DEVELOPMENT OF MATHEMATICAL THOUGHT. 637 



then as professor — exerted his great influence in the 

 famous lilcole Polytechnique, in the Sorbonne, in the 

 ColleKe de France.^ 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," owing to their unin- 

 telligible and novel enunciation, who hated lecturing 

 — Cauchy possessed the enthusiasm and patience of 

 the teacher,^ spent hours with liis pupils, and pub- 

 lished his lectures on the foundations of the Calculus 

 for the benefit of the rising mathematical generation. 

 Thus lie has the merit of having created a new school 

 of mathematical thought — not only in France but also 

 al)road, where the greatest intellects, such as that of 

 Abel,* expressed themselves indebted to him for hav- 

 ing ])ointed out the only right road of progress. Tt 

 will he 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- 



^ See Valson, ' La Vie et les genie des Euler, des Lagrange, des 



Travaux du Baron Cauchy,' Paris, Laplace, des Gauss, des Jacobi, 



1868, vol. i. p. 60 sqq. I'aniour de I'enseignement portd 



^ " On disait que sa manicre jusqu'Ji I'enthousinsnie, une rare 



d'exposer etait niauvaise, ou encoie bonte, une siniplicite, une chaleur 



qu'il faisait comuie le renard, qui de c(Kur qu'il a conservees jusqu'h 



efface avec sa ([ueue les traces de ses la fin de sa vie " (Combes, quoted 



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

 Al)el, ([ue tout ce qu'ecrit Gauss * See Bjerknes, 'N.-H. Abel,' p. 



n'est qu'abomination (Griiuel), car j 48 sqt). ; p. 300. Cauehy's ' Cours 



c'est si obscur qu'il est pres(iue d'Aiialyse' ajipcared in 1821 : the 



impossible d'y rien comprendre " ' Kdsume des lei;ons sur le caitul 



(Bjerknes, ' Niels Henrik Abe!,' infinitesimal,' to which .\bel refers 



Trad, fram/aise, Paris, 188."), p. 92). in a letter to Holmboe, dated 1826, 



■* " C'est que Cauchy alliait au appeared in 1823. 



