## New answers tagged math-communication

3

From the book Inexhaustibility by Torkel Franzen, which is about, let's say, natural numbers!
A Druidic myth relates how Lucanor, coming upon the other gods as they
sat at the banquet table, found them drinking mead in grand style, to
the effect that several were drunk, while others remained inexplicably
sober; could some be slyly swilling down ...

3

A round man cannot be expected to fit in a square hole right away. He must have time to modify his shape. (Mark Twain)
This epigraph is used in Bredon's book Topology in Geometry. It is a very nice illustration of the idea of homotopy theory. Also nice is the epigraph used in the preface:
The golden age of mathematics - that was not the age of ...

3

Since both Knuth and Sherlock Holmes have already been mentioned here, I'd like to add this one:
You will, I am sure, agree with me $\dots$ that if page 534 finds us only in the second chapter, the length of the first one must have been really intolerable. -- SHERLOCK HOLMES, in The Valley of Fear (1888)
[D.E.Knuth, The Art of Computer Programming, ...

2

I personally am fond of the epigraphs in Zettl, Anton. Sturm-liouville theory. No. 121. American Mathematical Soc., 2010. Here are a selected few:
(Chapter 10: Singular Self-Adjoint Operators)
One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.
In H. Eves Mathematical Circles ...

5

I am charmed by the epigraphs in Herrlich and Strecker's book on Category Theory, where the first substantive chapter (titled "Foundations") opens with these lines from Dr. Seuss's On Beyond Zebra:
Because finally he said:
"This is really great stuff!
"And I guess the old alphabet
"ISN'T enough!"
and the Appendix (also titled "Foundations") closes ...

12

"Algebraic Number Theory" by Cassels and Froehlich was (so Birch told me once) one of the first mathematics books typeset by Academic Press. According to Birch, when he received the first offprints of his article there was "about one error per line, on average", due perhaps to the combination of the way books were printed in the 1960s (lumps of metal with ...

3

Dennis Gaitsgory begins his "Outline of the proof of the
geometric Langlands conjecture for $GL_2$" (available here) with the following interesting quote in German:
“In jedem Minus steckt ein Plus. Vielleicht habe ich so etwas gesagt, aber man braucht das doch nicht allzu wörtlich zu nehmen.” - Robert Musil, Der Mann ohne Eigenschaften.

4

I was tempted to use this one for my PhD thesis (in the ended I didn't, out of fear it might sound pretentious):
There is nothing so practical as a good theory (Ludwig Boltzmann)
I like how it reconciles the concepts of theory and practice. All too often the former is dismissed as "yes, that's what would happen in theory; but in practice..."

2

Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. (John von Neumann, 1951)
Knuth, D. E. The art of computer programming. Volume 2.
Ch. 3 Random numbers.

9

From Streater & Wightman, "PCT, Spin and Statistics, and All That" (Ch. 2):
In the thirties, under the demoralizing influence of quantum-theoretic perturbation theory, the mathematics required of a theoretical physicist was reduced to a rudimentary knowledge of the Latin and Greek alphabets.
- R. Jost

8

Montesinos's Classical Tessellations and Three-Manifolds has an epigraph from Don Quixote in every chapter which is relevant to the content:
Preface: "You have said more than you know, Sancho", said Don Quixote, "for there are some who tire themselves out learning and proving things which, once learnt and proved, do not concern either the understanding ...

10

One of my personal favourites, which describes a lot of what goes on in maths:
In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics.
-- Hermann Weyl

25

Chapter 0 of Abstract and Concrete Categories - The Joy of Cats by Adamek, Herrlich and Strecker opens with
There’s a tiresome young man in Bay Shore.
When his fiancée cried, ‘I adore
The beautiful sea’,
He replied, ‘I agree,
It’s pretty, but what is it for?’
Morris Bishop
No category theorist needs any explanation why they chose ...

