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 defined 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 cole 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'Ecole 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 they could hope to do something 

 him Lejeune Dirichlet says : " It similar. . . . The success of this 

 was not his business to communicate unusual method was truly remark - 

 what was finished and what had able. If in Germany the knowledge 

 been communicated before ; his of the methods of analysis is now 

 lectures all treated of subjects spread to a degree unknown to 

 which lay outside of the field of former times, if numerous mathe- 

 the text-books, and covered only maticians extend the science in 

 those parts of science in which he every direction, this gratifying re- 

 had himself been creative. With suit is principally owing to Jacob!. 

 Mm this meant that they exhibited Nearly all have been his pupils," 

 the greatest variety. His lectures i &c. (Dirichlet's Discourse in the 

 were not remarkable for that kind Academy of Berlin, 1852, Jacobi's 

 of clearness which is character- ! Werke, vol. L p. 21.) 

 istic of intellectual poverty, but for i l The two mathematicians on 

 a clearness of a higher kind. He i whom A. L. Crelle (1780-1855) re- 

 tried primarily to show the leading j lied mainly for contributions when 

 ideas which underlay any theory, ! he started the ' Journal fiir die 

 and whilst he removed everything reine und angewandte Mathematik ' 

 that had an artificial appearance, { in 1826 were Abel and Steiner. 

 the solution of problems presented For originality of thought they 

 itself so easily to his hearers that I stand quite alone. Both extended 



