What are some examples of colorful language in serious mathematics papers?



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?

John Stillwell

Posted 2010-04-23T05:01:02.703

Reputation: 9 944

Question was closed 2011-12-25T19:17:42.973


There are some witty/funny titles (with a pun), see partial list compiled at http://ncatlab.org/nlab/show/punny+title

– Zoran Skoda – 2010-11-05T11:21:28.513

1I find Grillet's Book "Abstract Algebra" quite witty at places. Things like "The diligent reader will delightfully prove" or "so we take the elements, kicking and screaming, ..." turn up every some pages. Made me crack up from time to time. – Matthias Ludewig – 2011-10-22T18:11:40.930

2Was a little surprised to learn of Kollar's sentiment appearing in the Princeton Companion -- funny to see a great mathematician hating on stacks! – Todd Trimble – 2011-10-22T21:06:24.607

69Latest 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 – 2010-04-23T05:09:11.450

16Maybe I should expand the question to include colorful language cut from serious mathematics papers :) – John Stillwell – 2010-04-23T05:18:01.527

I like the idea, of course. – Will Jagy – 2010-04-23T05:34:07.513

37By 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 – 2010-04-23T07:49:36.560

2A paper I've co-authored on mathematical knowledge management ends with "More productive is to frankly embrace its complexity, and try to tame it with tools appropriate for a complex field rather than to do forensics on a carcass." One referee complained, but we left it in. – Jacques Carette – 2010-04-23T11:58:06.520

3Incidentally, in British, the phrase "colourful language" usually means coarse language (possibly from the idea that such language "turns the air blue"). Seeing the title, I came here expecting to vote-to-close but was pleasantly surprised when I read the actual question. – Loop Space – 2010-04-23T14:34:12.820

3Colorful language also means course language in American English, so I too was expecting a rather different set of posts... – Steven Gubkin – 2010-04-23T16:48:53.437


The answer with Andrew Granville's "Zaphod Beeblebrox" title reminded me of this news, Crocheting Adventures with Hyperbolic Planes by Daina Taimina won for oddest book title of 2009, see http://en.wikipedia.org/wiki/Bookseller/Diagram_Prize_for_Oddest_Title_of_the_Year and http://www.guardian.co.uk/books/2010/mar/26/oddest-book-title-award

– Will Jagy – 2010-04-23T17:59:41.887

2When framing the question, I hesitated between "colorful" and "vivid" (as in the old New Yorker fillers entitled "No vivid writing please") but decided to take a chance on "colorful". I'm glad that MO users are open to different interpretations of the word. – John Stillwell – 2010-04-24T01:39:22.977

33I 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 – 2010-04-24T02:31:50.960

28@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 – 2010-04-24T15:43:48.507

2I think this a fun question, but what I don't like about it is that it can go on indefinitely... – Kevin H. Lin – 2010-05-02T19:43:50.237

Here's one I just stumbled upon and made me immediately recall this thread. Too bad no more answers are taken. In Dodson & Parker's "A User's Guide to Algebraic Topology", we have in page 207, "Corollary 6.3.9 (CIA theorem). If odd people fit straight away, then there is no communication after the first level and most of the superstructure is irrelevant." This is a corollary for the fact that a spectral sequence has trivial differentials and thus converges, if $E_{p,q}^2=0$ when $p$ or $q$ is odd. – Bruno Stonek – 2016-01-04T02:04:52.330

Stasheff, Homotopy associativity of H-spaces II, definition 4.4. He defines sputnik homotopies. – Bruno Stonek – 2016-02-19T08:48:17.090

"....the method used to prove that theorem is really discombobulating.. " I don't know why a writer comes up with such a word. – Unknown – 2010-06-12T15:45:20.393

Three In a tree - Chudnovsky and Seymour. WAITING FOR A BAT TO FLY BY IN POLYNOMIAL TIME - , Lovasz – Anthony Hernandez – 2016-10-17T11:09:12.980

Snaith, 1979, Algebraic cobordism and K-theory, section 9: I have written this section in terms of spaces (infinite loopspaces) rather than spectra in order to emphasis the familiar space, BU, rather than the more metaphysical spectrum, BU. – Bruno Stonek – 2017-01-31T13:17:53.137

2This should be reopened because it was closed in a fit of pique in the prime of its life. – Harry Gindi – 2017-08-08T02:12:33.990



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.

Greg Muller

Posted 2010-04-23T05:01:02.703

Reputation: 7 413

9Greg, 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 – 2011-03-28T23:31:37.560

16Hmm, 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 – 2011-03-29T16:27:03.110

3Ah, that makes sense. I'm sure a lot of colorful language gets removed from preprints by nervous editors. – John Stillwell – 2011-03-29T21:26:52.227

7It 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 – 2011-08-23T00:56:26.087

20Do you know that all three parts of BanAnaMan means "I" (Me) in Turkish, Arabic and Persian, respectively? – M. Shahryari – 2014-03-10T17:17:12.147

30Heh. I am sure this was discovered by coincidence and kept by design. – Yemon Choi – 2010-04-25T00:49:23.660

4Greg, congratulations on the great answer badge! – John Stillwell – 2010-09-17T18:06:01.807

2Haha, I suppose I have to give Prof. Hubbard part of the credit. – Greg Muller – 2010-09-17T21:52:50.457


From the ground-breaking paper: On the complexity of omega-automata by Muli Safra

alt text alt text


The author thanks his advisor, Amir Pnueli, for his encouragement and many fruitful discussions on this research.

Moshe Vardi initiated this research by a most illuminating mini-course on ω-automata he presented at the Weizmann Institute. He suggested the problems and helped in clarifying the solutions. Without him the work would not have started, progressed or ended.

Indispensable was the help of Rafi Heiman, whose signature at the bottom of a proof is more valuable than a Q.E.D.

Noam Nisan helped in the complexity evaluation of the determination construction.

Which leaves open the question of what is the author's contribution to the paper.

Gil Kalai

Posted 2010-04-23T05:01:02.703

Reputation: 12 545

10+2 ! while almost all answers made me smile, this literally made my day! – vaxquis – 2014-12-06T15:13:50.623


Does merely transposing two words count? "It is also hard not to show that ..." [Arnold W. Miller, "Some Properties of measure and category," Trans. A.M.S. 266, 1981, p. 106]

Andreas Blass

Posted 2010-04-23T05:01:02.703

Reputation: 53 585

27+1 A very nice alternative for using "it's easy to show", "trivial", "as one easily checks" etc. – Johannes Hahn – 2010-04-25T11:24:02.700


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

Steven Landsburg

Posted 2010-04-23T05:01:02.703

Reputation: 15 393

1so either the systems collapses, either we have proved that the authors are not model theorists. – Maurizio Monge – 2011-12-12T23:45:37.890

8Or that they have dedicated some other book to themselves (perhaps secretly?) – Will Sawin – 2012-01-09T23:07:43.707


The reader who makes it to the later chapters of M. N. Huxley's Area, Lattice Points and Exponential sums is rewarded with the following gem:

"If mathematics were an orchestra, the exponentials would be the violins. The $\rho(t)$ would be the flutes; they are introduced by the exponentials. The Poisson summation formula would be the tuba: powerful, but ridiculous when used too much"

Ben Green

Posted 2010-04-23T05:01:02.703

Reputation: 3 898


Andre Weil (Oeuvres, vol. 2, page 558) purporting to be R.Lipschitz writing from Hades:

"Unfortunately, it appears that there is now in your world a race of vampires, called referees, who clamp down mercilessly upon mathematicians unless they know the right passwords. I shall do my best to modernize my language and notations, but I am well aware of my shortcomings in that respect ; I can assure you, at any rate, that my intentions are honourable and my results invariant, probably canonical, perhaps even functorial.But please allow me to assume that the characteristic is not 2"

Georges Elencwajg

Posted 2010-04-23T05:01:02.703

Reputation: 32 258

1Where was this first published? (Sorry - don't have access to the CW) – Charles Stewart – 2010-04-23T15:05:10.863

3Dear Charles: Ann. of Math. 69, 1959, pages 247-252. – Georges Elencwajg – 2010-04-23T15:27:57.297

28This was a letter to the editor, not a math paper. – KConrad – 2010-04-23T15:36:22.270

9Wow, I'll remember that one for some time. – Pete L. Clark – 2010-04-23T20:12:20.470


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.


Posted 2010-04-23T05:01:02.703

Reputation: 46

9This reminds me of one of Professor Imre Leader's example sheets, which features the question "what can you infer from the previous question about the lecturer's ability to typeset matrices?". Another one, interspersed with serious questions asking for proofs of various equivalences involving the well-ordering principle, was "what's yellow and equivalent to the axiom of choice?". – Adam P. Goucher – 2014-06-28T17:40:39.393

67I 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 – 2010-05-06T05:02:28.747


This reminds me of an exercise (C.67) from the chapter about linear transformations in Peter Hackman's Linear Algebra textbook Kossan (http://users.mai.liu.se/petha45/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 – 2010-07-01T08:25:11.650


A paper of David Bachman-Cooper-White describes a proof that a hyperbolic 3-manifold containing large embedded balls has large Heegaard genus. As they say at the end of the introduction,

a proper subset of the authors wish to subtitle this paper “Big balls imply big genus”

whch is indeed the best way to memorize the result.

Bruno Martelli

Posted 2010-04-23T05:01:02.703

Reputation: 6 731


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.

