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.
- Sylvester's Mathematical Papers, Volume 2, page 214.
- Bigeometric Calculus: A System with a Scale-Free Derivative by Michael Grossman, page 31.
- 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.
- Memorabilia Mathematica by Robert Edouard Moritz, quote #129.
- Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.
- Sylvester's Collected Mathematical Papers, Volume 1, page 91.
- 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.
- "A plea for the mathematician", Nature, Volume 1, page 261.
Quotes of others about Sylvester 
- To know him was to know one of the historic figures of all time, one of the immortals; and when he was really moved to speak, his eloquence equalled his genius.
- G. B. Halsted, in F. Cajori's Teaching and History of Mathematics in the United States (Washington, 1890), page 265.
- Professor Sylvester's first high class at the new university Johns Hopkins consisted of only one student, G. B. Halsted, who had persisted in urging Sylvester to lecture on the modern algebra. The attempt to lecture on this subject led him into new investigations in quantics.
- Florian Cajori, in Teaching and History of Mathematics in the United States (Washington, 1890), page 264.
- James Joseph Sylvester: Jewish Mathematician in a Victorian World, a biography of Sylvester by Karen Hunger Parshall.