Proceedings of London Royal Society, Vol. 58 (1895), pp. 23-24.
[933]. Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.—Forsyth, A. R.
Proceedings London Royal Society, Vol. 58 (1895), pp. 11-12.
[934]. Bertrand, Darboux, and Glaisher have compared Cayley to Euler, alike for his range, his analytical power, and, not least, for his prolific production of new views and fertile theories. There is hardly a subject in the whole of pure mathematics at which he has not worked.—Forsyth, A. R.
Proceedings London Royal Society, Vol. 58 (1895), p. 21.
[935]. The mathematical talent of Cayley was characterized by clearness and extreme elegance of analytical form; it was re-enforced by an incomparable capacity for work which has caused the distinguished scholar to be compared with Cauchy.—Hermite, C.
Comptes Rendus, t. 120 (1895), p. 234.
[936]. J. J. Sylvester was an enthusiastic supporter of reform [in the teaching of geometry]. The difference in attitude on this question between the two foremost British mathematicians, J. J. Sylvester, the algebraist, and Arthur Cayley, the algebraist and geometer, was grotesque. Sylvester wished to bury Euclid “deeper than e’er plummet sounded” out of the schoolboy’s reach; Cayley, an ardent admirer of Euclid, desired the retention of Simson’s Euclid. When reminded that this treatise was a mixture of Euclid and Simson, Cayley suggested striking out Simson’s additions and keeping strictly to the original treatise.—Cajori, F.
History of Elementary Mathematics (New York, 1910), p. 285.
[937]. Tait once urged the advantage of Quaternions on Cayley (who never used them), saying: “You know Quaternions are just like a pocket-map.” “That may be,” replied Cayley, “but you’ve got to take it out of your pocket, and unfold it, before it’s of any use.” And he dismissed the subject with a smile.—Thompson, S. P.