Jeffrey Giansiracusa

Posted 2010-04-23T05:01:02.703

Reputation: 4 249

4Ravenel's Nilpotence and Periodicity book also lists "jokes" in the index, perhaps as an homage to Infinite Loop Spaces. For "jokes", it says "see humor". For "humor", it says "see comedy". For "comedy", it says, "see Whitehead's initials", and finally, the entry for "Whitehead's initials" sends you back to "jokes". – Sam Nolen – 2011-09-03T21:26:15.110

1I was supposed to be being lectured by Frank Adams for undergraduate ring theory in the late 1980s; but he wrapped his car round a lamp post and killed himself a couple of weeks before the lectures began, so I never got to meet him. These comments just make me regret this even more. – Kevin Buzzard – 2010-04-23T18:17:19.353

1@Kevin: Definitely a great loss. Still, as a modular forms expert, I would expect you to defend double coset calculations as being inevitable despite one's personal feelings about them. No? – Pete L. Clark – 2010-04-23T20:08:06.110

4Did you use (expletive deleted) for "damn", or was it rather more colorful? – Harry Gindi – 2010-04-23T22:16:30.710


Harry, it's here http://books.google.com/books?id=e2rYkg9lGnsC&lpg=PP1&ots=2iYWHQCAYC&dq=Infinite%20Loop%20Spaces&pg=PA131#v=onepage&q&f=false and the text itself has (expletive deleted)

– Charles Siegel – 2010-04-24T00:58:49.797

5Yes, 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 – 2010-04-24T08:13:08.540

15@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 – 2010-04-24T15:23:33.523

7I 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 – 2010-04-25T00:54:05.037


At the risk of blowing my own horn, I will mention the line in the book, Category Theory for Computing Science" by Charles Wells and me. After mentioning the Russell paradox and how to avoid it, we say, "This prophylaxis guarantees safe sets." I caught at least one colleague rolling on the floor laughing, but only after reading it aloud.

Michael Barr

Posted 2010-04-23T05:01:02.703

Reputation: 1


P. T. Johnstone's On a Topological Topos has some interesting choices of words. Sometimes the words are discussed in parenthetical notes.

([...] we are tempted also to introduce the term 'consequential space' for an arbitrary object of $\mathcal{E}$, apart from a slight reluctance to give the name 'space' to an object of a category whose underlying-set functor is not faithful—and, we must admit, the fear that somebody will at once invent a notion of 'inconsequential space'.)

Sometimes there is no more than a reference to existing literature.

The rest of the proof of Theorem 5.1 is a fairly straightforward woozle-hunt (Milne [27])

Reference [27] is, as you may have guessed, A. A. Milne's Winnie The Pooh.

François G. Dorais

Posted 2010-04-23T05:01:02.703

Reputation: 35 811

8isn't there some humorous intention in the choice of the name "pointless topology" ? – Pietro Majer – 2011-01-17T23:54:16.963

43+1 for Pooh, but: It should be remarked that Woozle-Hunting is a rather poor proof technique, given that it involves going in circles for a Long Time, and ends without capturing any Woozles at all. In fact, a proof by Woozle-hunt (that actually proved something) would be a remarkable achievement. – Ketil Tveiten – 2011-02-04T09:27:56.043


From Ravi Vakil's notes "Foundations of algebraic geometry."

He says about spectral sequences:

"They have a reputation for being abstruse and difficult. It has been suggested that the name 'spectral' was given because, like spectres, spectral sequences are terrifying, evil, and dangerous. I have heard no one disagree with this interpretation, which is perhaps not surprising since I just made it up."


Posted 2010-04-23T05:01:02.703

Reputation: 143


For what it's worth, Timothy Chao had a piece "You could have invented spectral sequences" in the Notices (http://www.ams.org/notices/200601/fea-chow.pdf) that claims the name "spectral" is from some sort of analogy with eigenvalues.

– Michael Lugo – 2010-11-05T21:10:37.953

16I thought it was Timothy Chow? – Todd Trimble – 2011-10-22T21:13:18.810


In the acknowledgment to Thomason and Trobaugh's paper on localization in algebraic K-theory, Thomason writes:

The first author must state that his coauthor and close friend, Tom Trobaugh, quite intelligent, singularly original, and inordinately generous, killed himself consequent to endogenous depression. Ninety-four days later, in my dream, Tom's simulacrum remarked, "The direct limit characterization of perfect complexes shows that they extend, just as one extends a coherent sheaf." Awakening with a start, I knew this idea has to be wrong, since some perfect complexes have a non-vanishing $K_0$ obstruction to extension. I had worked on the problem for 3 years, and saw this approach to be hopeless. But Tom's simulacrum had been so insistent, I knew he wouldn't let me sleep undisturbed until I had worked out the argument and could point to the gap. This work quickly led to the key results of this paper. To Tom, I could have explained why he must be listed as a coauthor.

Michael Harris has a rather interesting literary analysis of this quote on his webpage.

As far as I know, this was Trobaugh's only foray into mathematics.

Dan Ramras

Posted 2010-04-23T05:01:02.703

Reputation: 5 258

3+1: A fantastic example. – Todd Trimble – 2011-10-22T21:24:24.973


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.

Dror Bar-Natan

Posted 2010-04-23T05:01:02.703

Reputation: 1 400

12I 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-Álvarez – 2010-10-21T13:46:03.533


The paper "Division by three" by Peter Doyle and John Conway has a wealth of colorful language including:

"If the arrows are good, straight, American arrows, it is very natural for each arrow to dream of marrying the arrow next door."


"Not that we believe there really are any such things as infinite sets, or that the Zermelo-Fraenkel axioms for set theory are necessarily even consistent. Indeed, we’re somewhat doubtful whether large natural numbers (like $80^{5000}$ , or even $2^{200}$) exist in any very real sense, and we’re secretly hoping that Nelson will succeed in his program for proving that the usual axioms of arithmetic—and hence also of set theory—are inconsistent. (See Nelson [6].) All the more reason, then, for us to stick with methods which, because of their concrete, combinatorial nature, are likely to survive the possible collapse of set theory as we know it today."

Steven Gubkin

Posted 2010-04-23T05:01:02.703

Reputation: 6 931

23Yes, although is good to remember that this is an unpublished manuscript, and that Conway "has never approved of this exposition, which he regards as full of fluff." I think this paper would benefit itself immensely if 20 or so pages were left out. – Andrés E. Caicedo – 2010-05-16T14:39:11.780

4"Any large number is finite, and you can start thinking about it as 3." - Conway, 2003. – Akiva Weinberger – 2015-09-01T05:18:37.103


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:

Erratum: In the article, "On the Ph.D. in Mathematics," by I. N. Herstein, on page 821, line 26, of the August-September 1969 issue of the Monthly, please read "damn" instead of "darn."

American Mathematical Monthly volume 77 (1970) p. 78

darij grinberg

Posted 2010-04-23T05:01:02.703

Reputation: 15 489

19I 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 – 2011-08-29T13:52:38.280

2Ah, that makes a lot of sense. – darij grinberg – 2011-08-29T19:24:21.193


From Vector Calculus, Linear Algebra, And Differential Forms. A Unified Approach. by Hubbard:

When a matrix is described, height is given first, then width: an m x n matrix is m high and n wide. After struggling for years to remember which goes first, one of the authors hit on a mnemonic: first take the elevator, then walk down the hall.


Posted 2010-04-23T05:01:02.703

Reputation: 281

7Unless there are two elevators in the building... – Sándor Kovács – 2010-10-21T13:47:16.703

3Works in my building. – Louigi Addario-Berry – 2010-09-15T18:46:59.960

60But then going home transposes the matrix. – Gerry Myerson – 2010-09-16T00:41:28.293


One of my favorites has always been Hermann Weyl's "... the gods have imposed upon my writing the yoke of a foreign language that was not sung at my cradle" (in the preface to his classic text `The Classical Groups: their Invariants and Representations') to excuse his supposedly poor English. This was a conceit of course---as the quote itself shows his command of English was impeccable.

Dick Palais

Posted 2010-04-23T05:01:02.703

Reputation: 12 083


Jon Barwise's Admissible Sets and Structures contains the following on page 69:

When used in a class or seminar, section 6 should be supplemented with coffee (not decaffeinated) and a light refreshment. We suggest Heatherton Rock 'Cakes. (Recipe: Combine 2 cups of self-rising flour with 1 t. allspice and a pinch of salt. Use a pastry blender or two cold knives to cut in 6 T butter. Add 1/3 cup each of sugar and raisins (or other urelements). Combine this with 1 egg and enough milk to make a stiff batter (3 or 4 T milk). Divide this into 12 heaps, sprinkle with sugar, and bake at 400 °F. for 10 — 15 minutes. They taste better than they sound.)

There is a response to this (with stronger ingredients) somewhere in Aki Kanamori's The Higher Infinite but I forgot exactly where. Later in that book, on page 289, Kanamori writes:

But first, a respite from the rigors: Instead of yet another recipe, we offer the following chess problem (M. Henneberger, first and second prize, "Revista de Sah" 1928):

White. King on b1, Rooks on b7 and c7, and Bishop on b5.

Black. King on a8, Rook on a3, and Pawn on f2.

White to play and win.

Send complete solutions to the author for a small prize.

François G. Dorais

Posted 2010-04-23T05:01:02.703

Reputation: 35 811


Masaki Kashiwara writes, in the introduction to his Systems of microdifferential equations:

Although this was a course at a French university, several examples of hyperfunctions are given just before Theorem 3.2.45.

and shortly after that:

The reader is adviced not to commit seppuku instantly if he feels he does not quite understand 2. of chapter 1.

Mariano Suárez-Álvarez

Posted 2010-04-23T05:01:02.703

Reputation: 36 267

2:D :D quote two made me laugh out loud. – David Roberts – 2011-03-11T00:58:26.317


From Strichartz's A Guide to Distribution Theory and Fourier Transforms:

(p.2) "You have almost seen the entire definition of generalized functions. All you are lacking is a description of what constitutes a test function and one technical hypothesis of continuity. Do not worry about continuity--it will always be satisfied by anything you can construct (wise-guys who like using the axiom of choice will have to worry about it, along with wolves under the bed, etc)."


