On James J Sylvester

"It is true that, in the eyes of the pure mathematician, Quaternions have one grand and fatal defect. They cannot be applied to space of n dimensions, they are contented to deal with those poor three dimensions in which mere mortals are doomed to dwell, but which cannot bound the limitless aspirations of a Cayley or a Sylvester. From the physical point of view this, instead of a defect, is to be regarded as the greatest possible recommendation. It shows, in fact, Quaternions to be the special instrument so constructed for application to the Actual as to have thrown overboard everything which is not absolutely necessary, without the slightest consideration whether or no it was thereby being rendered useless for application to the Inconceivable." (Peter G Tait, Nature Vol. 4, [Presidential Address British Association for the Advancement of Science] 1871)

"The flights of the imagination which occur to the pure mathematician are in general so much better described in his formulas than in words, that it is not remarkable to find the subject treated by outsiders as something essentially cold and uninteresting - […] the only successful attempt to invest mathematical reasoning with a halo of glory - that made in this section by Prof. Sylvester - is known to a comparative few, […]" (Peter G Tait, Nature Vol. 4,[Presidential Address British Association for the Advancement of Science] 1871)

"His [J.J. Sylvester’s] lectures were generally the result of his thought for the preceding day or two, and often were suggested by ideas that came to him while talking. The one great advantage that this method had for his students was that everything was fresh, and we saw, as it were, the very genesis of his ideas. One could not help being inspired by such teaching." (William Durfee) [as quoted by Florian Cajori,"Teaching and History of Mathematics in the United States" 1890)] 

"If we survey the mathematical works of Sylvester, we recognize indeed a considerable abundance, but in contradistinction to Cayley - not a versatility toward separate fields, but, with few exceptions - a confinement to arithmetic-algebraic branches. […] The concept of Function of a continuous variable, the fundamental concept of modern mathematics, plays no role, is indeed scarcely mentioned in the entire work of Sylvester - Sylvester was combinatorist [combinatoriker]." (Max Noether, "Mathematische Annalen", 1898)

"The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method - more daring than anything that the history of philosophy records - of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason." (Nicholas M Butler, "What Knowledge is of Most Worth?", [Presidential address to the National Education Association] 1895)