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James Joseph Sylvester Biography

James Joseph Sylvester

James Joseph Sylvester FRS (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership role in American mathematics in the later half of the 19th century as a professor at the Johns Hopkins University and as founder of the American Journal of Mathematics. At his death, he was professor at Oxford.

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James Joseph Sylvester Quotes

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.

Described, Dream, Music, Sense, Thinking, Thinks

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

Distinct, Ideas, Numbers, Thought, Three

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.

Dissevered, Life, Math, Soul, Ties, Together

Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be supposed to have on a Browning or a Tennyson. Indeed it seems to me that an exact homology exists between painting and poetry on the one hand and modem chemistry and modem algebra on the other. In poetry and algebra we have the pure idea elaborated and expressed through the vehicle of language, in painting and chemistry the idea enveloped in matter, depending in part on manual processes and the resources of art for its due manifestation.

Art, Browning, Due, Hands, Ideas

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.

Mathematics, Natural, Point, Prerogative, Stimulate, Taste

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

Ideas, Rivers, Should, Considered, Idea, Instead

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.

Law, Laws, Math, Position, Procreation, Real

Mathematics is the music of reason.

Math, Mathematics, Music, Reason

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.

Atrophying, Cutting, Learning, Math, Surest

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.

Down And, Expected, Journey, Parnassus, Stock, Two

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.

Actual, Ideas, Mind, Nature, Possible, Science

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

Study, Euclid, Made, Geometry, Early

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

Humans, Law, Mathematic, Object, Pure, Unfolding

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.

Action, Brings, Higher, Intellectual, Math, Mind