Posted 2010-04-23T05:01:02.703

Reputation: 1


A few days ago, some colorful quotes from Michael Spivak's A Comprehensive Introduction to Differential Geometry were posted here. Yesterday I noticed they were missing, which is a great loss, so I am attempting to restore them. The only one I remember immediately is

Bourbaki has apparently decided that the theory of manifolds has now entered that domain of "dead" mathematics to which he hopes to give definitive form. In this summary of results the corpse is laid out to public view; the complete autopsy is eagerly awaited.

(Volume 5, p.608, of the 2nd edition, 1975)

If anyone recalls some others, please add them.

John Stillwell

Posted 2010-04-23T05:01:02.703

Reputation: 9 944

13"A differential geometer whose work often uses the simplifications obtained by considering the complex domain explained to me that the additional structure of complex manifolds makes them more interesting, just as two sexes are more interesting than one, but various aspects of this argument are open to debate." Volume 5, pg. 394, 3rd edition. – Pait – 2011-07-05T16:44:03.837


From Tilman Bauer's "p-compact groups as framed manifolds:"

For our purposes, it is enough to work in the category of so-called naive G-spectra. I will drop the word “naive” since it will make this work appear so puny.

And in Tilman's paper with Natalia Castellana, "Adjoint spaces and flag varieties of p-compact groups:"

This comment is only meant to intimidate the reader and is insubstantial for what follows.

Craig Westerland

Posted 2010-04-23T05:01:02.703

Reputation: 2 780


In his article "Lectures on Mixed Motives" (Proceedings of Symposia in Pure Mathematics, Volume 62.1, 1997), Spencer Bloch writes:

"My experience with these lectures suggests that motives are like onions; they are complicated, multi-layered objects, and any attempt to cut too quickly to the heart of the matter can leave the audience in tears."

I've actually gotten some mileage out of this analogy in my teaching. When doing the first iterated chain-rule examples in calculus classes, for example, I advocate working "from the outside in" as opposed to the other way around, and employ a variant of Bloch's statement.


Posted 2010-04-23T05:01:02.703

Reputation: 2 258


I was always amazed that Clifford Truesdell could get away with a quote like this:

Nowadays, when the common student seeks a secure berth by grafting himself upon some modest little professor whom he regards as prone to foster painlessly his limaceous glide toward a dissertation not too strenuous or, even better, to draught it for him, tradition is moribund (...)

This is from his introduction to the selected papers of W. Noll. Admittedly, Truesdell was the chief editor himself, and could write therefore whatever he wanted, but it's still pretty strong. Felt too close to home when I first read it as a graduate student!


Posted 2010-04-23T05:01:02.703

Reputation: 887

17I believe that Bass gets credit for a book review with the line- "this book fills a much needed gap in the literature". – aginensky – 2011-01-12T02:52:47.077

5@aginesky: Actually the "much needed gap" is due to my colleague Lee Neuwirth. He put it in a review that the wrote either as a grad student or recent post-doc. Ralph Fox (his advisor) read it and roared with laughter. It was excised from the published version, but quickly made the rounds. – Victor Miller – 2011-01-16T16:03:32.843

108Truesdell is also the author of the single best Math Review ever: "In this paper are presented incorrect solutions to trivial problems. The basic error, however, is not new." – Allen Knutson – 2010-04-25T16:05:19.543


If you have access to MathSciNet, here's the review: http://www.ams.org/mathscinet-getitem?mr=39515

– Jonas Meyer – 2010-04-30T06:47:26.107

13To be nitpicky, the quotation is not quite right. The exact words are "This paper, whose intent is stated in its title, gives wrong solutions to trivial problems. The basic error, however, is not new: [...]." – Hans Lundmark – 2010-07-01T08:06:38.030


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.


Posted 2010-04-23T05:01:02.703

Reputation: 294

13I mentioned this to my supervisor, who immediately responded "why do you need more than one?" – Yemon Choi – 2011-06-14T21:36:53.337

10@Yemon: more than one thermus? – Mariano Suárez-Álvarez – 2011-06-15T01:53:43.730

4@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 – 2011-06-15T06:02:42.983


I like the following footnote that appears in a paper by G. Baumslag:

"I thank Graham Higman for allowing the dust of Oxford to rest on my unopened manuscript for thirty months."


Posted 2010-04-23T05:01:02.703

Reputation: 902

This is the second time I have heard of Higman being careless with manuscripts sent his way - the first was this quote from Lee Lady's article *How Does One Do Mathematical Research?": "Dave [Arnold] thought that it might work to submit it to the editor in chief, Graham Higman. What we weren't aware of was that Graham Higman's desk was a notorious black hole (or Bermuda triangle), where papers disappeared never to be seen again." He then describes their work as undergoing a two-year delay before seeing publication. – silvascientist – 2017-09-12T06:06:45.497


You'll find a whole host of colourful language and allusions scattered throughout the works of Kato. To quote just one example from his Lecture on the approach to Iwasawa theory for Hasse Weil L-functions via $B_{dR}$:

Where is the homeland of zeta values to which the true reasons of celestial phenomena of zeta values are attributed ? How can we find a galaxy train to approach it, which runs through the galaxy of p-adic zeta elements and whose engine is the theory of p-adic periods ? I imagine that one coach of the train has the name 'explicit reciprocity law of p-adic Galois representations'.


Posted 2010-04-23T05:01:02.703

Reputation: 2 024

The "love of girl" also appears in the introduction to Kato and Usui's book Classifying spaces of degenerating polarized Hodge structures. – S. Carnahan – 2012-06-13T02:29:43.440

As a note: he still does this. Kato is currently infamous among UChicago graduate students for having the strangest imaginable analogies for everything.

And somehow, it all works anyway. – Eric Astor – 2014-03-10T17:34:52.977

7Kato lectures like this too. His lectures (at least in the 1990s) often used to start with various bits of philosophy of this nature. I remember vividly his explaining at the IAS that the reason Bloch and Beilinson constructed the right zeta elements in K_2 was that they had very large mouths and loved their wives (and then a long explanation of why these things were relevant, which unfortunately this margin won't contain). It wouldn't surprise me if these comments ended up in print at some point---that's Kato. – Kevin Buzzard – 2010-04-24T08:16:06.350

1Kato teaches like this as well. I remember him teaching theta functions, circa 2004, and coming through as a member of some strange cult (to me at least). Lots of mysticism, lots of references to the occult and kabbala and how the theta function is part of some spiritual realm, and the search for the "true theta function". – Daniel Moskovich – 2010-04-29T04:43:39.913

@Kevin Buzzard: They are in print, in the same lecture mentioned by dke. – Olivier – 2010-04-29T09:16:17.613

Not wishing to mislead, on reflection I can't actually think of that many examples of his 'interesting' lecture style escaping into his writings. Another good lecture involved him attempting to convince the audience that the 'log' in log-structure actually stands for the 'love of girl' that allows the Beauty to tame the Beast residing at logarithmic poles, but I don't recall seeing that appear in print. – dke – 2010-04-29T11:06:53.107


That is on the poster for the log-conf in Bordeaux in June. There's a picture to go with it, see http://www.math.u-bordeaux1.fr/Log_Conf_2010/

– Laurent Berger – 2010-04-30T15:40:04.327

Kaballah? I can only dream of the kind of intense numerology that man must do. How many mathematicians have been numerologists? There is no way other numerologists could compete against them! – Steven Gubkin – 2010-04-30T16:54:51.123


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."


Posted 2010-04-23T05:01:02.703


What a gem! I'm glad that this question is still attracting good answers. – John Stillwell – 2011-08-04T03:14:07.063

21How 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 – 2011-08-04T05:48:49.793


The English translation by Kenji Iohara of Minoru Wakimoto's "Infinite dimensional Lie algebras" is as colourful as it gets, I think. For example on page 8

Namely, we can think of an element of U(A) as an element of A. But since U(A)and A are not isomorphic, this thinking is not an identification but a lonely unrequited love.
Or on page 26

An elegant shape of the left half of Mt. Fuji reflected in the surface of a lake, this is the proportion of the finite-dimensional representations of $\mathfrak{sl}(2,\mathbb{C})$.

Or on page 27

Since ancient times, it has been the charm of music that has soothed the fiercest warriors (or samurai). This law seems to be universal in the physical universe, and it is also true in the world of Lie algebras.
My personal favourite is on page 289
Moreover, the conformal superalgebra (CSA for short) has recently been discovered by Kac, and its definition is given in 2.7 of [K5]. This representation theory has been started in [CK], It is like a matsutake mushroom derived from a big tree called a vertex operator algebra, and it is a portable version of a super-conformal algebra and a vertex operator algebra. There is an experimental report saying that it is more delicious to munch a matsutake mushroom than its landlord- i.e. a Japanese red pine.
Let us munch it a bit.
Unfortunately perhaps, the language is not nearly as colourful in the original Japanese (it's just an outstandingly good book), and is an artifact of the translation. I've long had a dream of doing a more sober translation... but I suppose that Iohara's translation is not without its charm. Anyway, the colourful language is in my opinion is to be attributed to Iohara rather than to Wakimoto.

