James Joseph Sylvester Quotes

41 Sourced Quotes

As lightning clears the air of impalpable vapours, so an incisive paradox frees the human intelligence from the lethargic influence of latent and unsuspected assumptions. Paradox is the slayer of Prejudice.

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
No mathematician now-a-days sets any store on the discovery of isolated theorems, except as affording hints of an unsuspected new sphere of thought, like meteorites detached from some undiscovered planetary orb of speculation.

James Joseph Sylvester
Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. "Omne exit in infinitum " is their favorite motto and accepted axiom.

James Joseph Sylvester
The interval between the two [geometry and analysis] is as wide as between empiricism and science, as between the understanding and the reason; or as between the finite and the infinite.

James Joseph Sylvester
[Tschebycheff] was the only man ever able to cope with the refractory character and erratic flow of prime numbers and to confine the stream of their progression with algebraic limits, building up, if I may so say, banks on either side which that stream, devious and irregular as are its windings, can never overflow.

James Joseph Sylvester
Geometry may sometimes appear to take the lead over analysis but in fact precedes it only as a servant goes before the master to clear the path and light him on his way.

James Joseph Sylvester
The early study of Euclid made me a hater of geometry.

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 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
For what is the theory of determinants? It is an algebra upon algebra; a calculus which enables us to combine and foretell the results of algebraical operations, in the same way as algebra itself enable us to dispense with the performance of the special operations of arithmetic. All analysis must ultimately clothe itself under this form.

James Joseph Sylvester
It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of Language.

James Joseph Sylvester