GEORGE BRUCE HALSTED-THE ESSENCE OE TEACHING. 
3 
A university should wish to feed the mental leaders of the next gen- 
eratiqn. 
For this nothing can take the place of contact with the living spirit of 
research, original work, creative authorship. 
Without fostering and requiring such work of students, and still more 
of all its professors, no institution can be a university of the first class. 
Intimate contact with a producer of the first rank is worth more than the 
whole world of so-called training by use of retailed convictions. 
The most inspiring teacher must have known how to acquire convic¬ 
tion where no predecessor had ever been before him; to show others how 
to conquer new regions, he must himself have broken barriers for human 
thought. As Rector of the University of Berlin, Helmholtz said: “Our 
object is to have instruction given only by teachers who have proved 
their own power to advance science.” 
There is no honest test or proof of scholarship or acquirement but pro¬ 
duction. The characteristic quality of all the highest teaching lies in the 
fact that it comes from a creator. 
No more convincing demonstration of my thesis could be wished for 
than the work of Sylvester for America. On page 233, I, of his hoehere 
Geometrie, 1893, Felix Klein, as high an authority as any living, says: 
“ Sylvester hat noch 1874 als 60 jaehriger Mann den Mut gehabt an die 
Johns Hopkins University in Baltimore ueberzusiedeln und durch eine 
ganz specifisclie durch 10 Jalire fortgesetzte Lehrthaetigkeit hoehere 
mathematische Studien auf amerikanischen Boden zu initiiren.” 
The birth of higher mathematics in America will always date from 
Sylvester’s advent at the Johns Hopkins. Then and there with his 
mighty head he raised the whole western continent and made it a worthy 
associate in the profoundest thought-life of our world. But few know 
that this epoch-making period was not Sylvester’s first advent in the 
United States. The immortal glory now belonging to the Johns Hop¬ 
kins University might have been anticipated by another, and with the 
very same instrument. 
An adequate life of James Joseph Sylvester has never been written, 
and probably never will be while he lives. At Cambridge he was most 
impressed by a classmate of his own, the celebrated George Green, who 
had already then produced the remarkable Green’s Theorem, and much 
of the work which still stands as a foundation stone in the edifice of 
modern electrical science. As Sylvester would not sign the thirty-nine 
articles of the Established Church, he was not allowed to take his degree, 
nor to stand for a Fellowship, to which his rank in the tripos entitled him. 
Sylvester always felt bitterly this religious disbarment. His denuncia¬ 
tion of the narrowness, bigotry, and intense selfishness exhibited in these 
creed tests was a wonderful piece of oratory in his celebrated address at 
