Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in the gift of clear exposition.

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

The mathematics of probability enters when we seek a method for enumerating possible cases without actually counting them off

Today it is given in the textbooks as an example which young students dispose of in twenty minutes or less. Yet it held Newton up for twenty years. He finally solved it, of course

Replying two weeks later he states his opinion of Fermat’s Last Theorem. “I am very much obliged for your news concerning the Paris prize. But I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

Clarity is, indeed, all the more necessary when one essays to lead the reader farther from the beaten path and into wilder territory- Joseph Liouville

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

[As a young teenager] Galois read Legendre]'s geometry from cover to cover as easily as other boys read a pirate yarn.