The object of pure Mathematic (is) that of unfolding the laws of human intelligence.

There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being.

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.

Mathematics is the music of reason.

[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.

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

Surely with as good reason as had Archimedes to have the cylinder, cone and sphere engraved on his tombstone might our distinguished countrymen leave testamentary directions for the cubic eikosiheptagram to be engraved on theirs. Spirit of the Universe! wither are we drifting, and when, where, and how is all this to end?