GEORGE BRUCE HALSTED-THE ESSENCE OF TEACHING. 
5 
by Kelland in the Encyclopaedia Brittannica as the foremost living 
English mathematician. The only possible sharer of this proud pre-emi¬ 
nence was his life-long friend Cayley. 
Appointed among the first twenty fellows at the organization of the 
Johns Hopkins University, and having an intense desire to study Sylves¬ 
ter’s own creations with him, I became alone his first class in the new 
University. Sylvester gives in his celebrated address a graphic account 
of the formation of that first class as illustrating the mutual stimulus of 
student and professor. 
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. Everything, 
from music to Hegel’s metaphysics, linked into the theory of Invariants, 
combined with the precious personal data, and charming unpublished 
reminiscences of all the great mathematicians of the preceding genera¬ 
tion. 
Such a course in the creation of modern mathematics, with most pre¬ 
cious, elsewhere unattainable, historic indications, will perhaps never be 
paralleled. It went on not only at the appointed hours, but the profes¬ 
sor would send for his class late at night, while at other times they took 
excursions together to Washington. The incidents of those 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 activ¬ 
ity and marvelous results of which can be faintly estimated by consult¬ 
ing the pages upon pages taken up in the Johns Hopkins Bibliographia 
Mathematica merely to enunciate the titles of the memoirs and papers 
produced. The very complete and profound historic and bibliographic 
account of the theory of Invariants given by Meyer in the Berichte of 
the deutsche mathematische Gesellschaft indicates very fairly Sylvester’s 
final place in the history of that all-pervading subject. His original 
contributions to many other parts of the vast structure of modern pure 
analysis are of nearly as great weight. 
Sylvester was completely of the opinion that no teaching for a real 
university can be ranked high which is not vitalized by abundant origi¬ 
nal creative work. He maintained 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 already been copiously and creative^ productive. 
He believed that without unceasing original research and published 
original work there could be no real university teaching, and that any 
