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The popular MO question "Famous mathematical quotes" has turned up many examples of witty, insightful, and humorous writing by mathematicians. Yet, with a few exceptions such as Weyl's "angel of topology," the language used in these quotes gets the message across without fancy metaphors or what-have-you. That's probably the style of most mathematicians.

Occasionally, however, one is surprised by unexpectedly colorful language in a mathematics paper. If I remember correctly, a paper of Gerald Sacks once described a distinction as being

as sharp as the edge of a pastrami slicer in a New York delicatessen.

Another nice one, due to Wilfred Hodges, came up on MO here.

The reader may well feel he could have bought Corollary 10 cheaper in another bazaar.

What other examples of colorful language in mathematical papers have you enjoyed?

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closed as off topic by Loop Space, Felipe Voloch, Kevin Buzzard, Mark Sapir, quid Dec 25 '11 at 19:17

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Latest paper, my co-author put in "but we will choose a more painful way, because there is nothing like pain for feeling alive" but the referee jumped on it. –  Will Jagy Apr 23 '10 at 5:09
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Maybe I should expand the question to include colorful language cut from serious mathematics papers :) –  John Stillwell Apr 23 '10 at 5:18
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By the way, your remark reminds me of another in a similar spirit that made it into the Princeton Companion. In his article on algebraic geometry, János Kollár says of stacks: "Their study is strongly recommended to people who would have been flagellants in earlier times." –  John Stillwell Apr 23 '10 at 7:49
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I was actually rather surprised recently by a referee who did not know the phrase “red herring”, and had to look it up. He insisted that we change it to something more understandable. It makes me wonder how much “colourful” language is weeded out by referees, and whether the mathematical literature is poorer for it. –  Harald Hanche-Olsen Apr 24 '10 at 2:31
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@Harald: If you intend your mathematical papers to be read by a wide range of readers, then write them in simple language, suitable for those who are relative beginners in English. I remember reading long ago some metaphoric phrase in a mathematics research paper, then imagining students all over the world getting out their English dictionaries, looking it up, and still not understanding what it meant. (I no longer remember what the phrase was, just this reaction to it.) –  Gerald Edgar Apr 24 '10 at 15:43

108 Answers 108

Frank Adams was notorious for slipping little gems of humour into his paper and books. For instance, from his book, "Infinite Loop Spaces,"

(p. 128)

The reader may expect me to say something about "double coset fomulae." I shall indeed; I advise you to avoid them.

(p. 131)

Of course, this still leaves the question: what do you say to the algebraist who loves double cosets and insists that this is the same thing really? I suggest that you smile politely and say that you are maximizing your chance of finding a helpful and congenial interpretation of the double cosets. There is no need to say that the best interpretation is one which allows you to avoid mentioning the (expletive deleted) things at all.

For further entertainment, look at the entry [85] in the bibliograph, and look at "jokes" in the index.

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Did you use (expletive deleted) for "damn", or was it rather more colorful? –  Harry Gindi Apr 23 '10 at 22:16
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Harry, it's here books.google.com/… and the text itself has (expletive deleted) –  Charles Siegel Apr 24 '10 at 0:58
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Yes, I disagree with Adams about double cosets. Then again the colourful stories about him that came out after he died seemed to me to indicate that I disagreed with him about a number of things (for example the merits of attacking people with axes) –  Kevin Buzzard Apr 24 '10 at 8:13
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@Kevin: Hmm, I don't know which side of the axe issue you stand on. You know what -- it'll come up eventually. Why don't you surprise me? –  Pete L. Clark Apr 24 '10 at 15:23
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I hope this is not seen as mean-spirited, but some years ago, once when I mentioned Adams over coffee (probably in the context of his Lie Groups book) someone asked if I'd heard the joke about the "unstable Adams spectral sequence". (It tickled my fancy; everyone else went back to talking about traffic or football.) –  Yemon Choi Apr 25 '10 at 0:54

A famous Sherlock Holmes meta-mystery is the identity of the giant rat of Sumatra. In The Adventure of the Sussex Vampire, Sherlock Holmes declares to Dr. Watson:

Matilda Briggs was not the name of a young woman, Watson, . . . It was a ship which is associated with the giant rat of Sumatra, a story for which the world is not yet prepared.

