290
$\begingroup$

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?

$\endgroup$
26
  • 127
    $\begingroup$ Latest paper, my co-author put in "but we will choose a more painful way, because there is nothing like pain for feeling alive" but the referee jumped on it. $\endgroup$
    – Will Jagy
    Apr 23, 2010 at 5:09
  • 34
    $\begingroup$ Maybe I should expand the question to include colorful language cut from serious mathematics papers :) $\endgroup$ Apr 23, 2010 at 5:18
  • 56
    $\begingroup$ By the way, your remark reminds me of another in a similar spirit that made it into the Princeton Companion. In his article on algebraic geometry, János Kollár says of stacks: "Their study is strongly recommended to people who would have been flagellants in earlier times." $\endgroup$ Apr 23, 2010 at 7:49
  • 46
    $\begingroup$ I was actually rather surprised recently by a referee who did not know the phrase “red herring”, and had to look it up. He insisted that we change it to something more understandable. It makes me wonder how much “colourful” language is weeded out by referees, and whether the mathematical literature is poorer for it. $\endgroup$ Apr 24, 2010 at 2:31
  • 43
    $\begingroup$ @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.) $\endgroup$ Apr 24, 2010 at 15:43

125 Answers 125

1
2 3 4 5
362
$\begingroup$

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.

$\endgroup$
9
  • 55
    $\begingroup$ Heh. I am sure this was discovered by coincidence and kept by design. $\endgroup$
    – Yemon Choi
    Apr 25, 2010 at 0:49
  • 13
    $\begingroup$ Greg, I've just had a look at Hubbard's Teichmüller Theory, and a wonderful book it is. But, alas, I think your memory has deceived you, because his abbreviation for the category of Banach analytic manifolds (page 165) is in fact BanMan. $\endgroup$ Mar 28, 2011 at 23:31
  • 30
    $\begingroup$ Hmm, since my observation came from a course with Prof. Hubbard using a preprint of the book, I guess he changed it before publication. Thats a little disappointing. $\endgroup$ Mar 29, 2011 at 16:27
  • 9
    $\begingroup$ It has belatedly struck me that there should really be a contravariant equivalence of categories between Ban(Ana)Man and some category of algebraic objects, which could be abbreviated to ERIC. $\endgroup$
    – Yemon Choi
    Aug 23, 2011 at 0:56
  • 66
    $\begingroup$ Do you know that all three parts of BanAnaMan means "I" (Me) in Turkish, Arabic and Persian, respectively? $\endgroup$
    – Sh.M1972
    Mar 10, 2014 at 17:17
269
$\begingroup$

From the ground-breaking paper: On the complexity of omega-automata by Muli Safra (DOI: 10.1109/SFCS.1988.21948)

alt text alt text

Acknowledgements

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.

$\endgroup$
1
  • 25
    $\begingroup$ +2 ! while almost all answers made me smile, this literally made my day! $\endgroup$
    – user56218
    Dec 6, 2014 at 15:13
251
$\begingroup$

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]

$\endgroup$
3
  • 46
    $\begingroup$ +1 A very nice alternative for using "it's easy to show", "trivial", "as one easily checks" etc. $\endgroup$ Apr 25, 2010 at 11:24
  • 4
    $\begingroup$ In terms of small changes with large effects, I remember a colleague who, I forget whether by typo or because they didn't know the correct phrase, saying that a step in a proof proceeded "without lots of generality". $\endgroup$
    – LSpice
    Sep 28, 2021 at 10:55
  • 5
    $\begingroup$ A student of mine once used the phrase "without loss of generosity" which to this day makes me smile. $\endgroup$ Nov 15, 2022 at 14:37
227
$\begingroup$

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

$\endgroup$
3
  • 6
    $\begingroup$ so either the systems collapses, either we have proved that the authors are not model theorists. $\endgroup$ Dec 12, 2011 at 23:45
  • 17
    $\begingroup$ Or that they have dedicated some other book to themselves (perhaps secretly?) $\endgroup$
    – Will Sawin
    Jan 9, 2012 at 23:07
  • 1
    $\begingroup$ Since the sentence is past tense, it technically doesn't give rise to a contradiction. Regardless, it's funny either way. $\endgroup$
    – Hank Igoe
    Jan 6, 2021 at 19:02
183
$\begingroup$

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"

$\endgroup$
159
$\begingroup$

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"

$\endgroup$
3
  • 1
    $\begingroup$ Where was this first published? (Sorry - don't have access to the CW) $\endgroup$ Apr 23, 2010 at 15:05
  • 3
    $\begingroup$ Dear Charles: Ann. of Math. 69, 1959, pages 247-252. $\endgroup$ Apr 23, 2010 at 15:27
  • 41
    $\begingroup$ This was a letter to the editor, not a math paper. $\endgroup$
    – KConrad
    Apr 23, 2010 at 15:36
158
$\begingroup$

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.

