[Math] Most intriguing mathematical epigraphs

big-listmath-communicationmathematical-writingsoft-question

Good epigraphs may attract more readers. Sometimes it is necessary.
Usually epigraphs are interesting but not intriguing.

To pick up an epigraph is some kind of nearly mathematical problem: it should be unexpectedly relevant to the content.

What successful solutions are known for you?
What epigraphs attracted your attention?

Please post only epigraphs because quotes were collected in Famous mathematical quotes.

There are certain common Privileges of a Writer,
the Benefit whereof, I hope, there will be no Reason to doubt;
Particularly, that where I am not understood, it shall be concluded,
that something very useful and profound is coucht underneath.
(JONATHAN SWIFT, Tale of a Tub, Preface 1704)

[Taken from Knuth, D. E. The art of computer programming. Volume 3: Sorting and searching.]

Best Answer

The most interesting epigraphs I have seen in mathematical books are in:

  1. 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 justification of our life's work? (Conan Doyle, The Valley of Fear)

Just feel like re-reading Sherlock Holmes:-)

  1. Reed and Simon, Methods of Mathematical physics, especially volume 1. For example, the chapter on Unbounded Operators has this:

I tell them that if they will occupy themselves with the study of mathematics, they will find that it is the best remedy against the lusts of the flesh. (Th. Mann, Magic Mountain).

But my favorite one is the following, from Kirillov, What's a number?:

Examiner: What is a multiple root of a polynomial?

Student: Well, this is when we plug a number to a polynomial and obtain zero; plug it again and obtain zero again... And this happens $k$ times. But on the $(k+1)$-st time we do not obtain zero.

Cannot help citing one more. Brocker, Lander, Differentiable germs and catastrophes:

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