Daniel Moskovich

Posted 2010-04-23T05:01:02.703

Reputation: 12 674

Surely some fellow MOer who can read the original can tell us whose colourfulness is this? – Mariano Suárez-Álvarez – 2010-04-29T05:10:50.293

4@Mariano I've read the original, which is an outstanding book BTW, but the colourfulness is pretty much (90% at least) Iohara's in my opinion. Or perhaps, it sounds better in Japanese (the translator isn't making stuff up, but he certainly makes it sound more colourful than it was). Contrary to what my appearance might suggest, I speak and read Japanese fluently. – Daniel Moskovich – 2010-04-29T07:19:32.773

I would have put quotes from Michio Kuga's book Galois' Dream, which is more of an undergraduate book, but is very Kuga-ish. I can't find my copy, but the translation was a joint effort that deliberately kept all the Kugaisms. – Will Jagy – 2010-05-01T01:42:51.603


This isn't so much a serious mathematical paper, but Miles Reid - Undergraduate Algebraic Geometry is full of bizarre sentences:

If $I(X)$ is defined as the set of functions vanishing at all points of $X$, then for any point of $X$, all functions of $I(X)$ vanish at it. And indeed conversely, if not more so, just as I was about to say myself, Piglet.


The name of the theorem (Nullstelle = zero of a polynomial + Satz = theorem) should help to remind you of the content (but stick to the German if you don't want to be considered an ignorant peasant).


Posted 2010-04-23T05:01:02.703

Reputation: 145

2Miles Reid is an extraordinarily entertaining speaker. I heard him once call a theorem "Ice-cream of Tuesday" in a talk. More amazing still was that this was indeed a good, descriptive name, for the theorem! – Daniel Moskovich – 2011-02-03T22:47:20.863


From S. Skewes's "On the difference $\pi(x)-\mathrm{Li}(x)$", Proc. LMS 5, 1955:

"I wish in conclusion to express my humble thanks to Professor Littlewood, but for whose patient profanity this paper could never have become fit for publication."

David Hansen

Posted 2010-04-23T05:01:02.703

Reputation: 7 795


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.

Hans Stricker

Posted 2010-04-23T05:01:02.703

Reputation: 3 211


I must post some more examples from Frank Adams. I recommend reading the last section of his paper "Finite H-Spaces and Lie Groups", which contains a letter to the reader written in the voice of the exceptional lie group E8. Two excerpts :

"This is as if one were to award a title for drinking beer, having first fixed the rules so as to exclude all citizens of Heidelberg, Munich, Burton-on-Trent, and any other place where they actually brew or drink much of the stuff."

"In the second place, to consider the question at all reveals a certain preoccupation with ordinary cohomology. Any impartial observer must marvel at your obsession with this obscure and unhelpful invariant."


Posted 2010-04-23T05:01:02.703

Reputation: 131


From Donagi and Smith "The Structure of the Prym Map":

Wake an algebraic geometer in the dead of night, whispering: "27". Chances are, he will respond: "lines on a cubic surface".

Charles Siegel

Posted 2010-04-23T05:01:02.703

Reputation: 10 673

-1 as per your wishes. But +1 and +1 again for the answer. – David Roberts – 2011-03-11T06:19:30.830

Oops! I just voted up and destroyed the magic of 27! I am really sorry, now if I downvote it becomes 26! – auniket – 2012-12-09T18:29:42.480

7Voted back down to 27, although it feels strange to downvote this. – Todd Trimble – 2012-12-16T13:32:18.090

62I hate to comment like this, but for community wiki, I feel less bad, and it won't affect the ranking at this moment...could someone vote this one up? I'd rather like it to have 27 votes, but no more. It feels fitting. – Charles Siegel – 2010-06-02T13:07:53.250

If you edit your post, I will remove my upvote so you can be at 27 again. My vote is currently to old to change without your editing the post. BTW will your total go down to 27 or 26 if I click "downvote?" – Steven Gubkin – 2010-06-07T19:58:12.483

I just edited to include a link to the paper. – Charles Siegel – 2010-06-08T00:37:39.200

2voting down per your wishes... – S. Carnahan – 2010-06-08T00:45:59.333

4Now we just have to get your comment to 27 upvotes as well. – Steven Gubkin – 2010-06-08T13:05:45.503

36+1 but not voted up! – Abhishek Parab – 2010-06-08T13:27:58.160

2228 votes are not a problem: just replace "lines on a cubic surface" by "bitangents to a plane quartic". I'm sure it works. – Laurent Moret-Bailly – 2010-10-10T09:54:11.100


In this MO answer, I mentioned Arnold Miller's lecture notes, where he gives an entertaining account of the MM proof system (for Micky Mouse), having as axioms all validities and modus ponens as the only rule of inference. Although it is easy to prove the Completness theorem from Compactness in this system, it is nevertheless a kind of joke system, since the set of validities is not a decidable set, and so we would be fundamentally unable to recognize whether something is a proof or not in this system. Miller uses this example to illustrate the point as follows:

The poor MM system went to the Wizard of OZ and said, “I want to be more like all the other proof systems.” And the Wizard replied, “You’ve got just about everything any other proof system has and more. The completeness theorem is easy to prove in your system. You have very few logical rules and logical axioms. You lack only one thing. It is too hard for mere mortals to gaze at a proof in your system and tell whether it really is a proof. The difficulty comes from taking all logical validities as your logical axioms.” The Wizard went on to give MM a subset Val of logical validities that is recursive and has the property that every logical validity can be proved using only Modus Ponens from Val.

And he then goes on to describe how one might construct Val, and give what amounts to a traditional proof of Completeness.

Joel David Hamkins

Posted 2010-04-23T05:01:02.703

Reputation: 152 193


From William Thurston's "Hyperbolic Structures on 3-Manifolds I: Deformation of Acylindrical Manifolds":

Let us stick to the case that $M$ is a compact, acylindrical manifold. Then $H(M)$ is a hard-boiled egg. The egg complete with shell is $AH(M)$; it appears to be homeomorphic to a closed unit ball. $GH(M)$ is obtained by thoroughly cracking the egg shell on a convenient hard surface. Apparently no material is physically separated from the egg, but many cracks are developed -- cracks are dense in the boundary -- and at the same time, the material of the egg just inside the shell is weakened, so that neighborhood systems of points on the boundary become thinner. Finally, $QH(M)$ has uncountably many components, which are obtained by peeling off the shell and scattering the pieces all over.

Henry Segerman

Posted 2010-04-23T05:01:02.703

Reputation: 1 051


"Indeed, I wrote the outline of this book while wandering across India, so that, in my mind, Henkin's method is inexorably linked to the droves of wild elephants I met while crawling among the swamp plants of the preserves of Kerala; the elimination of imaginaries, to the gliding vultures above the high Himalayan peaks; and the theorem of the bound, to the naked bodies of the Mauryan women that the traveler saw on the bends of a jungle trail, before they had time to cover themselves. I dare hope only that this book will evoke similarly pleasant images in my reader; I wish it will be as pleasant a companion for you as it was for me."

From Bruno Poizat's "Model Theory". He also constantly belittles the readers of the English edition of the book. Highly recommended!

Steven Gubkin

Posted 2010-04-23T05:01:02.703

Reputation: 6 931


I think we could fill this entire question with Bruno Poizat (aka Johnny B. Goode) quotes. I highly recommend browsing the titles in his bibliography - http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=140590

– François G. Dorais – 2010-04-23T17:11:26.057

2«Quelques modestes remarques à propos d'une conséquence inattendue d'un résultat surprenant de Monsieur Frank Olaf Wagner» is amazing. – Mariano Suárez-Álvarez – 2010-04-23T22:21:46.990

3«Deux ou trois choses que je sais de $L_{n}$» surely beats that one, though! – Mariano Suárez-Álvarez – 2010-04-26T04:47:36.170

2Poizat coined the terms belle paire and the dope. (The first is often translated beautiful pair, but big rack would be a more accurate.) – François G. Dorais – 2010-04-27T02:52:29.983

1@François: I think that "the dope" in the English translation of Cours de théorie des modèles comes from French "la DOP", from English "DOP" (Dimensional Order Property), which is a Shelahian term. I think the story here is that the French-to-English translator wasn't familiar with the English word for the concept... – John Goodrick – 2010-09-15T19:38:07.460


In the Book "Introduction to lattices and order", the authors (B. A. Davey and Hilary A. Priestley) talk about ordered sets with a bottom/top. In this context, they say the following:

Computer scientists commonly choose models which have bottoms, but prefer them topless.


Posted 2010-04-23T05:01:02.703

Reputation: 833


John (Horton) Conway unrelentingly gets away with colorful, even whimsical language in definitions, in explanations, in paper titles, even in some book titles (The Sensual (Quadratic) Form.) Even in SPLAG, there is the following:

"...we earnestly recommend that you use

The Best Method: guess the correct answer, and then justify it." SPLAG, p. 302

On Numbers and Games is just rife with colorful stuff. (I'm surprised no one has pointed out this elephant in the room yet.) The next to last theorem of the book is

THEOREM 99: Any short all-small game G which has atomic weight zero is infinitesimal with respect to (double-up) and dominated by some superstar.

And the last words of the book are famously

"...a certain feeling of incompleteness prompts us to add a final theorem.

THEOREM 100. This is the last theorem in this book.

(The proof is obvious.)" ONAG p. 224

Robert Haraway

Posted 2010-04-23T05:01:02.703

Reputation: 696

1SPLAG?${}{}{}{}$ – Gerry Myerson – 2011-02-03T22:33:07.037

5/Sphere Packing, Lattices, and Groups/, I believe. – Alison Miller – 2011-02-04T19:49:03.207

@Alison, thanks. – Gerry Myerson – 2011-02-04T22:20:57.243

13Theorem 100 reminds me of the second edition of Serre's "Cohomologie galoisienne" (1964, LNM 5) which contains a page of errata numbered E-1. The last line of that page is:

"Page E-1: supprimer la dernière ligne." – Laurent Moret-Bailly – 2011-04-06T09:07:34.443


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

Dave Futer

Posted 2010-04-23T05:01:02.703

Reputation: 894

44As 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 – 2011-07-05T14:24:50.310


There is a paper entitled Zaphod Beeblebrox's Brain and the Fifty-ninth Row of Pascal's Triangle.

