DEVELOPMENT OP MATHEMATICAL THOUGHT. 637 



then as professor exerted his great influence in the 

 famous F^cole Polytechnique, in the Sorbonne, in the 

 College de France. 1 In contrast with Gauss who was 

 self-contained, proud, and unapproachable, whose finished 

 and perfect mathematical tracts were, even to those who 

 worshipped him, an abomination, 2 owing to their unin- 

 telligible and novel enunciation, who hated lecturing 

 Cauchy possessed the enthusiasm and patience of 

 the teacher, 3 spent hours with his pupils, and pub- 

 lished his lectures on the foundations of the Calculus 

 for the benefit of the rising mathematical generation. 

 Thus he has the merit of having created a new school 

 of mathematical thought not only in France but also 

 abroad, where the greatest intellects, such as that of 

 Abel, 4 expressed themselves indebted to him for hav- 

 ing pointed out the only right road of progress. It 

 will be useful to define somewhat more closely wherein 

 this new school differed from that preceding it, which 

 culminated in the great names of Euler, Lagrange, and 

 Laplace. 



The great development of modern as compared with 

 ancient mathematics may be stated as consisting in the in- 



1 See Valson, ' La Vie et les j ge'nie des Euler, des Lagrange, des 



Travaux du Baron Cauchy,' Paris, 

 1868, vol. i. p. 60 sqq. 



" On disait que sa maniere 



Laplace, des Gauss, des Jacobi, 

 1'amour de I'enseignement porte 

 jusqu'a 1'enthousiasme, une rare 



d'exposer etait mauvaise, ou encore bonte', une simplicite, une chaleur 



qu'il faisait comme le renard, qui de creur qu'il a conservees jusqu'a 



efface avec sa queue les traces de ses j la fin de sa vie" (Combes, quoted 



pas sur le sable. Crelle dit, selon I by Valson, vol. i. p. 63). 



Abel, que tout ce qu'e"crit Gauss j 4 See Bjerknes, 'N.-H. Abel,' p. 



n'est qu'abomination (Griiuel), car 48 sqq. ; p. 300. Cauchy's ' Cours 



c'est si obscur qu'il est presque i d' Analyse ' appeared in 1821 ; the 



impossible d'y rien comprendre" ! 'Re'sume' des Ie9ons sur le calcul 



(Bjerknes, ' Niels Henrik Abel,' 



Trad, fran^aise, Paris, 1885, p. 92). 



3 " C'est que Cauchy alliait au 



infinitesimal,' to which Abel refers 

 in a letter to Hohnboe, dated 1826, 

 appeared in 1823. 