Sherlock Holmes fans have tried to figure out what the Giant Rat of Sumatra is, and how it might be related to a ship.
The solution to this greatest of all Sherlock Holmes mysteries is to be found in a mathematics book- one whose topic is Catastrophe Theory. On Page 196 of Curves and Singularities by J.W. Bruce and P.J. Giblin, we learn that the giant rat of Sumatra is in fact the family of functions $f_a(t_1,t_2)=t_1t_2(t_1-t_2)(t_1-at_2)$. Section 11.2 (Pages 196-200) of the book explains how we have established that this is indeed the giant rat of Sumatra, and elucidates why indeed the world is not yet prepared for its story. The relationship between the giant rat and the Matilda Briggs is not discussed, although we are led to suspect the worst, given that Catastrophe Theory is the book's theme.

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I don't even know if this is intentional or not. In his book Teichmuller theory, John Hubbard frequently references the category of Banach Analytic Manifolds. He adheres to the convention that a category be referenced by the concatenation of the first three letters of each constituent word, making the category in question BanAnaMan. This still cracks me up to this day.

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Heh. I am sure this was discovered by coincidence and kept by design. –  Yemon Choi Apr 25 '10 at 0:49
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Greg, congratulations on the great answer badge! –  John Stillwell Sep 17 '10 at 18:06
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Greg, I've just had a look at Hubbard's Teichmüller Theory, and a wonderful book it is. But, alas, I think your memory has deceived you, because his abbreviation for the category of Banach analytic manifolds (page 165) is in fact BanMan. –  John Stillwell Mar 28 '11 at 23:31
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Hmm, since my observation came from a course with Prof. Hubbard using a preprint of the book, I guess he changed it before publication. Thats a little disappointing. –  Greg Muller Mar 29 '11 at 16:27
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It has belatedly struck me that there should really be a contravariant equivalence of categories between Ban(Ana)Man and some category of algebraic objects, which could be abbreviated to ERIC. –  Yemon Choi Aug 23 '11 at 0:56

Diaconis and Efron wrote a paper "Testing for Independence in a Two-Way Table: New Interpretations of the Chi-Square Statistic" that was followed by 10 papers discussing their suggestion. The following is from Diaconis and Efron's rejoiner:

alt text

The critical paper that they refer to starts with a speldid colorful language:

alt text

Update: This is an additional answer too good to be missed. textareaalt text

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According to http://en.wikipedia.org/wiki/Chandler_Davis, page 181 in Chandler Davis' "An extremum problem for plane convex curves" (in Victor L. Klee's "Convexity", Proceedings of Symposia in Pure Mathematics, American Mathematical Society, 1963), one has

"Research supported in part by the Federal Prison System. Opinions expressed in this paper are the author's and are not necessarily those of the Bureau of Prisons."

The paper was written while its author was in prison for refusing to cooperate with the House Unamerican Activities Committee.

The quote can be seen in Google books.

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I wonder if this was a joke or if it was required by the BoP, just as some funding agencies require a similar note. –  Mariano Suárez-Alvarez Oct 21 '10 at 13:46

How come no-one has mentioned Bloch's review of Milne's "Étale cohomology" yet?

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locked by François G. Dorais Dec 18 '11 at 20:37
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The whole review is a must-read... –  darij grinberg Dec 5 '11 at 5:03
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I would like to upvote this for being outrageous, but that would be giving it praise it does not deserve. –  Ryan Reich Dec 12 '11 at 22:41
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Right...thanks, but I doubt I'd have any more fun reading the review than I did reading that quote. –  Elizabeth S. Q. Goodman Dec 13 '11 at 4:47
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I am a bit shocked that something like this was printed in BAMS as late as in the earlier 80s. –  quid Dec 17 '11 at 13:09
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It may well be colourful; it strikes me as crass. –  Yemon Choi Dec 18 '11 at 3:22

There is the following apochryphal dedication of a doctoral thesis:

"I am deeply grateful to Professor X, whose wrong conjectures and fallacious proofs led me to the theorems he had overlooked."