Freudenthal made this quote about terminology:

A more imaginative nomenclature than one relying on overburdened terms such as "fundamental," "principal," "regular," "normal," "characteristic," "elementary," and so on is desirable. Inventors of important mathematical notions should give their inventions suggestive names. The disadvantage that good names might prevent the inventor's name from being immortalized as an adjective would be more than compensated by the advantage that this honor could not possibly be bestowed on noninventors.

(from twf:178)


Posted 2010-04-23T05:01:02.703

Reputation: 448


Not from a paper but rather from a book, the first page of the introduction to G. R. Kempf's Algebraic Varieties reads:

"Algebraic geometry is a mixture of the ideas of two Mediterranean cultures. It is the superposition of the Arab science of the lightning calculation of the solutions of equations over the Greek art of position and shape. This tapestry was originally woven on European soil and is still being refined under the influence of international fashion. Algebraic geometry studies the delicate balance between the geometrically
plausible and the algebraically possible. Whenever one side of this mathematical teeter-totter outweighs the other, one immediately loses interest and runs off in search of a more exciting amusement."


Posted 2010-04-23T05:01:02.703

Reputation: 771


This is taken from the seminal paper "Quantum error correction via codes over GF(4)" by A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane.

alt text

Gil Kalai

Posted 2010-04-23T05:01:02.703

Reputation: 12 545


Waldhausen once inserted a bit of music -- written out as notes on a staff -- in the final draft of one of his papers, explaining "This replaces an unnecessary axiom." The melody, by Grieg, was called "Fool's Morning Song".

Tom Goodwillie

Posted 2010-04-23T05:01:02.703

Reputation: 37 782

3@John, is this really an obstruction? – Mariano Suárez-Álvarez – 2010-10-18T18:50:08.170

5The piece (Alborada del Gracioso) is actually by Ravel. It is now an obstruction to republishing the paper in question, since the line of music was put in to avoid a retyping of the following pages, which would be hard to justify if the paper were redone in TeX. – John Rognes – 2010-10-03T13:19:37.920


I like George Kempf's succinct description in that same textbook, of the splitting of vector bundles on P^1 as a theorem "last proved by Grothendieck".

I never forgot Dieudonne's opinion in Foundations of modern analysis chapter 8, that defining a derivative as a number instead of a linear form, is "slavish subservience to the shibboleth of numerical interpretation at any cost."

In the section entitled "Woffle" of Miles Reid's Undergraduate algebraic geometry, he states delightfully that in the prerequisite algebraic chapter II, "the student who is prone to headaches could perhaps take some of the proofs for granted here, since the material is standard, and the author is a professional algebraic geometer of the highest moral fibre."

roy smith

Posted 2010-04-23T05:01:02.703

Reputation: 8 641

1Perhaps only Dickens scholars would laugh out loud at the algebraic geometer's use of "elephants" for "elements", apparently a reference to a remark of Mr. Micawber in David Copperfield, upon entering from outdoors, where he felt he had been buffeted by "the elephants, uh... I mean elements". This presumably is also due to Miles Reid. – roy smith – 2011-01-17T17:08:51.220


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.

Daniel Moskovich

Posted 2010-04-23T05:01:02.703

Reputation: 12 674


The last paragraph of E. Artin's "Theory of Braids":

Although it has been proved that every braid can be deformed into a similar normal form the writer is convinced that any attempt to carry this out on a living person would only lead to violent protests and discrimination against mathematics. He would therefore discourage such an experiment.

Autumn Kent

Posted 2010-04-23T05:01:02.703

Reputation: 9 242


I always liked

$L$ takes on the character of a very thin inner model indeed, bare ruined choirs appended to the slender life-giving spine which is the class of ordinals.

from Kanamori and Magidor `The evolution of large cardinal axioms in set theory' (1978).

Alex Collins

Posted 2010-04-23T05:01:02.703

Reputation: 463


I always liked Edward Burger's A Tail of Two Palindromes. It begins as follows:

Upon a preliminary perusal, this parable may appear to be about pairs of palindromes, periods, and pitiful alliteration. In actuality, however, it is the story of a real quadratic irrational number $\alpha$ and its long-lost younger sibling, its algebraic conjugate $\tilde{\alpha}$ ($\alpha > \tilde{\alpha}$). How in the dickens are all these notions connected? We begin at the beginning... Although the conjugates $\alpha$ and $\tilde{\alpha}$ are not *identical* twins, unlike the two zeros of $(x - 3)^2$, they do share a common family history: they each were born of the same irreducible parent polynomial having rational coefficients, $$P_{\alpha}(x) = P_{\tilde{\alpha}}(x) = (x - \alpha)(x - \tilde{\alpha}) = x^2 - \text{Trace}(\alpha)x + \text{Norm}(\alpha),$$ where $\text{Trace}(\alpha) = \alpha + \tilde{\alpha}$ and $\text{Norm}(\alpha) = \alpha \tilde{\alpha}$. Perhaps not surprisingly, some conjugate pairs exhibit similar personalities. But how similar can they be? And how can we detect those similarities simply by looking at $\alpha$? As we will discover as our tale unfolds, the answer - foreshadowed in the title - is encoded in what can be described as the number theoretic analogue of the DNA-sequence for $\alpha$. However, before delving into $\alpha$'s genes, we first motivate our results by weaving a lattice of algebra.

Qiaochu Yuan

Posted 2010-04-23T05:01:02.703

Reputation: 73 568


Spivak, A Comprehensive Introduction to Differential Geometry, Volume 1, p.94,

Now that we have a well-defined bundle map $TM \to T\;'M$ (the union of all $\beta_x^{-1} \circ \alpha_x$), it is clearly an equivalence $e_M$. The proof that $e_N \circ f_* = f \circ e_M$ is left as a masochistic exercise for the reader.

Volume 3, p. 103, indexed under "Idiot, any,"

These normalizations are usually carried out with hardly a word of motivation, as if they are so natural that any idiot would immediately think of doing them—in reality, of course, the authors already knew what results they wanted, since they were simply reformulating a classical theory.

From Volume 5, p.59,

We are going to begin by deriving certain classical PDE's which describe important (somewhat idealized) physical situations. The word "derive" had better be taken with a hefty grain of salt, however. What I have really tried to do is give plausible reasons why the physical situations should be governed by those PDE's which the physicists have agreed upon. I've never really been able to understand which parts of the standard derivations are supposed to be obvious, which are mathematically simplifying assumptions, which steps are supposed to correspond to empirically discovered physical laws, or even what all the words are supposed to mean.

Incidentally, Spivak gave an entertaining series of lectures on the subject of classical mechanics, whence

I haven't the slightest idea what any of this means! But I'm almost certain that it amounts to the similarity argument we have given. Aren't you glad that you aren't a mathematician of the 17th century!?


Posted 2010-04-23T05:01:02.703

Reputation: 91

Thanks for these! I've been hoping to see more Spivak for a long time. – John Stillwell – 2010-11-05T21:10:49.607


In Berger's "A panoramic view of Riemannian Geometry" :

"The Cayley projective plane $\mathbb{CaP}^2$ is beautiful. In the Riemannian zoo we like to call it the panda."


Posted 2010-04-23T05:01:02.703

Reputation: 40


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

Gil Kalai

Posted 2010-04-23T05:01:02.703

Reputation: 12 545


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)."


"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....


Posted 2010-04-23T05:01:02.703

Reputation: 126

7TMI, Will Turner. – Todd Trimble – 2014-03-25T12:19:22.500


S. S. Abhyankar's book, "Algebraic Geometry for Scientists and Engineers" is actually more for mathematicians, and algebraic geometers in particular. It has the following quip(meant for Andre Weil who wanted to eliminate elimination theory):

Eliminate, eliminate, eliminate, Eliminate the eliminators of elimination theory.

The whole lengthy polemic can be read at this google books link.


Posted 2010-04-23T05:01:02.703

Reputation: 4 101

The google books result actually doesn't contain the whole poem. The extended version, which is certainly more colorful, can be found on pages 18 and 19 of this book:


– Jamie Weigandt – 2010-12-01T00:20:04.270


You might want to read http://www.ucs.louisiana.edu/~avm1260/lenstra.html for hilarious language during lecturing.

Nicky Hekster

Posted 2010-04-23T05:01:02.703

Reputation: 213


In section 3 of

  • J. Frank Adams -- Stable homotopy theory (3rd ed., LNM 3, 1969)

the author discusses two different attitudes towards what the "proper" definition of the stable homotopy category should be, which he personifies by the tortoise and the hare:

The hare is an idealist: his preferred position is one of elegant and all embracing generality. He wants to build a new heaven and a new earth and no half-measures. ... The tortoise, on the other hand, takes a much more restrictive view. He says that his modest aim is to make a cleaner statement of known theorems, and he'd like to put a lot of restrictions on his stable objects so as to be sure that his category has all the good properties he may need. Of course, the tortoise tends to put on more restrictions than are necessary, but the truth is that the restrictions give him confidence.

You can decide which side you're on by contemplating the Spanier-Whitehead dual of an Eilenberg-MacLane object. This is a "complex" with "cells" in all stable dimensions from $-\infty$ to $-n$. According to the hare, Eilenberg-MacLane objects are good, Spanier-Whitehead duality is good, therefore this is a good object: And if the negative dimensions worry you, he leaves you to decide whether you are a tortoise or a chicken. According to the tortoise, on the other hand, the first theorem in stable homotopy theory is the Hurewicz Isomorphism Theorem, and this object has no dimension at all where that theorem is applicable, and he doesn't mind the hare introducing this object as long as he is allowed to exclude it. Take the nasty thing away!

Beren Sanders

Posted 2010-04-23T05:01:02.703

Reputation: 1 731


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".

Tom LaGatta

Posted 2010-04-23T05:01:02.703

Reputation: 4 525


Does Serre's naming of the Pin group count as "colorful language"?