10

I think that many a MO-er will find very intriguing the epigraph at the beginning of chapter one of the book A=B by Marko Petkovšek, the late Herbert Wilf, and Doron Zeilberger:
The ultimate goal of mathematics is to eliminate any need for intelligent thought. — Alfred N. Whitehead
By the way, when I shared it in the thread on "Famous mathematical ...

12

Here are some mathematical and quasi-mathematical head-of-chapter epigraphs that I used in my book The Big Questions:
To create a healthy philosophy, you should renounce metaphysics but be a good mathematician. --- Bertrand Russell
They are ill discoverers who think there is no land, when they can see nothing but sea. --- Sir Francis Bacon
The ...

6

Flajolet-Sedgewick's Analytic Combinatorics is very rich in epigraphs, the most interesting being Painlevé's famous
Entre deux vérités du domaine réel, le chemin le plus facile et le plus court passe bien souvent par le domaine complexe.
("The shortest and easiest path between two truths of the real domain most often passes through the complex ...

21

A famous quote by John von Neumann:
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

8

If we read Frege's Grundlagen der Arithmetik from the end, the following note in the appendix would be the most courageous of epigraphs all.
A scientist can hardly meet with anything more undesirable than to
have the foundations give way just as the work is finished. I was put
in this position by a letter from Mr. Bertrand Russell when the work
...

6

Another one - not so much intriguing maybe but charming imo -
« La mer était étale mais le reflux commençait à se faire sentir. »
Hugo, Les travailleurs de la mer
("Étale cohomology" by J. S. Milne)

10

Lévy [...] once remarked to me that reading other mathematicians’ research gave him actual physical pain.
A quotation from J.L. Doob, on Paul Lévy, used as an epigraph by Tom Leinster in A survey of definitions of n-category. Lightly amusing on first reading; more seriously so when one recalls it while going through that pain; most serious, and less ...

16

The preface to the 2nd edition of John McCleary's A User's Guide to Spectral Sequences has the following epigraph:
"For I know my transgressions, …" (Psalm 51)
See p. 185ff for transgressions in spectral sequences. And note the title "Sins of Omission" for Part III of the book.

24

Mathematics is the art of giving the same name to different things.
—Henri Poincaré, in Science and Méthode, 1908. English translation.

29

The most interesting epigraphs I have seen in mathematical books are in:
Bender and Orszag, Advanced mathematical methods for scientists and engineers. I. Asymptotic methods and perturbation theory. Every chapter is decorated by an epigraph from Sherlock Holmes. For example:
The triumphant vindication of bold theories - are these not the pride and ...

18

Though this has not really much to do with mathematics, you might be intrigued by the epigraph of Compact complex surfaces by Barth, Peters, Van de Ven (+ Hulek for the 2nd edition):
Par une belle matinée du mois de mai,
une élégante amazone parcourait, sur
une superbe jument alezane, les allées
fleuries du Bois de Boulogne.
(A. Camus, La peste)
...

9

The two volumes Computational Commutative Algebra by Martin Kreuzer and Lorenzo Robbiano (Springer, 2000 and 2005) contain lots of epigraphs. Some of them are rather weird.
Here are some examples from Volume 1:
Dura Lex, sed Lex. (Ancient Latin Proverb)
(Section on term orderings)
Divide et impera. (Philip of Macedonia)
(Section on the division ...

8

The distinction between "epigraph" and mere "quote" is not entirely clear, since the latter may be used as the former. For example, I used Millay's "Euclid alone has looked on Beauty bare ..." as an epigraph to the Introduction of my Friendly Intro to Number Theory book, but of course, it did not originate as an epigraph. Similarly, I used "It is the star to ...

24

My immediate reaction to this question was - the epigraph used for "Methods of Homological Algebra" by Gelfand and Manin
I find this a golden standard for good epigraphs - intriguing, cool, and truly holding the quintessence of the subject.

19

this seems intriguing enough:
Development of mathematics resembles a fast revolution of a wheel:
sprinkles of water are flying in all directions. Fashion – it is the
stream that leaves the main trajectory in the tangential direction.
These streams of epigone works attract most attention, and they
constitute the main mass, but they inevitably ...

Top 50 recent answers are included