In fact this is a description of excellent supervision, in giving confidence to a student!

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@Yemon: It is told of Pontrjagin that his students gradually realised he had already solved the suggested problem , and this was very offputting. The image of "line manager" is false. A supervisor can suggest a good area in which the student might make some progress, and also to show by example how to cope with failure. "In research, the secret of success is the successful management of failure!" Also, one key question is after failure:"Why did I think this might be a good idea?" Others are: "What are the fall back positions? What are the fall forward positions?" How to manage risk? –  Ronnie Brown Nov 4 '12 at 11:00

From page 329 of Carothers' Real Analysis textbook, where uses Fatou's lemma to prove Lebesgue's dominated convergence theorem: "Now we unleash Fatou!"

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Chang and Keisler's book on Model Theory is dedicated to all those model theorists who have never dedicated a book to themselves.

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Or that they have dedicated some other book to themselves (perhaps secretly?) –  Will Sawin Jan 9 '12 at 23:07

I am rather fond of Sylvester's "Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble and vain attempts of geometry proper to rise to its level or to emulate it in its flights." (1850)

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Jeremy Avigad in Computability and Incompleteness (2002)

... in a sense,computability is similar to the Supreme Court Justice Stewart's characterization of pornography, it may be hard to define precisely, but I know it when I see it."

Not quite from a 'paper' but floating around in the net:

"Who has not been amazed to learn that the function $y = e^x$, like a phoenix rising from its own ashes, is its own derivative?" -- Francois le Lionnais

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Here is a colorful rejoinder by D. Zagier (in his reprinted article on the dilogarithm) to colorful language by Ph. Elbaz-Vincent and H. Gangl:

[Ph. Elbaz-Vincent and H. Gangl] called these functions "polyanalogs," an amalgam of the words "analogue," "polylog," and "pollyanna" (an American term suggesting exaggerated or unwarranted optimism). Presumably the correct term for the case $m=2$ would then be "dianalog," which has a pleasing British flavo(u)r.

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In a paper of F.A.Muller — Sets, Classes and Categories — Solomon Feferman is cited:

I realise that workers in category-theory are so at home in their subject that they find it more natural to think in category-theoretic rather than set-theoretical terms, but I would liken this to not needing to hear once one has learned to compose music.

Colin McLarty in Learning from Questions on Categorical Foundations does mention this, too.

[Feferman 1977] S., 'Categorical Foundations and Foundations of Category Theory', in Logic, Foundations fo Mathematics and Computability Theory, R.E. Butts & J. Hintikka (eds.), Dordrecht: D. Reidel, 1977; pp.149-169

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I confess to such an 'ailment'. But a lot of my work is internal to categories other than Set, so I have no choice, really... –  David Roberts Aug 28 '11 at 22:39
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@David: Please don't feel offended, it's about colorful language, not about category theory. –  Hans Stricker Aug 28 '11 at 23:07
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Still, Feferman is quite mistaken, I believe. Categorists, like other mathematicians, won't hesitate to think in set-theoretic terms if that is what works best in a given situation. –  Todd Trimble Dec 13 '11 at 6:41

While this is not necessarily the meaning of "colorful" intended by the OP, there is probably no better way to find out what motivated the editors of the American Mathematical Monthly to reiterate a damnation by publishing the following erratum, than posting it here:

American Mathematical Monthly volume 77 (1970) p. 78

American Mathematical Monthly volume 77 (1970) p. 78

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I couldn't possibly know, but my suspicion would be that a copyeditor bowdlerized the article without the author's knowledge or permission, and that the author, upon finding out, complained strongly enough for the magazine to give in and publish the correction. –  Ilmari Karonen Aug 29 '11 at 13:52

In Jacquet and Langlands' "Automorphic forms on GL(2)", page 154, they discuss a construction which uses some choices of intermediate objects -- of course the question whether the final result depends on those choices comes up ; here is how they treat it :

We prefer to pretend that the difficulty does not exist. As a matter of fact for anyone lucky enough not to have been indoctrinated in the functorial point of view it doesn’t.

