Ixix 



Bologna, of tlie Roj-al and Imperial Geographical Society of Vienna, and 

 the Mathematical Society of Hamburg. He was elected a Foreign Mem- 

 ber of the Royal Society in 1860. 



The preceding notice has been extracted from a manuscript memoir of 

 Professor Bache kindly supplied by Dr. Joseph Henry. 



Georg Friedrich Bernhard Riemann was born on the 1 7th of Sep- 

 tember 1826 at the village of Breselenz, near Dannenberg, in Hanover. He 

 was the second of six children born to the Pastor of Breselenz. Under his 

 father's sole tuition till eight years of age, he exhibited great powers of 

 arithmetical calculation. An able tutor, who from this time assisted in 

 teaching him, was forced to make unusual exertions in order to follow the 

 short and original solutions of the problems proposed to his pupil. 



In the spring of 1840 Riemann was sent to the Lyceum in Hanoaer, 

 where he remained two years. He was then placed in the Gymnasium of 

 Liineburg under Director Schmalfuss. The latter soon discovered Rie- 

 mann's mathematical talent, and not only gave him problems made 

 expressly for him during school hours, but lent him works on the higher 

 mathematical subjects, which he brought back after having thoroughly 

 mastered them in the course of a few days. A week sufficed to make 

 Legendre's theory of numbers his own for life. 



He entered the University of Gottingen at Easter 1846, by his father's 

 wish, as a student of theology. Here the lectures of Gauss stirred up in 

 him such a passion for exact science that he sought and obtained permis- 

 sion from his father to devote himself entirely to the studies of his choice. 

 For two years, commencing with Easter 1847, he studied under Jacobi at 

 Berlin, He then returned to Gottingen, and graduated, his dissertation 

 on the foundations of a general theory of functions of a variable complex 

 magnitude obtaining the warm approval of Gauss. 



In 1854 he qualified for the post of a teacher by a lecture on the hypo- 

 theses on which geometry is founded, and by writing a memoir on the re- 

 presentation of a function by a trigonometric series. In September of the 

 same year he wrote on the distribution of electricity in non-conductors. 

 In 1855 he contributed to Poggendorff's ' Annalen ' a paper on the theory 

 of Nobili's coloured rings, and one on the mathematical theory of the gal- 

 vanic current. During the two following years he suffered much from 

 failing health. 



In 1857 he became Professor Extraordinarius, and wrote four papers 

 which appeared in vol. liv. of Crelle's Journal. In 1859 he was elected 

 a Corresponding Member of the Academy of Sciences of Berlin, and con- 

 tributed to the ' Abhandlungen ' of the Academy a memoir on the num- 

 ber of primes below a given number, and was nominated Professor Ordi- 

 narius. In 1860 he was elected a member of the Academy of Sciences of 

 Gottingen, and in the course of this and the following year wrote a me- 

 moir on the propagation of plane waves of finite amphtude in air, and one 



