James Joseph Sylvester Quotes

#1. Mathematics is the music of reason.

James Joseph Sylvester

#2. 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

#3. 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

#4. [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

#5. 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

#6. The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.

James Joseph Sylvester

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

James Joseph Sylvester

#8. 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

#9. 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

#10. 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

#11. 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

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

James Joseph Sylvester

#13. 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

#14. 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!

James Joseph Sylvester