Kevin H. Lin

Posted 2010-04-23T05:01:02.703

Reputation: 11 992


I don't agree with this quote by Errett Bishop (a constructivist who developed real analysis along constructive lines), but I admire its brio:

Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself.

It's an odd spin on that famous Kronecker quote about the integers and God.


Posted 2010-04-23T05:01:02.703

Reputation: 3 929


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 http://epublius.de/mathoverflow/approach.png

Ori Gurel-Gurevich

Posted 2010-04-23T05:01:02.703

Reputation: 5 956

What is the complete exercise? – Mariano Suárez-Álvarez – 2010-10-21T13:46:47.900

I didn't have the patience to type in the NYT article itself. Take a look at the link. – Ori Gurel-Gurevich – 2010-10-21T15:53:57.197


In a paper by Stark where he proves Gauss conjecture that there are only nine imaginary qudratic fields where the integers form a UFD writes that Heegner used "classified theory".

I once met Stark and asked him if did not correct the misprint on purpose, but he did not even remember it.

Gert Almkvist

Posted 2010-04-23T05:01:02.703

Reputation: 111


I've always marveled that the abbreviated terminology for "thickenings of the corresponding special Lagrangian" on the bottom of page 26 of this paper of Richard Thomas made it into print:



Posted 2010-04-23T05:01:02.703

Reputation: 810

I had to look up the U.K. slang usage. I knew of only "partially vitreous by-product of smelting ore" as in the wikipedia page. – Will Jagy – 2010-04-23T19:52:17.790

25That's an example of colourful language, not colorful language :) – François G. Dorais – 2010-04-23T19:55:00.567


He was inspired by the following famous UK comic: (http://en.wikipedia.org/wiki/The_Fat_Slags) I saw him give a talk on the subject once. When the phrase came up all the English people in the audience laughed and everyone else looked around with very confused expressions on their faces.

– Joel Fine – 2010-04-24T08:14:53.483

5This is more colloquial than you think! The Fat Slags are a pair of well-known cartoon characters from Viz magazine. Given that he's a Brit, it's surely a reference to them. – Kevin Buzzard – 2010-04-24T08:20:47.823


Masaaki Yoshida's book "Hypergeometric Functions, My Love" is packed with many colorful passages. For example, opening at random I find:

"(Do you think I should write $R^{(A)}_b =P^{-1}R^{(H)}_a P$? The notation would smother you!)"

But I think my favorite is:

"I believe that developments of mathematics are made by generalizations followed by specializations. You should jump and fly like an eagle and then fly down toward a game. To establish a story of modular interpretation of $X(3,6)$ we must jump at least as a grasshopper."

Douglas Bowman

Posted 2010-04-23T05:01:02.703

Reputation: 256


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

Hans Stricker

Posted 2010-04-23T05:01:02.703

Reputation: 3 211

2I 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 – 2011-08-28T22:39:41.477

1@David: Please don't feel offended, it's about colorful language, not about category theory. – Hans Stricker – 2011-08-28T23:07:52.680

3Still, 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 – 2011-12-13T06:41:18.173


"quantization commutes with seduction"

Was it a typo? Or was it intentional?

Kevin H. Lin

Posted 2010-04-23T05:01:02.703

Reputation: 11 992

44I can't say whether this is more than Freudian typo, but I know of another Freudian typo that nearly got into print. When Springer was preparing the 2nd edition of my book on topology and combinatorial group theory they sent me (in all seriousness) a copy of the intended new cover with the title Classical Topology and Combinatorial Group Therapy. – John Stillwell – 2010-04-30T21:26:02.523

7Seeing that it is in quotes, I bet it is an intentional pun on _s_ymplectic reduction. – Willie Wong – 2010-05-03T09:37:24.213


I once had to make the point that the theory of spectra-with-group-action which I was using was much simpler, more naive, than the sort of beautiful and elaborate equivariant stable homotopy created by Peter May and his school. In the preprint I described the latter as the "Chicago, or deep-dish" theory. I took those words out of the final version, thinking of international readers who might not get the pizza reference. (I substituted some other humorously intended words which were a gentle dig at Peter.)

Tom Goodwillie

Posted 2010-04-23T05:01:02.703

Reputation: 37 782

2You should have added a footnote with an explanation! – Mariano Suárez-Álvarez – 2010-10-21T14:37:52.647


From Jim Stasheff's Homotopy Associativity of H-spaces I, the magisterial-sounding

To study spaces which admit $A_n$-structures, we can work directly with the maps…. In the case of a topological group, this amounts to working only with the classifying bundle and never mentioning group operations. This would be an exercise in rectitude of thought of which it would be pointless to countenance the austerity, for not only would it eliminate a useful perspective on the subject, but, by disguising its own main point, it would place the reader beneath a cloud of unknowing.

Note 1: this is partly a subtle dig at Claude Chevalley's Fundamental Concepts of Algebra, whose preface ends, "Secondly, that one of the important pedagogical problems which a teacher of beginners in mathematics has to solve is to impart to his students the technique of rigorous mathematical reasoning; this is an exercise in rectitude of thought, of which it would be futile to disguise the austerity."

Note 2: Stasheff is exhibiting his awareness of religious literature (The Cloud of Unknowing is a 14th century work of Christian mysticism, written in Middle English).

Todd Trimble

Posted 2010-04-23T05:01:02.703

Reputation: 41 195


Number theorist Andrew Granville wrote a paper called "Prime number races" in which he studies the "race" between prime numbers $\equiv$ 1 (mod 4) and prime numbers $\equiv$ 3 (mod 4). The introduction is most certainly a colorful one:

There’s nothing quite like a day at the races...The quickening of the pulse as the starter’s pistol sounds, the thrill when your favorite contestant speeds out into the lead (or the distress if another contestant dashes out ahead of yours), and the accompanying fear (or hope) that the leader might change. And what if the race is a marathon? Maybe one of the contestants will be far stronger than the others, taking the lead and running at the head of the pack for the whole race. Or perhaps the race will be more dramatic, with the lead changing again and again for as long as one cares to watch. Our race involves the odd prime numbers, separated into two teams depending on the remainder when they are divided by 4:


Posted 2010-04-23T05:01:02.703

Reputation: 833

See also Granville's "Zaphod Beeblebrox's Brain and the Fifty-ninth Row of Pascal's Triangle" (http://www.dms.umontreal.ca/~andrew/PDF/beeb.pdf)

– Michael Lugo – 2011-02-03T19:42:43.793


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

Gil Kalai

Posted 2010-04-23T05:01:02.703

Reputation: 12 545


According to http://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 – 2011-04-07T07:25:37.287


More Weyl, all Mancosu's translation, all in his fierce days advocating Brouwer's mathematics:

Weyl (1921) On the New Foundational Crisis of Mathematics,

It must have the effect of a deliverance from a nightmare for whoever has maintained any sense for intuitively given facts in the abstract formalism of mathematics.

Weyl (1925) The current epistemological situation in mathematics:

At set theory's outermost borders, blurred in fog, crevices (i.e., flagrant contradictions) soon appeared.

and ibid, of the intuitionistic conception of the continuum:

The ice cover was burst into floes, and now the element of flux was soon altogether master over the solid.

Though these were published in mathematical journals, they are maybe not what the question was after, since they are not part of normal mathematical exposition.

Charles Stewart

Posted 2010-04-23T05:01:02.703

Reputation: 1 890


Math Reviews used to be much more colorful. In the 1950s, Haefliger was working on groupoids, developing a lot of what is now fundamental in the theory of stacks. Palais reviewed a 1958 paper of Haefliger's, concluding with,

The first four chapters of the paper are concerned with an extreme, Bourbaki-like generalization of the notion of foliation. After some twenty-five pages and several hundred preliminary definitions, the reader finds that a foliation of $X$ is to be an element of the zeroth cohomology space of $X$ with coefficients in a certain sheaf of groupoids. Holonomy, the Reeb-Ehresmann stability theorems, etc., are then generalized to this setting. While such generalization has its place and may in fact prove useful in the future, it seems unfortunate to the reviewer that the author has so materially reduced the accessibility of the results, mentioned above, of Chapter V, by couching them in a ponderous formalism that will undoubtedly discourage many otherwise interested readers.

Tara Holm

Posted 2010-04-23T05:01:02.703

Reputation: 416

3I don't think I'd consider this language colorful so much as grumpy and annoyed. I'm mildly curious whether Palais would feel at all differently today. – Todd Trimble – 2012-12-16T13:57:49.153


I came across this little gem when preparing for a talk on Kakeya sets and the ball multiplier problem, found on page 437 of E. Stein's Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals:

We will use this process to generate our monster, which will have a tiny heart and many arms.


Posted 2010-04-23T05:01:02.703

Reputation: 185


R.Coleman writing about the Dwork Principle in Section III of "Dilogarithms, Regulators and $p$-adic $L$-functions":

"Rigid analysis was created to provide some coherence in an otherwise totally disconnected $p$-adic realm. Still, it is often left to Frobenius to quell the rebellious outer provinces".


Posted 2010-04-23T05:01:02.703

Reputation: 1


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

Chris Estrada

Posted 2010-04-23T05:01:02.703

Reputation: 1


This is perhaps more of a silly play on words than colourful, but I still got a laugh out of it. One page 58 of Conway's 'The sensual (quadratic) form' while discussing Kneser's gluing method a sentence begins:

To further illuminate the utility of glue, ...

