THE SCIENTIFIC SPIRIT IN GERMANY. 



185 



however, tliat 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 I 

 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.^ He was first 



mained unknown and unnoticed. 

 See on the history of the subject, 

 Hankel, ' Theorie der comijlexen 

 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 ' Traite des fonctions 

 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- 

 l^erties of the " doubly periodical " 

 functions. Full details will be 

 found in the historical introduction 

 to Enneper's ' Elliptische Func- 

 tionen,' 2nd 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, ' N. H. Abel,' Paris, 

 1885; Koenigsberger, 'Zur Ges- 

 chichte der Theorie der elliptischen 

 Transcendenten,' Leipzig, 1879. 



^ Carl Gustav Jacob Jacobi (born 

 at Potsdam 1804, died at Berlin 

 1851) was the first great mathe- 



