James Joseph Sylvester Quotes

41 Sourced Quotes

May not Music be described as the Mathematic of Sense, Mathematics as Music of the Reason?

James Joseph Sylvester
I think it would be desirable that this form of word [mathematics] should be reserved for the applications of the science, and that we should use mathematic in the singular to denote the science itself, in the same way as we speak of logic, rhetoric, or (own sister to algebra) music.

James Joseph Sylvester
Music the Algebra of sense, Algebra the Music of the reason; Music the dream, Algebra the waking life - the soul of each the same!

James Joseph Sylvester
It is not without a feeling of surprise and trepidation at my own temerity that I find myself in the position of one about to address this numerous and distinguished assembly.

James Joseph Sylvester
Some people have been found to regard all mathematics, after the 47 proposition of Euclid, as a sort of morbid secretion, to be compared only with the pearl said to be generated in the diseased oyster.

James Joseph Sylvester
Algebraists (who are wont to regard each other as the flower and salt of the earth) are a set of mere calculating-machines endowed with organs of locomotion, or, at best, a sort of poor visionary dumb creatures only capable of communicating by signs and symbols with the outer world.

James Joseph Sylvester
Space is the Grand Continuum from which, as from an inexhaustible reservoir, all the fertilizing ideas of modern analysis are derived...

James Joseph Sylvester
When called upon to speak in public [the mathematician] feels as a man might... who has passed all his life in peering through a microscope, and is suddenly called upon to take charge of an astronomical observatory. He has to get out of himself, as it were, and change the habitual focus of his vision.

James Joseph Sylvester
It often happens that the pursuit of the beautiful and appropriate, or, as it may be otherwise expressed, the endeavor after the perfect, is rewarded with a new insight into the true.

James Joseph Sylvester
Mathematical pursuits unfit a person for the discharge of the common duties of life and cut him off from the exercise of Man's highest prerogative, "discourse of reason and faculty of speech divine,".

James Joseph Sylvester
The two functions of teaching and working in science should never be divorced.

James Joseph Sylvester
Divide et impera: is as true in algebra as in statecraft; but no less true and even more fertile is the maxim auge et impera. The more to do or to prove, the easier the doing or the proof.

James Joseph Sylvester
Would it sound too presumptuous to speak of perception as a quintessence of sensation, language (that is, communicable thought) [as that] of perception, mathematics [as that] of language? We should then have four terms differentiating from inorganic matter and from each other: the Vegetable, Animal, Rational, and Supersensual models of existence.

James Joseph Sylvester
Geometry formerly was the chief borrower from arithmetic and algebra, but it has since repaid its obligations with abundant usury...

James Joseph Sylvester
Most, if not all, of the great ideas of modern mathematics have had their origin in observation.

James Joseph Sylvester
It always seems to me absurd to speak of a complete proof, or of a theorem being rigorously demonstrated. An incomplete proof is no proof, and a mathematical truth not rigorously demonstrated is not demonstrated at all.

James Joseph Sylvester
As all roads are said to lead to Rome, so I find, in my own case at least, that all algebraic inquiries sooner or later end at the Capitol of Modern Algebra over whose shining portal is inscribed "Theory of Invariants."

James Joseph Sylvester
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
No endeavor that is worthwhile is simple in prospect; if it is right, it will be simple in retrospect.

James Joseph Sylvester
It is difficult to estimate the lengths to which human self-delusion can be carried.

James Joseph Sylvester
Perhaps I may without immodesty lay claim to the appellation of Mathematical Adam, as I believe that I have given more names (passed into general circulation) of the creatures of the mathematical reason than all the other mathematicians of the age combined.

James Joseph Sylvester
The beautiful theory of atomicity has its home in the attractive but somewhat misty border land lying between fancy and reality and cannot, I think, suffer from any not absolutely irrational guess which may assist the chemical enquirer to rise to a higher level of contemplation of the possibilities of his subject.

James Joseph Sylvester
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.

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

James Joseph Sylvester
I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty... as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.

James Joseph Sylvester
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
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
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