Question

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?

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

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 ...

Answer 6

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

Answer 7

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).

Answer 8

Pretentiousness is repulsive. (see page 9)

Answer 9

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

Answer 10

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.

Answer 11

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").

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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.

Answer 16

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.

Answer 17

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)

Answer 18

From one of the papers on integrable systems

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