$\endgroup$
3
  • 87
    $\begingroup$ I was a TA on a course taught by Sarason himself following this book. I had two students "solve" that Exercise during one of my office hours. $\endgroup$ May 6, 2010 at 5:02
  • 20
    $\begingroup$ This reminds me of an exercise (C.67) from the chapter about linear transformations in Peter Hackman's Linear Algebra textbook Kossan (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." $\endgroup$ Jul 1, 2010 at 8:25
  • 16
    $\begingroup$ This 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?". $\endgroup$ Jun 28, 2014 at 17:40
133
$\begingroup$

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.

$\endgroup$
126
$\begingroup$

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.

$\endgroup$
1
  • 8
    $\begingroup$ +1: A fantastic example. $\endgroup$
    – Todd Trimble
    Oct 22, 2011 at 21:24
124
$\begingroup$

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 formulae." 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.

$\endgroup$
12
  • 18
    $\begingroup$ Harry, it's here books.google.com/… and the text itself has (expletive deleted) $\endgroup$ Apr 24, 2010 at 0:58
  • 8
    $\begingroup$ Yes, I disagree with Adams about double cosets. Then again the colourful stories about him that came out after he died seemed to me to indicate that I disagreed with him about a number of things (for example the merits of attacking people with axes) $\endgroup$ Apr 24, 2010 at 8:13
  • 24
    $\begingroup$ @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? $\endgroup$ Apr 24, 2010 at 15:23
  • 8
    $\begingroup$ I hope this is not seen as mean-spirited, but some years ago, once when I mentioned Adams over coffee (probably in the context of his Lie Groups book) someone asked if I'd heard the joke about the "unstable Adams spectral sequence". (It tickled my fancy; everyone else went back to talking about traffic or football.) $\endgroup$
    – Yemon Choi
    Apr 25, 2010 at 0:54
  • 5
    $\begingroup$ Ravenel'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". $\endgroup$
    – Sam Nolen
    Sep 3, 2011 at 21:26
112
$\begingroup$

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."

$\endgroup$
3
  • 3
    $\begingroup$ For what it's worth, Timothy Chao had a piece "You could have invented spectral sequences" in the Notices (ams.org/notices/200601/fea-chow.pdf) that claims the name "spectral" is from some sort of analogy with eigenvalues. $\endgroup$ Nov 5, 2010 at 21:10
  • 22
    $\begingroup$ I thought it was Timothy Chow? $\endgroup$
    – Todd Trimble
    Oct 22, 2011 at 21:13
  • 20
    $\begingroup$ Off-topic, but the first spectral sequence I know in the literature is in A Christmas Carol. $\endgroup$ Dec 15, 2018 at 22:10
111
$\begingroup$

According to https://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.

$\endgroup$
1
  • 27
    $\begingroup$ I wonder if this was a joke or if it was required by the BoP, just as some funding agencies require a similar note. $\endgroup$ Oct 21, 2010 at 13:46
106
$\begingroup$

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.

$\endgroup$
3
  • 12
    $\begingroup$ isn't there some humorous intention in the choice of the name "pointless topology" ? $\endgroup$ Jan 17, 2011 at 23:54
  • 56
    $\begingroup$ +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. $\endgroup$ Feb 4, 2011 at 9:27
  • 1
    $\begingroup$ @KetilTveiten : So a Woozle-Hunt is actually Circular Reasoning, which is why it Proves Nothing. $\endgroup$ Dec 18, 2018 at 22:16
100
$\begingroup$

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

$\endgroup$
2
  • 42
    $\begingroup$ I couldn't possibly know, but my suspicion would be that a copyeditor bowdlerized the article without the author's knowledge or permission, and that the author, upon finding out, complained strongly enough for the magazine to give in and publish the correction. $\endgroup$ Aug 29, 2011 at 13:52
  • 2
    $\begingroup$ Ah, that makes a lot of sense. $\endgroup$ Aug 29, 2011 at 19:24
92
$\begingroup$

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.

$\endgroup$
6
  • 6
    $\begingroup$ Works in my building. $\endgroup$ Sep 15, 2010 at 18:46
  • 87
    $\begingroup$ But then going home transposes the matrix. $\endgroup$ Sep 16, 2010 at 0:41
  • 11
    $\begingroup$ Unless there are two elevators in the building... $\endgroup$ Oct 21, 2010 at 13:47
  • 5
    $\begingroup$ I'm glad to discover that I'm not the only person with this problem! $\endgroup$ Dec 9, 2018 at 4:36
  • 13
    $\begingroup$ For those who speak German: Zeilen Zuerst, SPalten SPäter. $\endgroup$ Jul 15, 2019 at 11:58
85
$\begingroup$

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."

and

"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."

