James Joseph Sylvester: If I were asked to name, in one word, the pole...

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.

James Joseph Sylvester

beauty men order

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.

James Joseph Sylvester

music dream thinking

Mathematics is the music of reason.

James Joseph Sylvester

mathematics reason math

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.

James Joseph Sylvester

wings life long

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.

James Joseph Sylvester

intellectual mind math

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.

James Joseph Sylvester

physics law world

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

James Joseph Sylvester

ties math life

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

should rivers ideas

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.

James Joseph Sylvester

nature math talking

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

James Joseph Sylvester

euclid study made

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

James Joseph Sylvester

three numbers ideas

[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.

James Joseph Sylvester

effort imagination exercise

Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble and vain attempts of geometry proper to rise to its level or to emulate it in its flights.

James Joseph Sylvester

analysis levels looks

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?

James Joseph Sylvester

tombstone might science

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

James Joseph Sylvester

mathematics taste natural

What a glorious title, Nature, a veritable stroke of genius to have hit upon. It is more than a cosmos, more than a universe. It includes the seen as well as the unseen, the possible as well as the actual, Nature and Nature's God, mind and matter. I am lost in admiration of the effulgent blaze of ideas it calls forth.

James Joseph Sylvester

nature science ideas

So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.

James Joseph Sylvester

learning cutting math

The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.

James Joseph Sylvester

real law math

It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.

James Joseph Sylvester

down-and journey two

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

James Joseph Sylvester

unfolding humans law

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!