THE SCIENTIFIC SPIRIT IN GERMANY. 



185 



however, that the spirit of exact and specially mathe- 

 matical research owed its right of domicile within the 

 universities to others who came after him, and to cir- 

 cumstances with which he was hardly connected. 



The man to whom Germany owes its first great school 

 of mathematicians was Jacobi. He was self-taught like 

 Gauss ; but whilst Gauss followed in the footsteps of 

 Newton and the ancients, Jacobi followed in those of 

 Euler, Lagrange, and Laplace. The style and methods 

 of these mathematicians, being more suited for didactic 

 purposes than the classical style of Euclid, Newton, and 

 Gauss, was probably more congenial to the mind of 

 Jacobi, who from his twenty-first year (1825) developed 

 a great activity as an academic teacher. 1 He was first 



17. 



Jacobi's 

 mathemati- 

 cal school. 



maiued unknown and unnoticed. 

 See on the history of the subject, 

 Hankel, ' Theorie der complexen 

 Zahlensysteme,' 1867, pp. 71, 82. 

 Gauss, through hiding his researches 

 on this subject so long, lost the 

 claim to the priority of the inven- 

 tion, though not of the effectual 

 use of it. In another instance he 

 allowed others to appropriate the 

 merit of cultivating a large new 

 field which had been familiar to 

 him many years before. It was 

 known all through the first half of 

 the century that Gauss was in pos- 

 session of valuable discoveries in 

 what he termed the " new transcen- 

 dent functions." References in the 

 ' Disquisitiones,' 335, in his corres- 

 pondence with Schumacher, Bessel, 

 Olbers, and Crelle, had made his 

 friends curious to see the " amplum 

 opus " which he had promised. It 

 appears, however, that, independ- 

 ently of him, Jacobi and Abel 

 (1802-29) following the investiga- 

 tions of Legendre (whose labours 

 began in 1786 and culminated in 



his great work ' Trait^ des f onctious 

 elliptiques, &c.,' 1825-28, 2 vols. 

 and 3 supplements), succeeded in 

 developing the theory very much 

 on the same lines as Gauss had 

 taken nearly a generation earlier. 

 Eminent mathematicians who, since 

 the publication of Gauss's posthu- 

 mous papers, have fully investi- 

 gated the subject, assign to Jacobi 

 and Abel the undisputed priority 

 of publishing, but to Gauss that of 

 discovering, the fundamental pro- 

 perties of the " doubly periodical " 

 functions. Full details will be 

 found in the historical introduction 

 to Enneper's ' Elliptische Func- 

 tionen,' 2d ed., Halle, 1890. See 

 also Gauss's Werke, vol. iii. p. 491- 

 496 ; Dirichlet's Discourse on Jacobi 

 in Jacobi's Werke, vol. i. p. 11 ; C. 

 A. Bjerknes, J N. H. Abel,' Paris, 

 1885; Koenigsberger, ' Zur Ges- 

 chichte der Theorie der elliptischen 

 Transcendenten,' Leipzig, 1879. 



1 Carl Gustav Jacob Jacobi (born 

 at Potsdam 1804, died at Berlin 

 1851) was the first great mathe- 



