James Joseph Sylvester quotes

James Joseph Sylvester was an influential English mathematician renowned for his contributions to matrix theory, invariant theory, and number theory. His work laid important foundations for modern algebra and mathematical research. He also played a key role in advancing mathematics education and mentoring other notable mathematicians. Here are 10 of his quotes:

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

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 point, to stimulate the faculty of invention.

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 other of his journey sit down and invent a definite integral or two towards the increase of the common stock.

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 mathematician thinks music: music the dream, mathematics the working life.

James Joseph Sylvester

Mathematics is the music of reason.

James Joseph Sylvester

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

James Joseph Sylvester

It has been said that to appreciate what virtue and morals mean, men must live virtuous and moral lives. It is equally true, that a knowledge of the objects of science is not to be attained by any scheme of definitions, however carefully contrived. He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer.

James Joseph Sylvester

As a public teacher of mere striplings, I am often amazed by the facility and absence of resistance with which the principles of the infinitesimal calculus are accepted and assimilated by the present race of learners. When I was young, a boy of sixteen or seventeen who knew his infinitesimal calculus would have been almost pointed at in the streets as a prodigy, like Dante, as a man who had seen hell. Now-a-days, our Woolwich cadets at the same age, talk with glee of tangents and asymptotes and points of contrary flexure and discuss questions of double maxima and minima, or ballistic pendulums, or motion in a resisting medium, under the familiar and ignoble name of sums.

James Joseph Sylvester

It always seems to me absurd to speak of a complete proof of a theorem being rigorously demonstrated. An incomplete proof is no proof and a mathematical truth not rigorously demonstrated is not demonstrated at all. I do not mean to deny that there are mathematical truths, morally certain, which defy and will probably to the end of time to defy proof, as, e.g. that every indecomposable integer polynomial function must represent an infinitude of primes. I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitation of our faculties in regard to time, which like space may be in its essence poly-dimensional, and that this and such sort of truths would become self-evident to a being whose mode of perception is according to superficially as distinguished from our own limitation to linearly extended time.

James Joseph Sylvester