases in Banach spaces of continuous functions. Lecture Notes in Mathematics 918. Springer 1982. v+136 pp. MR83g:46023.

  • John W. Gray, Formal category theory: adjointness for 2-categories, Lecture Notes in Mathematics 391, Springer-Verlag 1974. xii+282 pp. has been envisioned as a m3 volume project on formal category theory, some material is mentioned in volume 1 and never appeared. The monograph is very innovative and some of the material from the latter volumes was undoubtfully sketched by the author in some detail. The author later drifted to theoretical computer science.

  • John Duskin started a paper in several parts "Nerves of bicategories", part I appeared with great delay as http://www.tac.mta.ca/tac/volumes/9/n10/n10.pdf, partly due serious health problem the author experienced few years ago. Second part "Bicategory morphisms and simplicial maps" and the promised third part did not appear, although the contents description looks very promising. We wish the author good health and more to be seen!

  • H. Amann, Linear and Quasilinear Parabolic Problems, Volume II: Function Spaces and Linear Differential Operators. This second volume was cited as "in preparation" already in 1997 (see doi:10.1002/mana.3211860102) and continued to be cited this way even in 2016 (see doi:10.1007/s00028-016-0347-1). As of 2017, it seems the book still has not appeared. The structure has changed at least to some extent, too, so that what was meant to be the first chapter will no longer be included (it is made available for free from http://user.math.uzh.ch/amann/books.html instead).

Grothendieck planned not only later EGAs but also later SGA (e.g. some Berthelot's works in SGA 8). Bourbaki Elements are of course never finished as well (an now are very slow, asymptotically stalling) as the German encyclopedic work by Klein's students at the beginning of the 20th century. M. M. Postnikov wrote two volumes of a course on algebraic topology in Russian about basics of homotopy theory and promised the homology in "next semester", but no books appeared on that.

$\endgroup$
4
  • 1
    $\begingroup$ Zoran, I am holding in my hand Banach Spaces of Continuous Functions, Volume 1, Warsawa 1971. Do you mean that it is Volume II which never appeared? $\endgroup$
    – Yemon Choi
    Mar 10, 2011 at 0:17
  • $\begingroup$ Was any of the rest of Demazure–Gabriel ever written (but not completed in book form), or did it not even get that far? $\endgroup$
    – LSpice
    May 11, 2017 at 17:24
  • $\begingroup$ Yes, Yemon Choi, the 2nd volume of Semadeni's book never appeared. $\endgroup$ Aug 24, 2018 at 15:06
  • $\begingroup$ Volume II of Amann's work was published recently, in the foreword it mentions a future 'next volumne' $\endgroup$
    – daw
    Sep 27, 2019 at 11:30
7
$\begingroup$

This one is famous. It has been at the origin of a huge mathematical activity (conservation laws, homogenization, weak KAM, Hamilton-Jacobi equations, etc ...):

P.-L. Lions, G. Papanicolaou, SRS Varadhan. Homogenization of Hamilton-Jacobi equations

$\endgroup$
1
  • $\begingroup$ one of my favorite unpublished paper :) $\endgroup$
    – Hung Tran
    Dec 7, 2010 at 5:07
7
$\begingroup$

Kurt Gödel referred to part II (Der wahre Grund für die Unvollständigkeit, welche allen formalen Systemen der Mathematik anhaftet, liegt, wie im II. Teil dieser Abhandlung gezeigt werden wird, darin, daß die Bildung immer höherer Typen sich ins Transfinite fortsetzen läßt) in his seminal paper Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik 38 (1931) p. 191. This part never appeared.

$\endgroup$
6
$\begingroup$

B. Farb. Automorphisms of $F_n$ which act trivially on homology.

$\endgroup$
6
$\begingroup$

J. Berge. Some knots with surgeries yielding lens spaces.

(c. 1990; cited by 92 on Google Scholar.)

$\endgroup$
4
$\begingroup$

A. Bertrand-Mathis, Le $\theta$-shift sans peine

$\endgroup$
3
$\begingroup$

W. Crawley-Boevey. The Deligne-Simpson problem.

$\endgroup$
3
$\begingroup$

"The Aarhus integral of rational homology 3-spheres IV," by Bar-Natan, Garoufalidis, Rozansky and D. Thurston, never appeared. I think developments in the field overtook the need for the paper, which was referred to in the first paper in the series. This is a great series of papers by the way. Very clearly written.

$\endgroup$
4
  • $\begingroup$ What were to be its results, I think, are the contents of a very recently completed preprint by Kuriya, Le, and Ohtsuki: front.math.ucdavis.edu/1005.3895 I have a different theory as to why "IV" never came out- that understanding the relationship of the Aarhus integral with the Ohtsuki series is a harder problem which requires more techniques, and the authors might not have fully appreciated that at the time "I" was written. I'm very happy that it's done now! $\endgroup$ Dec 19, 2010 at 0:49
  • $\begingroup$ I'm not sure what you mean by "developments in the field overtook the need for the paper"... to which developments were you refering? $\endgroup$ Dec 19, 2010 at 2:10
  • $\begingroup$ I actually was basing my theory on an overheard remark of Stavros Garoufalidis. He was asked if IV was ever coming out, and he said something like "Now that X has appeared, there doesn't seem to be as much need for this." However, I don't know what X was. $\endgroup$
    – Jim Conant
    Dec 19, 2010 at 2:25
  • $\begingroup$ Updated link for The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant from @DanielMoskovich 's comment: arxiv.org/abs/1005.3895 (even published as doi.org/10.1112/jtopol/jts010) $\endgroup$
    – David Roberts
    Sep 24, 2021 at 0:52

Not the answer you're looking for? Browse other questions tagged or ask your own question.