I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty ... as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!

Mathematics is the music of reason.

The early study of Euclid made me a hater of geometry.

The object of pure Physic[s] is the unfolding of the laws of the intelligible world; the object of pure Mathematic[s] that of unfolding the laws of human intelligence.

The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life.

A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.