It is easier to square the circle than to get round a mathematician.

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.

[When asked about his age.] I was *x* years old in the year *x*^{2}.

In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.

The moving power of mathematical invention is not reasoning but imagination.

The imaginary expression √(-*a*) and the negative expression -*b*, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - *a* is as inconceivable as √(-*a*).

Said in 1831

Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.

I don't quite hear what you say, but I beg to differ entirely with you.

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

The moving power of mathematical invention is not reasoning but imagination.

The gambling reasoner is incorrigible; if he would but take to the squaring of the circle, what a load of misery would be saved.

[The Astronomer's Drinking Song]

Astronomers! What can avail

Those who calumniate us;

Experiment can never fail

With such an apparatus...

Great fleas have little fleas upon their backs to bite 'em,

And little fleas have lesser fleas, and so ad infinitum.

And the great fleas themselves, in turn, have greater fleas to go on;

While these again have greater still, and greater still, and so on.

*A Budget of Paradoxes.*

[He was imitating:

So, naturalists observe, a flea

Has smaller fleas that on him prey;

And these have smaller still to bite 'em;

And so proceed ad infinitum.

Jonathan Swift: *Poetry, a Rhapsody*.]