Background
Johann Georg Rosenhain was born on June 10, 1816, in Konigsberg, Prussia. His parents were Nathan Rosenhain and Röschen Joseph.
University of Königsberg, Kaliningrad, Russia
Rosenhain studied at the University of Königsberg where he was taught by Carl Jacobi and Julius Richelot. He was awarded a doctorate by Königsberg for his thesis. In his thesis, which he wrote with Jacobi as his thesis advisor, he examined periodic functions in two variables.
University of Königsberg, Kaliningrad, Russia
Rosenhain studied at the University of Königsberg where he was taught by Carl Jacobi and Julius Richelot. He was awarded a doctorate by Königsberg for his thesis. In his thesis, which he wrote with Jacobi as his thesis advisor, he examined periodic functions in two variables.
https://www.amazon.com/Memoire-Fonctions-Variables-Quatre-Periodes/dp/1169701248/ref=sr_1_1?keywords=Sur+les+Fonctions+de+Deux+Variables+et+%C3%A0+Quatre+Periodes%2C+Qui+Sont+les+Inverses+des+Int%C3%A9grales+Ultra-%C3%A9lliptiques+de+la+Premi%C3%A8re+Classe&qid=1578054901&s=books&sr=1-1
1850
https://www.amazon.com/Abhandlung-Functionen-Zweier-Variabler-Perioden/dp/0270997466/ref=sr_1_3?qid=1578054940&refinements=p_27%3AGeorg+Rosenhain&s=books&sr=1-3&text=Georg+Rosenhain
1895
Johann Georg Rosenhain was born on June 10, 1816, in Konigsberg, Prussia. His parents were Nathan Rosenhain and Röschen Joseph.
Rosenhain studied at Friedrich College in Konigsberg, then at the University of Königsberg where he was taught by Carl Jacobi and Julius Richelot. He was close to Jacobi and was inspired by him to undertake mathematical research into topics that interested Jacobi. While he was still a student he attended Jacobi's lectures and he edited them for publication. This was an outstanding start to his career and over the next few years, he was exceptionally successful. He was awarded a doctorate by Königsberg for his thesis. In his thesis, which he wrote with Jacobi as his thesis advisor, he examined periodic functions in two variables.
In 1844 Rosenhain qualified as a lecturer at the University of Breslau and remained there as a Privatdozent until 1848. His participation in the revolutionary activities of 1848 deprived him of any chance to further his career at Breslau. He, therefore, qualified as a lecturer again in 1851, this time at the University of Vienna. In 1857 he returned to Königsberg, where he was an associate professor until a year before his death.
While studying at Königsberg, Rosenhain was especially close to Jacobi; and while still a student in the 1830’s he edited some of Jacobi’s lectures. His own scientific activity was mainly inspired by Jacobi, who had enriched the theory of elliptic functions with many new concepts and had formulated, on the basis of Abel’s theorem, the inverse problem, named for him, for an Abelian integral on a curve of the arbitrary genus p. The next step was to solve this problem for p = 2.
In 1846 the Paris Academy had offered a prize for the solution of that problem, and Rosenhain won it in 1851 for his work entitled “Sur les fonctions de deux variables à quatre périodes, qui sont les inverses des intégrales ultra-elliptiques de la première classe.” Göpel had solved this problem at almost the same time, but he did not enter the competition. Rosenhain’s work followed Jacobi even more closely than did Göpel’s.
In his unpublished dissertation, Rosenhain had already treated triple periodic functions in two variables. The solution of the inverse problem for p = 2 presented him with considerable difficulties, as can be seen in his communications to Jacobi published in Crelle’s Journal. It was not until chapter 3 of his prize essay that he introduced, in the same manner as Göpel, the sixteen θ functions in two variables and examined in detail their periodic properties and the algebraic relations.
Most important, Rosenhain demonstrated (in modern terminology) that the squares of the quotients of these sixteen θ functions can be conceived of as functions of the product surface of a hyperelliptic curve of p = 2 with itself. Starting from this point and employing the previously derived addition theorem of the θ quotients, Rosenhain succeeded in demonstrating more simply than Göpel that these quotients solve the inverse problem for p = 2. Rosenhain never fulfilled the expectations held for him in his younger years and published nothing after his prize essay.
It was not only as a mathematician that Rosenhain was extremely gifted for he was also gifted in languages and music.