THE SCIENTIFIC SPIRIT IX GERMANY. 



181 



though not by its universities, was aheady an import- 

 ant power in the Eepublic of exact science which 

 then had its centre in Paris. Just at the beginning 

 of the nineteenth century two events happened which 

 foreboded for the highest branches of the mathematical 

 sciences a revival of the glory which in this depart- 

 ment Kepler and Leibniz had already given to their 

 country. These two events are both coupled with the 

 name of Carl Friedrich Gauss. They added greatly 15. 

 to the reputation of the University of GiJttingen, with mathemati- 



*" cal re- 



which this remarkable man was connected for half a searches, 

 century.^ The first was the pulilication of the ' Dis- 

 quisitiones Arithmeticse ' in Latin in 1801 a work by 

 which Gauss placed himself on a level with the great 

 mathematicians, Euler, Lagrange, and Legendre." The 



1 Carl Friedrich Gauss (1777- 

 1855), a native of Brunswick, called 

 by Laplace the first mathematician 

 of Europe, may be considered as 

 the first and foremost representa- 

 tive of the modern mathematical 

 school, of which we shall have to 

 treat later on. Unlike most of 

 the great mathematicians of the 

 Continent, he was self-taught, and 

 followed in his earliest works quite 

 independent lines of thought ; re- 

 sembling in this the great isolated 

 thinkers of Britain whose ideas take 

 a generation or more to penetrate 

 into the test-books of the school. 

 Gauss had the highest opinion of 

 the dignity of pure science, and it 

 almost appears as if, among the 

 moderns, only Newton had come 

 up to his ideal. For him alone 

 he reserves the adjective " sum- 

 mus," and he adopts his synthetic 

 and classical methods of exposition, 

 removing, as has been said, the 

 scaffoldings by the aid of which he 

 had erected his monumental works. 



Gauss trained few mathematicians ; 

 but among the few who penetrated 

 the secret of his ideas are such 

 original thinkers as the Hungarian 

 Bolyai (1775-1856), the geometers 

 Mobius (1790-1868) and Von Staudt 

 (1798-1867), who all mark quite 

 independent lines of research. On 

 Gauss see Sartorius, ' Gauss zum 

 Gediichtniss,' Leipzig, 1856 ; Han- 

 selmann, ' K. F. Gauss,' Leipzig, 

 1878 ; E. Schering, ' C. F. Gauss,' 

 Gottingen, 1887. 



'^ It appears that Gauss, to whom 

 the arithmetical discoveries of For- 

 mat and the proofs of Euler, La- 

 grange, and Legendre remained for 

 a long time unknown (see his Works, 

 edited by Schering, vol. i. p. 6 ; 

 vol. ii. p. 444), had independently, 

 in his eighteenth year, as a student 

 at Gottingen, already arrived at a 

 great number of propositions refer- 

 ring to the properties of numbers, 

 and had then also found methods 

 of geometrically constructing the 

 regular polygon of seventeen sides. 



