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 Copy Share Image
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… — James Joseph Sylvester Copy Share Image
...There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like… — James Joseph Sylvester Copy Share Image
Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred. — James Joseph Sylvester Copy Share Image
The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of… — James Joseph Sylvester Copy Share Image
The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the… — James Joseph Sylvester Copy Share Image
As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to… — James Joseph Sylvester Copy Share Image
[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and… — James Joseph Sylvester Copy Share Image
Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble… — James Joseph Sylvester Copy Share Image
“Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it need only patience to ransack; it is… — James Joseph Sylvester Copy Share Image
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… — James Joseph Sylvester Copy Share Image
Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be… — James Joseph Sylvester Copy Share Image
The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these… — James Joseph Sylvester Copy Share Image
![“...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....” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/bc5/james-joseph-sylvester-23602_action_there-is-no-study-in-the-world-which-bri_23809.jpg)
![“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…” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/e72/james-joseph-sylvester-23602_absolutes_the-world-of-ideas-which-it-mathematics_338576.jpg)
![“[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.” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg)
![“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.” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/36a/james-joseph-sylvester-23602_human-intelligence_the-object-of-pure-physic-s-is-the-unfol_679113.jpg)