That made me chuckle.

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At the end of the introduction to Spin Glasses: a challenge for mathematicians, Michel Talagrand writes:

It is customary for authors, at the end of an introduction, to warmly thank their spouse for having granted them the peaceful time needed to complete their work. I find that these thanks are far too universal and overly enthusiastic to be believable. Yet, I must say that in the present case even what would sound for the reader as exaggerated thanks would not truly reflect the extraordinary privileges I have enjoyed. Be jealous, reader, for I yet have to hear the words I dread the most: "Now is not the time to work".

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From the introduction of Model Theory by Wilfrid Hodges:

"Finally a dedication. If this book is a success, I dedicate it to my students and colleagues, past and present, in the field of logic. Many of them appear in the pages which follow; but of those who don't, let me mention here two thoughtful and generous souls, Geoffrey Kneebone and Chris Fernau, both now retired, who ran the logic group of London University at Bedford College when I first came to London. If the book is not a success, I dedicate it to the burglars in Boulder, Colorado, who broke into our house and stole a television, two typewriters, my wife Helen's engagement ring and several pieces of cheese, somewhere about a third of the way through Chapter 8."

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How a television, two typewriters, a ring and several pieces of cheese got into Chapter 8, I'll never know. Sorry, just found myself channelling Groucho Marx for a minute there. –  Gerry Myerson Aug 4 '11 at 5:48

Sorry for blowing my own horn: if you read both French and English, you will probably appreciate the title of section 4 in http://archive.numdam.org/ARCHIVE/AIF/AIF_1997__47_4/AIF_1997__47_4_1195_0/AIF_1997__47_4_1195_0.pdf

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In French, Jolissaint is pronounced as "joli seins", which translates as "nice tits" in English. –  ACL Aug 23 '11 at 6:44

According to the book "King of Infinite Space" Coxeter, "tickled his readers with unexpected turns of phrase such as":

... dividing the product of the first three expressions by the product of the last two, and indulging in a veritable orgy of cancellation, we obtain ...

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A gem of R.H. Bing:

Dimension 4 is the most difficult dimension. It is too old to spank, the way we might deal with the little dimensions 1, 2, and 3; but it is also too young to reason with, the way we deal with the grown-up dimensions 5 and higher.

Source here: http://www.ams.org/journals/bull/2011-48-03/S0273-0979-2011-01320-9/S0273-0979-2011-01320-9.pdf

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As an aside, I discovered by experience that searching for "Bing too old to spank" is NOT a good way to find a source for this quote. –  Dave Futer Jul 5 '11 at 14:24

the book "Combinatorial optimization: algorithms and complexity" by Christos H. Papadimitriou, Kenneth Steiglitz contains the following exercise (19, pg 380):

The following is from the New York Times of November 27, 1979. Determine, when possible, whether each statement is (a) true, (b) false, (c) misleading, (d) equivalent to a well-known conjecture, the solution of which was probably not known to Mr. Browne.

alt text

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The following is taken from The paper "Rational points near curves and small nonzero $|x^3-y^2|$ via lattice" by Noam Elkies It was discussed in a previous MO question.

Citing the Simpsons is rather surprising and I wonder what is the story behind it.

alt text

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According to en.wikipedia.org/wiki/Alt.tv.simpsons "The writers also use the newsgroup to test how observant the fans are. In the seventh season episode "Treehouse of Horror VI", the writer of segment Homer3, David S. Cohen, deliberately inserted a false equation into the background of one scene. The equation that appears is $1782^{12} + 1841^{12} = 1922^{12}$." –  Gerry Myerson Apr 7 '11 at 7:25

The AMS Memoirs 947 "Rock Blocks" by Will Turner is full of colorful lanuage. For example in the introduction one finds out that:

"Hannah Turner supported me financially (partly), and libidinously (entirely)."