Robby McKilliam

Posted 2010-04-23T05:01:02.703

Reputation: 836

1I have the book but I don't get the pun, and I feel the lesser for it. Could you please explain it, if not in comments or answers here then, say, in your MO "profile" autobiography field or in email to me? – Will Jagy – 2010-04-24T04:08:11.380

2It's likely that I have a very dry sense of humour. But, if Conway was being formal he would write "To further illuminate the utility of the gluing method,..". I can't help but feel that it is written the way it is quite deliberately. – Robby McKilliam – 2010-04-24T21:48:17.240

2I think I see, and I agree that it was deliberate. I was looking for song titles that rhymed, as "Cupidity Fondue," "Venality of You," "Morality Imbue." – Will Jagy – 2010-04-24T22:50:25.283


Fulton and Harris's "Representation Theory" has a few examples of colourful language. Two of my favorites:

In recent work their* Lie-theoretic origins have been exploited to produce their representations, but to tell their story would go far beyond the scope of these lecture(r)s.

*: The finite Chevalley groups.

Any mathematician, stranded on a desert island with only these ideas and the definition of a particular Lie algebra $\mathfrak{g}$ such as $\mathfrak{sl}_n \mathbb{C}$, $\mathfrak{so}_n \mathbb{C}$, or $\mathfrak{sp}_n \mathbb{C}$, would in short order have a complete description of all the objects defined above in the case of $\mathfrak{g}$. We should say as well, however, that at the conclusion of this procedure we are left without one vital piece of information about the representations of $\mathfrak{g}$ ... this is, of course, a description of the multiplicities of the basic representations $\Gamma_a$. As we said, we will, in fact, describe and prove such a formula (the Weyl character formula); but it is of a much les straightforward character (our hypothetical shipwrecked mathematician would have to have what could only be described as a pretty good day to come up the idea) and will be left until later.


Posted 2010-04-23T05:01:02.703

Reputation: 8 364


I like the following from the Introduction of Iwaniec-Kowalski: Analytic number theory (AMS, 2004):

Poisson summation for number theory is what a car is for people in modern communities – it transports things to other places and it takes you back home when applied next time – one cannot live without it.

This is not the only good one in that introduction, I let you find the others!

GH from MO

Posted 2010-04-23T05:01:02.703

Reputation: 51 076


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.

Julien Puydt

Posted 2010-04-23T05:01:02.703

Reputation: 1 463

Yeah, heh. Good one. – Todd Trimble – 2012-12-16T15:19:16.903


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.

Robert Haraway

Posted 2010-04-23T05:01:02.703

Reputation: 696


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)

Andrew Ranicki

Posted 2010-04-23T05:01:02.703

Reputation: 3 261


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!

Ronnie Brown

Posted 2010-04-23T05:01:02.703

Reputation: 9 589

At the risk of taking too literally something meant in jest -- it strikes me as a vision of shoddy supervision. That's like saying every incompetent line manager deserves credit for inspiring those under them to ignore, or compensate for, their own failings – Yemon Choi – 2011-12-18T20:04:11.000

1@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 – 2012-11-04T11:00:56.247


Two from Casselman's "A companion to Macdonald's book on p-adic spherical functions":

The word ‘´epingler’ means ‘to pin’, and the image that comes to mind most appropriately is that of a mounted butterfly specimen. [Kottwitz:1984] uses ‘splitting’ for what most call ‘´epinglage’, but this is not compatible with the common use of ‘deploiement’, the usual French term for ‘splitting’.) Ian Macdonald, among others, has suggested that retaining the French word ´epinglage in these notes is a mistake, and that it should be replaced by the usual translation ‘pinning.’ This criticism is quite reasonable, but I rejected it as leading to noncolloquial English. The words ‘pinning’ as noun and ‘pinned’ as adjective are commonly used only to refer to an item of clothing worn by infants, and it just didn’t sound right.


These phenomena are part of what Langlands calls endoscopy, a word that might be roughly justified by saying that endoscopy is concerned with some fine aspects of the structure of harmonic analysis on a reductive p-adic group. Langlands attributes the term to Avner Ash, praising his classical knowledge, but I was pleased to find recently the following quotation that shows a more vulgar intrusion of endoscopy into the modern world:

Jeeves: “ . . . I had no need of the endoscope.”

Bertie: “The what?”

Jeeves: “Endoscope, sir. An instrument which enables one to peer into the . . . interior and discern the core.”

From Chapter 12 of Jeeves and the feudal spirit by P. G. Wodehouse.

This discussion is about distingishing fae jewlry from real. Since the endoscope also has medical uses, one could imagine an even more vulgar usage.

He has modified the notes several times so these might not be there anymore, but I have the older copies =)

Sean Rostami

Posted 2010-04-23T05:01:02.703

Reputation: 712

I sent a bunch of information on James Arthur and endoscopy to a high-school classmate who is a gastroenterologist. As near as I can tell he never got any amusement out of it. I also sent him a copy of the book "Communion" by Whitley Streiber, which seems to be the source of the idea that aliens visiting from distant galaxies like to, well, examine us. Same outcome. – Will Jagy – 2010-04-24T01:58:34.783

29My girlfriend is a surgeon and once a month our copy of "Endoscopy" drops through the post box. I tried to out-do her recently by sitting on the sofa reading a paper of Waldspurger about "twisted endoscopy" and she suggested he was doing it wrong. – Kevin Buzzard – 2010-04-24T08:22:49.837

4You made the effort, that's what counts in the end. – Will Jagy – 2010-04-24T19:05:17.333

This is off-topic, but the remarks about "epinglage" versus "pinning" reminded me: has anyone followed the grumbly remarks in Lang's Algebra and tried to use the terminology of "(co)eraseable resolutions" in homological algebra? – Yemon Choi – 2010-04-25T01:21:21.130


Edward Nelson, Predicative Arithmetic, p. 50:

The intuition that the set of all subsets of a finite set is finite -- or more generally, that if $A$ and $B$ are finite sets, then so is the set $B^A$ of all functions from $A$ to $B$ -- is a questionable intuition. Let $A$ be the set of some $5000$ spaces for symbols on a blank sheet of typewriter paper, and let $B$ be the set of some $80$ symbols of a typewriter; then perhaps $B^A$ is infinite. Perhaps it is even incorrect to think of $B^A$ as being a set. To do so is to postulate an entity, the set of all possible typewritten pages, and then to ascribe some kind of reality to this entity -- for example, by asserting that one can in principle survey each possible typewritten page. But perhaps it simply is not so. Perhaps there is no such number as $80^{5000}$; perhaps it is always possible to write a new and different page. Many ordinary activities are built up in a similar way from a rather small set of symbols or actions. Perhaps infinity is not far off in space or time or thought; perhaps it is while engaged in an ordinary activity -- writing a page, getting a child ready for school, talking with someone, teaching a class, making love -- that we are immersed in infinity.

Peter Doyle

Posted 2010-04-23T05:01:02.703

Reputation: 1

6Having just noticed this, I am rather disturbed by the thought that out there, somewhere, someone is looking into another person's eyes and asking "do you want to immerse yourself in infinity?" – Yemon Choi – 2011-06-14T21:40:41.703

4Or even using it as a line in a bar, heaven forfend... – Yemon Choi – 2011-06-14T21:41:02.120


André Weil uses some very colourful language in the introduction of his 1946 book Foundations of Algebraic Geometry. I recommend any mathematician to read it. Here are some excerpts:

"As in other kinds of war, so in this bloodless battle with an ever retreating foe which it is our good luck to be waging, it is possible for the advancing army to outrun its services of supply and incur disaster unless it waits for the quartermaster to perform his inglorious but indispensable task."

"Of course every mathematician has a right to his own language---at the risk of not being understood; and the use sometimes made of this right by our contemporaries almost suggests that the same fate is being prepared for mathematics as once befell, at Babel, another of man's great achievements."

"... however grateful we algebraic geometers should be to the modern algebraic school for lending us temporary accommodation, makeshift constructions full of rings, ideals and valuations, in which some of us feel in constant danger of getting lost, our wish and aim must be to return at the earliest possible moment to the palaces which are ours by birthright, to consolidate shaky foundations, to provide roofs where they are missing, to finish, in harmony with the portions already existing, what has been left undone."

"...it is hoped that these may be helpful to the reader, to whom the author, having acted as his pilot until this point, heartily wishes Godspeed on his sailing away from the axiomatic shore, further and further into open sea."

Beren Sanders

Posted 2010-04-23T05:01:02.703

Reputation: 1 731

Weil could be exceedingly florid in his language at times. Almost like reading Proust. – Todd Trimble – 2012-12-16T15:25:20.150


"Now life is too short to work over the integers all of the time, ..."

J. Morava, On the complex cobordism ring as a Fock representation.

Oscar Randal-Williams

Posted 2010-04-23T05:01:02.703

Reputation: 12 550


Daniel Mathews, Chord diagrams, contact-topological quantum field theory and contact categories, Algebraic & Geometric Topology 10 (2010) 2091–2189. Section 2.2.2, Page 2122:

We give a baseball interpretation of the partial order $\preceq$. The $m$th symbol in a word $w$ is the $m$th inning. The sum of the first $m$ symbols is the score after $m$ innings. The relation ${w_1\preceq w_2}$ means precisely that after every inning, ${w_1}$ is not losing.
(Note that this is low-scoring baseball: every inning, each team scores $\pm1$ run. It is also fixed: the end result is tied. The lead changes precisely when words are not comparable; comparable words are uninteresting as spectator sport. Two words are comparable if and only if they describe a low-scoring, fixed, and uninteresting baseball game.)

Later in the paper, there is proof by skiing (with comparably colourful language) and various bypass shennanigans.

Daniel Moskovich

Posted 2010-04-23T05:01:02.703

Reputation: 12 674


In "Théorie algébrique des nombres" (in french and a great book about Dedekind rings and basic number field theory btw), Samuel frequently uses "Mézalor" as a phonetic replacemecont for "Mais alors". I guess you could translate it as "Butzen" instead of "But then". I think it was just a geeky "wink wink" at other mathematicians considering how much that locution was used in "dévissage" but I liked it anyway.


