The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance.

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

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.

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.

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

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

[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.