I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General.

I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General.

The Pirates of Penzance. Act 1.

One of the principal objects of theoretical research in my department of knowledge is to find the point of view from which the subject appears in its greatest simplicity.

Lest men suspect your tale untrue,

Keep probability in view.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956. p. 1334.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect...geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

Quoted in J. Koenderink Solid Shape, Cambridge Mass.: MIT Press, 1990.

A great part of its [higher arithmetic] theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.

Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.

In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully, but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.

Letter to Bolyai, 1808.

[Attributed to him by H.B. Lubsen]

Theory attracts practice as the magnet attracts iron.

Foreword of H.B.
Lubsen's geometry
textbook.

[His second motto:]

Thou, nature, art my goddess; to thy laws my services are bound...

W. Shakespeare King Lear.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

In A. Arber The Mind and the Eye 1954.