Posted 2010-04-23T05:01:02.703

Reputation: 4 834


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 ...

Matthew Kahle

Posted 2010-04-23T05:01:02.703

Reputation: 4 188

I recognize that quote! It's from a proof of Pappus's theorem. IIRC, it's from his "Geometry Revisited." – Harry Altman – 2011-08-23T02:09:02.243


Although the article itself is standard, I've always been fond of the title (and contents) of the Burstall & Hertrich-Jeromin paper Harmonic maps in unfashionable geometries.

Matt Noonan

Posted 2010-04-23T05:01:02.703

Reputation: 2 026


In the huge and austere book "Groupes algébriques" by M. Demazure and P. Gabriel we find in the last pages a "Dictionaire "Fonctoriel"", a dictionary of terms related to category theory where they have:

Satellite- Voir Cartan-Eilenberg et non Paris-Match.

Gonçalo Marques

Posted 2010-04-23T05:01:02.703

Reputation: 456


This quote is taken from the paper "How to write a proof" by Leslie Lamport. The paper is about a system to write mathematical proofs in a more formal way. (Of course I do not share the opinion expressed in this paragraphs.)

alt text

Gil Kalai

Posted 2010-04-23T05:01:02.703

Reputation: 12 545

2In what way is this language colorful? It's a strongly expressed opinion, but that doesn't make it colorful. – Todd Trimble – 2012-12-16T15:18:06.103

Hi Todd, my new constribution was this http://mathoverflow.net/questions/22299/what-are-some-examples-of-colorful-language-in-serious-mathematics-papers/67796#67796 as for this on, it looked good when I posted it. One great colorful language I just learned from Barry Simon was that in Kelly's first edition of general topology he used "ways" instrad of "nets". His main motivation was to talk about "subways" rather than "subnets." However, Steenrod talked him out of this term.

– Gil Kalai – 2012-12-16T17:07:05.940


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.

Dave L Renfro

Posted 2010-04-23T05:01:02.703

Reputation: 1 037


I just came across a paper of Waldhausen (On Irreducible 3-manifolds Which are Sufficiently Large) where he says "Frequently, a proof involves a sequence of constructions, each of which in turn involves alterations of some things. To avoid an orgy of notation in such cases, we often denote the altered things by the old symbols."

Peter Samuelson

Posted 2010-04-23T05:01:02.703

Reputation: 1 859


From the references of the wikipedia page on large countable ordinals:

Wolfram Pohlers, Proof theory, ... (for Veblen hierarchy and some impredicative ordinals). This is probably the most readable book on large countable ordinals (which is not saying much).

David Roberts

Posted 2010-04-23T05:01:02.703

Reputation: 15 487

2Entertaining (and I'm sure we all know books like that in our respective fields)... but aren't we looking for instances of such language in serious math(s) papers, the point being to find levity defying gravity? – Yemon Choi – 2011-03-11T01:10:29.777

2@Yemon - you're right, of course, but the usually stuffy wikipedia (obligatory xkcd comic should be immediately obvious to the reader) doesn't have the freedom that an author has. The author is only constrained by personal adherence to social norms in writing, whereas wikipedia is Ahem controlled Ahem constantly edited towards improvement and encyclopedic style. :) – David Roberts – 2011-03-11T02:11:52.323

Fair point, David! – Yemon Choi – 2011-03-11T05:42:24.383


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").

Johannes Hahn

Posted 2010-04-23T05:01:02.703

Reputation: 4 895

3There is an important theorem by Shelah in PCF theory which is known as "the trichotomy theory" in which three possible situations are described: The good, in which things act like we want them to; the bad, in which things behave the opposite of what we want them to; and the ugly, in which things are just messed up. – Asaf Karagila – 2011-07-05T16:19:10.307


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

Zeeshan Mahmud

Posted 2010-04-23T05:01:02.703



There is the famous (and with contradictory interpretations) cry from Jean Dieudonné "à bas Euclide !", "Down with Euclide !". His books and prefaces are good sources for strong (and dated) opinions on what was "good" or "productive" mathematics and what was not.

Doron Zeilberger papers may contain also some colorful language.


Posted 2010-04-23T05:01:02.703

Reputation: 742

38> Doron Zeilberger papers may contain also some colorful language.

Is this perhaps like saying that oceans are sometimes wet? – LSpice – 2010-04-25T04:38:22.580


A new book on sieve methods is bizzarely called Opera de Cribro with chapter subtitles in an operatic theme.

Roy Maclean

Posted 2010-04-23T05:01:02.703

Reputation: 507


Frank Thorne

Posted 2010-04-23T05:01:02.703

Reputation: 3 920


Milne's web page contains a number of amusing anecdotes- http://www.jmilne.org/math/apocrypha.html


Posted 2010-04-23T05:01:02.703

Reputation: 555

Several books of anecdotes and apocrypha also exist, with the imaginative titles 'Mathematical Apocrypha' and (if I recall correctly) 'More Mathematical Apocrypha'. – Ketil Tveiten – 2011-01-12T09:13:54.393

The second one is called Mathematical Apocrypha Redux. – Pandora – 2011-01-19T17:28:23.220


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

Alain Valette

Posted 2010-04-23T05:01:02.703

Reputation: 8 606

Veuillez expliquer le blague? – Yemon Choi – 2011-08-23T00:51:03.753

2In French, Jolissaint is pronounced as "joli seins", which translates as "nice tits" in English. – ACL – 2011-08-23T06:44:54.550

Oh, for some reason I had "seins" and "reins" mixed up in my head earlier... – Yemon Choi – 2011-08-23T09:47:03.990


No-one seems to have mentioned Joe Diestel (although "colorful" is maybe the wrong word-- perhaps because of my English interpretation of what this means-- but "lighthearted" is correct). For example, "Sequences and Series in Banach Spaces" we have the section on "Mathematical Sociology" when introducing Ramsey Theory (to talk about one set "accepting" or "rejecting" another). It's hard to pick out any particular quote, but the whole book is somehow far more lively and informal (without, somehow, even managing to be less than 100% accurate) than most maths books.

Matthew Daws

Posted 2010-04-23T05:01:02.703

Reputation: 7 777


From Geoffrey Grimmett's monograph on Random Processes on graphs:

Within the menagerie of objects studied in contemporary probability theory, there are a number of related "animals" that have attracted great interest amongst probabilists and physicists in recent years.


Posted 2010-04-23T05:01:02.703

Reputation: 101


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


Posted 2010-04-23T05:01:02.703

Reputation: 817

1The whole review is a must-read... – darij grinberg – 2011-12-05T05:03:41.977

3I would like to upvote this for being outrageous, but that would be giving it praise it does not deserve. – Ryan Reich – 2011-12-12T22:41:28.420

6Right...thanks, but I doubt I'd have any more fun reading the review than I did reading that quote. – Elizabeth S. Q. Goodman – 2011-12-13T04:47:48.297

The first two pages are worth it, regardless of your mathematical orientation. – name – 2011-12-13T10:23:36.177

4I am a bit shocked that something like this was printed in BAMS as late as in the earlier 80s. – None – 2011-12-17T13:09:26.483

1It may well be colourful; it strikes me as crass. – Yemon Choi – 2011-12-18T03:22:38.677

1I can't believe the outrage this quote is causing. Translated into politically correct language, thus stripping the quote of all its expressiveness that lies in brevity, Bloch says that mathematics can be "sexy", and that this attractiveness is universal in the sense that anyone who understands enough of the details would appreciate its beauty, independently of his/her personal aesthetic tastes. Bloch has chosen a comparison that possibly seems very apt to him. By the way, what does "as late as 80s" mean? What would stop such a review from being printed today? – Alex B. – 2011-12-18T04:18:34.523


I like "Let's take this guy" (in German: Bursche) when a Graph theorist picks a vertex. (it's not colourful at first sight, but think about it)

Hans Stricker

Posted 2010-04-23T05:01:02.703

Reputation: 3 211

Brazilians say "a gente pega um cara" (more or less literally: let us take a guy) – Mariano Suárez-Álvarez – 2011-01-19T23:43:22.547

To say what?... – Hans Stricker – 2011-01-19T23:47:50.370

To say exactly the same thing as the Germans with "Let's take this guy". – Mariano Suárez-Álvarez – 2011-01-20T00:01:00.257

1My Intention was to say that (among others) mathematicians tend to anthropomorphize their subjects. – Hans Stricker – 2011-01-20T00:08:39.403

3@Hans: Really? anthropomorphize? When I look at how many "monsters", "beast" etc. are out there, then I tend to think that at least the "official" termininology is more animalistic. – Johannes Hahn – 2011-01-20T10:56:43.057

4I once followed a lecture of David Goss where he started calling his objects "guy", passed on to something like "unpleasant fellow" (when he was revealing some undesired properties of that object) and ended up calling it "sucker" - repeatedly and emotionally. – Peter Arndt – 2011-10-22T20:12:13.337

3"Sucker" reminds me inevitably of Chuck Weibel, who used to say this all the time. – Todd Trimble – 2011-12-13T12:29:21.860


This reminds me of the little blue book by Swan... It must be "Theory of Sheaves", I don't have it on my shelf here. But I remember clever chapter titles. Maybe someone else here can tell us.

Gerald Edgar

Posted 2010-04-23T05:01:02.703

Reputation: 25 496

I've just thumbed through The Theory of Sheaves, and I saw nothing in the titles (or in anything else there) that applies. The cover is blue all right, but I imagine you're thinking of something else. – Todd Trimble – 2011-03-02T02:15:18.223


From one of the papers on integrable systems

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


Posted 2010-04-23T05:01:02.703

Reputation: 380

4peace or piece? – David Roberts – 2011-04-06T06:01:01.447