Revolutions never occur in mathematics.

Revolutions never occur in mathematics.

Historia Mathematica. 1975.

In my experience most mathematicians are intellectually lazy and especially dislike reading experimental papers. He (Rene Thom) seemed to have very strong biological intuitions but unfortunately of negative sign.

What Mad Pursuit. London: Weidenfeld and Nicolson, 1988.

Mathematics is written for mathematicians.

De Revolutionibus.

[Upon proving that the best betting strategy for "Gambler's Ruin" was to bet all on the first trial.]

It is true that a man who does this is a fool. I have only proved that a man who does anything else is an even bigger fool.

In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

Don't talk to me of your Archimedes' lever. He was an absentminded person with a mathematical imagination. Mathematics commands all my respect, but I have no use for engines. Give me the right word and the right accent and I will move the world.

Preface to A Personal Record.

C'este donc par l'etude des mathematiques, et seulement par elle, que l'on peut se faire une idee juste et approfondie de ce que c'est qu'une science.

[It is through the study of mathematics, and only through it, that one can form a fair and comprehensive idea of what science is.]

Quoted by T. H.
Huxley in
*Fortnightly
Review,* Vol. II,
N.S. 5.

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.

...from the time of Kepler to that of Newton, and from Newton to Hartley, not only all things in external nature, but the subtlest mysteries of life and organization, and even of the intellect and moral being, were conjured within the magic circle of mathematical formulae.

The Theory of Life.

The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.

In J.E. Littlewood A Mathematician's Miscellany. Methuen and Co., Ltd. 1953.

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.