636 



SCIENTIFIC THOUGHT. 



7. 

 Gauss. 



Cauchy. 



It is right to place the name of Gauss at the head, for 

 his investigations regarding several fundamental and 

 critical questions in arithmetic and geometry date from 

 the .last years of the eighteenth century, long before 

 Cauchy's influence made itself felt. This is now abund- 

 antly clear through the publication of Gauss's works, and 

 from much of his correspondence with personal friends, 

 notably with the astronomer Bessel. We can now 

 understand how those who knew him regarded him as 

 a kind of mathematical oracle to whom " nothing in 

 theory existed that he had not looked at from all sides," 1 

 and who anticipated in his own mind the development 

 which mathematical thought was to take for a long 

 time after him. And yet it was not to him primarily 

 that the great change was due which came over mathe- 

 matical reasoning during the first half of the century. 

 Gauss was not a great teacher. In fact, there existed 

 in the first quarter of the period only one great training 

 school in advanced mathematics, and that was Paris. 

 There it was that Augustin Cauchy first as lecturer, 



tion of modern mathematics and 

 the refinement of the modern 

 theories have brought about the 

 desire "to create an abridged 

 system of mathematics adapted to 

 the needs of the applied sciences, 

 without passing through the whole 

 realm of abstract mathematics" 

 (Klein, loc. cit., p. 48). In this 

 country Prof. Perry has made a 

 beginning by publishing his well- 

 known work, ' Calculus for En- 

 gineers,' which has been welcomed 

 by Prof. Klein in Germany, and 

 which has led to an extensive 

 correspondence in the pages of 

 ' Nature ' ; it being recognised by 

 many that a quicker road must be 



made from the elements to the 

 higher applications of mathematics 

 in the natural sciences than the 

 present school system, beginning 

 with Euclid, admits of. The 

 separation of the logical and prac- 

 tical treatment of any science, as 

 likewise the independent develop- 

 ment in Germany of the poly- 

 technic school alongside of the uni- 

 versity, has, however, its dangers, 

 as is recognised by Prof. Klein 

 (' Chicago Mathematical Papers,' p. 

 136). 



1 See Bessel's letter to Gauss, 

 27th December 1810, in ' Brief - 

 wechsel zwischen G. and B., Leipzig, 

 1880, p. 132. 