Or:

"We choose not to spend time chomping on this old pie, since we have become aware of dishes with a more exotic, and alluring aroma."

and so on....

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TMI, Will Turner. –  Todd Trimble Mar 25 at 12:19

Two that I like can be found on p. 756 of Edgar R. Lorch's Amer. Math. Monthly paper "Continuity and Baire functions" (Volume 78, 1971, pp. 748-762):

[...] the reader is reminded of the fact that sets which are of type F_sigma_delta_sigma or G_delta_sigma_delta and not of lower type--with respect to any of the classic topologies--are very thinly scattered through the literature. In fact, looking for them is almost like hunting for unicorns.

In order to penetrate further into this subject it is necessary to give an appropriate structure to T, the set of all coherent topologies. As mentioned earlier, this appropriate structure is itself a topology. This circumstance, that a collection of topologies is topologized, may seem a bit incestuous.

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This is a little off the mark (from a textbook), but Exercise VIII.8.3 of Sarason's [Notes on] Complex Function Theory is:

Stand straight with feet about one meter apart, hands on hips. Bend at the waist, knees straight, and touch left foot with right hand. Straighten. Bend again and touch right foot with left hand. Straighten. Repeat 15 times.

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I was a TA on a course taught by Sarason himself following this book. I had two students "solve" that Exercise during one of my office hours. –  Alfonso Gracia-Saz May 6 '10 at 5:02
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This reminds me of an exercise (C.67) from the chapter about linear transformations in Peter Hackman's Linear Algebra textbook Kossan (mai.liu.se/~pehac/titta/kossaboken). It's in Swedish, but here's an attempt to translate it: "Seize the ends of a pointer between your extended arms, and turn yourself an angle of $v$ radians about your own vertical axis. What have you proved then? Try the same maneuver with the pointer in your right hand, aligned with your straigh arm. Show this to someone who has never studied Linear Algebra. Interpret the result." –  Hans Lundmark Jul 1 '10 at 8:25
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Just a little correction: It's Exercise VIII.8.3, not VII.8.3. –  Irene Adler Aug 18 '10 at 8:48

Yiannis Moschovakis, Notes on Set Theory (1994), p. 81:

6.26 About topology. General (pointset) topology is to set theory like parsley to Greek food: some of it gets in almost every dish, but there are no great "parsley recipes" that the Greek cook needs to know.

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What about Johnstone, in his introduction to Topos Theory (1977):

Finally, I have to state my position on the most controversial question in the whole of topos theory: how to spell the plural of a topos. The reader will already have observed that I use the English plural; I do so because [...] the word topos is not a direct derivative of its Greek root, but a back-formation from topology. I have nothing further to say on the matter, except to ask those toposophers who persist in talking about topoi whether, when they go out for a ramble on a cold day, they carry supplies of hot tea with them in thermoi.

That cracked me up. And for many years it was as far as I got into the book.

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I mentioned this to my supervisor, who immediately responded "why do you need more than one?" –  Yemon Choi Jun 14 '11 at 21:36
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@Yemon: more than one thermus? –  Mariano Suárez-Alvarez Jun 15 '11 at 1:53
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@Mariano: indeed. (I think my supervisor had read that line of Johnstone's before, or been exposed to it in lectures, and hence was indulging in some esprit d'escalier.) –  Yemon Choi Jun 15 '11 at 6:02

In T.Y.Lams book "Lectures on modules and rings" there is a chapter on quotient rings. The three subsections of which are named "The Good", "The Bad" and - of course - "The Ugly". The three subsections are about existence and uniqueness of a "localization" with the universal property in the noncommutative case ("The Good" though nothing is good about this localization in general, everything nice is lost in the general case), Mal'cev's example of a domain that cannot be embedded into a division ring ("The Bad") and further theorems about which classes of rings can be embedded together with example that there need not to be a unique minimal such division ring ("The Ugly").

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From one of the papers on integrable systems

"The authors X.X and Y.Y took only a small peace of the integrability cake...."

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peace or piece? –  David Roberts Apr 6 '11 at 6:01

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