206 



SCIENCE. 



[N. S. Vol. I. No. 8. 



by this time he was ranked by Kelland in the 

 Encyclopsedia Britaunica as the verj' fore- 

 most living English mathematician. The 

 only possible sharer of this proud preemi- 

 nence was his life-long friend Cayley. 



Appointed among the first twentj' fellows 

 at the organization of the Johns Hopkins 

 University, and having an intense desire to 

 study Sylvester's own creations with him, 

 I became alone his first class in the new 

 University. Sylvester gives in his cele- 

 brated address a graphic account of the 

 formation of that first class as illustrating 

 the mutual stimulus of student and pro- 

 fessor. 



The text-book was Salmon's Modern 

 Higher Algebra, dedicated to Sylvester 

 and Cayley as made up chiefly from their 

 original work. 



The professor broke every rule and canon 

 of the Normal Schools and Pedagogy, yet 

 was the most inspiring teacher conceivable. 

 Eveiy thing, from music to Hegel's meta- 

 physics, linked into the theory of Invari- 

 ants, combined with the precious personal 

 data, and charming unpublished reminis- 

 cences of all the great mathematicians of 

 the preceding generation. 



Such a course in the creation of modern 

 mathematics, with most precious, elsewhere 

 unattainable, historic indications, will per- 

 haps never be paralleled. It went on not 

 only at the appointed hours, but the pro- 

 fessor would send for his class at night, 

 while at other times they took excursions 

 together to Washington. The incidents of 

 these two formative years, spent in most 

 intimate association with one of the great 

 historic personages of science, can never be 

 forgotten. It was during this period that 

 Sylvester founded the American Journal of 

 Mathematics, and it is due to his particular 

 wish that it was given the quarto form. 



Then began a new productive period in 

 his life, the astounding activity and mar- 

 velous results of which can be faintly esti- 



mated by consulting the pages upon pages 

 taken up in the Johns Hojikins Bibliogra- 

 phia Mathematica, merely to enunciate 

 the titles of the memoirs and papers pro- 

 duced. The verj' complete and profound 

 historic and bibliographic account of the 

 theory of Invariants given by Meyer in the 

 Berichte of the deutsche mathematische Ge- 

 sellschaft indicates very fairlj' Sjivester's 

 final place in the history of that all-pervad- 

 ing subject. His origmal contributions to 

 many other parts of the vast structure of 

 modern pure analj'sis are of nearly as great 

 weight. 



Sylvester was completely of the opinion 

 that no teaching for a real universitj^ can be 

 ranked high which is not vitalized by abun- 

 dant original creative work. He main- 

 tained that it was the plain duty of any 

 mature man holding a professorship in a 

 real university to resign at once if he had 

 not ah'eady been copiouslj'^ and creatively 

 productive. 



He believed that without unceasing orig- 

 inal research and published original work 

 there could be no real university teaching, 

 and that any universitj' professor who, 

 without such a basis, pretended to be a 

 good teacher, was, consciously or unconsci- 

 ously, a selfish fraud. 



On page 6 of his address delivered on 

 Commemoration Day, 1877, he speaks of a 

 university * under its twofold aspect as a 

 teaching body and as a corporation for the 

 advancement of science.' He then con- 

 tinues; "I hesitate not to say that, in 

 my opinion, the two functions of teaching 

 and working in science should never be 

 divorced. 



" I believe that none are so well fitted to 

 impart knowledge as those who are engaged 

 in reviewing its methods and extending its 

 boundaries . . . May the time never come 

 when the two offices of teaching and re- 

 searching shall be sundered in this Univer- 

 ■sity !" 



