James Joseph Sylvester

...There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ...…

— James Joseph Sylvester

Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

— James Joseph Sylvester

The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious…

— James Joseph Sylvester

The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of…

— James Joseph Sylvester

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting…

— James Joseph Sylvester

[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to…

— James Joseph Sylvester

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

— James Joseph Sylvester

Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on…

— James Joseph Sylvester

“Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it need only patience to ransack;…

— James Joseph Sylvester

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

— James Joseph Sylvester

Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters…

— James Joseph Sylvester

The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used,…

— James Joseph Sylvester

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

— James Joseph Sylvester

May not music be described as the mathematics of the sense, mathematics as music of the reason?

— James Joseph Sylvester

So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct…

— James Joseph Sylvester

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the…

— James Joseph Sylvester

Mathematics is the music of reason.

— James Joseph Sylvester

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

— James Joseph Sylvester

Surely with as good reason as had Archimedes to have the cylinder, cone and sphere engraved on his tombstone might our distinguished…

— James Joseph Sylvester

What a glorious title, Nature, a veritable stroke of genius to have hit upon. It is more than a cosmos, more than…

— James Joseph Sylvester

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which…

— James Joseph Sylvester

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up…

— James Joseph Sylvester

I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty ... as the study…

— James Joseph Sylvester

It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or…

— James Joseph Sylvester

The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become…

— James Joseph Sylvester