$\endgroup$
2
  • 27
    $\begingroup$ Yes, 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. $\endgroup$ May 16, 2010 at 14:39
  • 15
    $\begingroup$ "Any large number is finite, and you can start thinking about it as 3." - Conway, 2003. $\endgroup$ Sep 1, 2015 at 5:18
85
$\begingroup$

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.

$\endgroup$
4
  • 32
    $\begingroup$ I mentioned this to my supervisor, who immediately responded "why do you need more than one?" $\endgroup$
    – Yemon Choi
    Jun 14, 2011 at 21:36
  • 18
    $\begingroup$ @Yemon: more than one thermus? $\endgroup$ Jun 15, 2011 at 1:53
  • 9
    $\begingroup$ @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.) $\endgroup$
    – Yemon Choi
    Jun 15, 2011 at 6:02
  • $\begingroup$ Cactus, cacti. Furnace, furni. $\endgroup$ Aug 4, 2023 at 10:43
74
$\begingroup$

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.

$\endgroup$
71
$\begingroup$

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 kindly advised not to commit seppuku instantly if he feels he does not quite understand 2. of chapter 1.

$\endgroup$
1
  • 3
    $\begingroup$ :D :D quote two made me laugh out loud. $\endgroup$
    – David Roberts
    Mar 11, 2011 at 0:58
67
$\begingroup$

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)."

$\endgroup$
1
  • 3
    $\begingroup$ or better, which wolves to face under each bed (if there are a lot of beds) $\endgroup$ Jun 14, 2021 at 12:24
61
$\begingroup$

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.

$\endgroup$
60
$\begingroup$

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."

$\endgroup$
2
  • 2
    $\begingroup$ What a gem! I'm glad that this question is still attracting good answers. $\endgroup$ Aug 4, 2011 at 3:14
  • 38
    $\begingroup$ How a television, two typewriters, a ring and several pieces of cheese got into Chapter 8, I'll never know. Sorry, just found myself channelling Groucho Marx for a minute there. $\endgroup$ Aug 4, 2011 at 5:48
57
$\begingroup$

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.

$\endgroup$
56
$\begingroup$

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.

$\endgroup$
3
  • 18
    $\begingroup$ "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. $\endgroup$
    – Pait
    Jul 5, 2011 at 16:44
  • 3
    $\begingroup$ It makes one wonder what sexual argument could possibly justify quaternionic manifold. $\endgroup$ Feb 6, 2020 at 13:01
  • 1
    $\begingroup$ @MaudPieTheRocktorate: Rainbow $\endgroup$
    – timur
    Jan 4, 2021 at 7:04
56
$\begingroup$

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.

$\endgroup$
56
$\begingroup$

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."

$\endgroup$
1
  • 7
    $\begingroup$ 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. $\endgroup$ Sep 12, 2017 at 6:06
50
$\begingroup$

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!

$\endgroup$
6
  • 131
    $\begingroup$ Truesdell 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." $\endgroup$ Apr 25, 2010 at 16:05
  • 12
    $\begingroup$ If you have access to MathSciNet, here's the review: ams.org/mathscinet-getitem?mr=39515 $\endgroup$ Apr 30, 2010 at 6:47
  • 17
    $\begingroup$ To 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: [...]." $\endgroup$ Jul 1, 2010 at 8:06
  • 24
    $\begingroup$ I believe that Bass gets credit for a book review with the line- "this book fills a much needed gap in the literature". $\endgroup$
    – meh
    Jan 12, 2011 at 2:52
  • 9
    $\begingroup$ @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. $\endgroup$ Jan 16, 2011 at 16:03
44
$\begingroup$

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.

or,

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).

$\endgroup$
3
  • 6
    $\begingroup$ Miles 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! $\endgroup$ Feb 3, 2011 at 22:47
  • 1
    $\begingroup$ Two more examples, which I remember fondly from my own undergraduate days: (1) "If you think this statement is obvious, congratulations on your intuition: you have just guessed a particular case of the Nullstellensatz. Now find your own proof (GOTO 2.6)." [The proof takes up the remainder of 2.5.] and (2) "For (ii), I use a rather nonobvious 'determinant trick' (which I didn't think of for myself)". I find myself wanting to teach from that book now! (My recollection is that he assumed too much commutative algebra background, but that's easily supplemented.) $\endgroup$ Jul 6, 2020 at 4:51
  • 1
    $\begingroup$ @JoshuaP.Swanson "he assumed too much commutative algebra background" — but he also has "Undergraduate Commutative Algebra". $\endgroup$
    – Z. M
    Nov 21, 2021 at 5:47
43
$\begingroup$

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

$\endgroup$
1
  • 78
    $\begingroup$ As an aside, I discovered by experience that searching for "Bing too old to spank" is NOT a good way to find a source for this quote. $\endgroup$
    – Dave Futer
    Jul 5, 2011 at 14:24
43
$\begingroup$

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.

$\endgroup$
1
2 3 4 5

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