ANNIVERSARY ADDRESS. 19 



tion, and was so wonderful in its richness as to be beyond the 

 reach of his contemporaries: — J. Bellavitis, of Padua, [1803 - 1880], 

 author of the calculus of sequipollences : — Benjamin Pierce [1809 

 - 1880] and his son C. S. Pierce, both of whom worked extensively 

 at the theory of multiple algebras: — Arthur Cayley [1821 - 1895] 

 in whose mind, the germs of the principle of invariants found in 

 the writings of Lagrange, Gauss and Boole, ripened into a complete 

 theory, thus creating a new branch of analysis : — J. J. Sylvester 

 [1814 — 1897] co-worker in the theory of invariants and author 

 of the theory of reciprocants : — Aronhold [1819 - 1884] also a 

 discoverer in invariants: — and Hermite [born 1822], discoverer of 

 evectants. Quite a host of other names, whose work was scarcely 

 less brilliant should be mentioned, but time will not permit. 



In the wider reaches of analysis, and in the theory of functions 



and theory of numbers we must not omit the name of Gauss [1777 



- 1855] who according to the dictum of Laplace was the greatest 



mathematician in all Europe : — of Cauchy [1789 - 1857] whose 



researches covered almost the whole domain of mathematics, and 



whose critical work was invaluable : — of Abel [1802 - 1829] whose 



idea of inversion of the elliptic functions of Legendre led to such 



splendid developments, surpassed only by his investigations in 



what are now called abelian functions, studied since by E. Picard, 



Weierstrass [1815-1897], Madame Kowalevski [1853-1891], 



and Poincare [born 1854]: — of Riemann [1826 - 1866] celebrated 



for his invention of the multiply-connected surfaces which bear 



his name, the theory of which has been extended by the researches 



of Liiroth, Clebsch, and Clifford [1845 - 1879]:— of Schwarz [born 



1845] Weierstrass' pupil, notable for his work on hypergeometric 



series, and on developments on minimum surfaces : — of Kummer 



[1810 - 1893], who with Eisenstein [1823 - 1852], and Dedekind 



[born 1831] extended the work of Gauss and Dirichlet [1805- 



1859] on the theory of complex numbers. Besides these ought to 



be mentioned as contributors to the modern theory of functions, 



Hankel, Cantor, Dini, Heine, Du Bois-Reymond, Thomae, Darboux 



and Forsyth and others. But reluctantly we must pass on. 



