186 



SCIENTIFIC THOUGHT. 



at Berlin, then at Konigsberg; these two universities 

 having become through him and Bessel the German 

 teaching centres of the higher mathematics, both pure 

 and applied. They have up to the present day fully 

 maintained this pre-eminent position. They were teach- 

 ing centres in the sense denned above not only as 

 regards mathematical knowledge and method, but like- 

 wise as regards mathematical research. For this pur- 

 pose as in the philological sciences the lecture-room 

 was not sufficient; there was also wanted a repository 

 for the independent and original contributions of the 

 school. Like the lcole polytechnique thirty years before 

 in Paris, the Berlin school of mathematicians started with 

 an important periodical. This was known as Crelle's 

 Journal. Together with the Memoirs of the Paris Aca- 

 demy and the Journal de 1'^cole polytechnique, it forms 

 the principal repository for the higher mathematical work 

 of the first half of the century. 1 It was also through 



matical teacher of Germany. Of 

 him Lejeune Dirichlet says : " It 

 was not his business to communicate 

 what was finished and what had 

 been communicated before ; his 

 lectures all treated of subjects 

 which lay outside of the field of 

 the text-books, and covered only 

 those parts of science in which he 

 had himself been creative. With 

 him this meant that they exhibited 

 the greatest variety. His lectures 

 were not remarkable for that kind 

 of clearness which is character- 

 istic of intellectual poverty, but for 

 a clearness of a higher kind. He 

 tried primarily to show the leading 

 ideas which underlay any theory, 

 and whilst he removed everything 

 that had an artificial appearance, 

 the solution of problems presented 

 itself so easily to his hearers that 



they could hope to do something 

 similar. . . . The success of this 

 unusual method was truly remark- 

 able. If hi Germany the knowledge 

 of the methods of analysis is now 

 spread to a degree unknown to 

 former times, if numerous mathe- 

 maticians extend the science in 

 every direction, this gratifying re- 

 sult is principally owing to Jacobi. 

 Nearly all have been his pupils," 

 &c. (Dirichlet's Discourse hi the 

 Academy of Berlin, 1852, Jacobi's 

 Werke, vol. i. p. 21.) 



1 The two mathematicians on 

 whom A. L. Crelle (1780-1855) re- 

 lied mainly for contributions when 

 he started the ' Journal fur die 

 reine und angewandte Mathematik ' 

 in 1826 were Abel and Steiner. 

 For originality of thought they 

 stand quite alone. Both extended 



