He entered the University of Halle in the spring of 1862 and there he studied mathematics and physics. At Halle he was taught mathematics by Eduard Heine, August Rosenberger and Carl Neumann, and physics by H Knobloch. From Halle Wangerin moved to the University of Königsberg in 1864 where he undertook research under Franz Neumann's supervision. He was awarded his doctorate on 16 March 1866 for his thesis De annulis Newtonianis Ⓣ. It is clear, both from Wangerin's subsequent career, and from his writings, that he was greatly influenced by Neumann. Wangerin went on to undertake research for the rest of his life on topics suggested by Neumann. Also Wangerin :-
... later wrote a book (1907) and a highly appreciative article on his former teacher.In fact the book was entitled Franz Neumann und sein Wirken als Forscher und Lehrer Ⓣ while Wangerin actually published three articles on his former teacher, one in Jahresberichte der Deutschen Mathematiker vereinigung (1894-95), one in Leopoldina (1896), and the article Franz Neumann als Mathematiker in Zeitschrift für Physik (1910).
Although Jacobi had died over ten years before Wangerin began his studies at Königsberg, his influence was still strongly felt and it would not be unreasonable to say that Wangerin, through his teachers at Königsberg, was strongly influenced by Jacobi's style of mathematics. After he was awarded his doctorate, he took the examinations to become a school teacher and trained at the Friedrichswerdersche Gymnasium in Berlin during the year 1866-67. He then taught for a year at another Berlin school, later named the Andreasrealgymnasium. He was appointed as a teacher of mathematics in a Gymnasium in Posen on 1 October 1868. Wangerin moved from Posen back to Berlin where again he taught mathematics in a Gymnasium from 1 April 1869 until 31 March 1876.
In addition to his teaching activities, Wangerin also took on the role of coeditor of the yearbook Jahrbuchs über die Fortschritte der Mathematik Ⓣ in 1869. He held this editorial role up to 1878, but he also had an advisory role which he continued until 1924. Wangerin married Johanna Thorn on 14 April 1871; they had five children, three sons and two daughters. Their first son Ernst (born 6 May 1872) went on to obtain a doctorate in history, a second son Albert (born 19 June 1873) went on to obtain a doctorate in chemistry, a daughter Ella (born 21 September 1874) became a piano teacher, a daughter Kaethe (born 5 August 1878) became a draftswoman, and a son Walter (born 15 April 1884) became a professor of plant ecology at the Technische Hochschule in Danzig.
In the spring of 1876 Wangerin was appointed as an extraordinary professor at the University of Berlin. His appointment was specifically to teach first year undergraduates, for neither Kronecker nor Weierstrass lectured at this level. Wangerin remained in Berlin until 1882 when he was offered the position of ordinary professor at the University of Halle-Wittenberg. The chair had fallen vacant when Heine died in October 1881, and Wangerin was appointed to succeed his former teacher.
Back in the university in which he had studied as an undergraduate, Wangerin held his professorship there until he retired in 1919. His most prestigious position he held during this period was rector of the university for the academic year 1910-11. He continued to live in Halle after his retirement and was active in mathematical research almost until his death at the age almost 89.
Wangerin's research was on potential theory, spherical functions and differential geometry. A major work was Reduction der Potentialgleichung für gewisse Rotationskörper auf eine gewöhnliche Differentialgleichung Ⓣ published in 1875. He wrote an important two volume treatise on potential theory and spherical functions Theorie des Potentials und der Kugelfunktionen Ⓣ (1909, 1921). Despite great expertise in applications to mathematical physics, research was not the most important of Wangerin's contributions to the development of mathematics. Wangerin's main contribution was his writing of textbooks, writing for encyclopaedias and his historical writings. As examples of Wangerin's historical writing, in addition to the articles on his teacher Franz Neumann which we mentioned above, we should point in particular to the article he wrote on Eduard Heine in 1928 as well as to his input to editing the works of Gauss, Euler, Lambert, and Lagrange. His two major encyclopaedia articles were both written for Encyklopädie der mathematischen Wissenschaften Ⓣ, the first in 1904 being Theorie der Kugelfunktionen und der verwandten Funktionen, insbesondere der Laméschen und Besselschen (Theorie spezieller, durch lineare Differentialgleichungen definierter Funktionen) Ⓣ on functions such as the Lamé and Bessel functions, while his second written in 1909 was Optik ältere Theorie an erticle on optics for the physics volume of the encyclopaedia.
He also played a major role in the reviewing of mathematical papers. We mentioned above that he was coeditor of Fortschritte der Mathematik from 1869 to 1921 and in this role he had a major influence in the policy of the only reviewing journal for mathematics that there was at the time. His influence as a teacher was also strongly felt :-
While at Berlin he directed his lectures to a fairly broad audience, and even at Halle he continued to be greatly interested in the training of high school teachers.He taught many courses at the University of Halle including: linear partial differential equations; calculus of variations; theory of elliptical functions; synthetic geometry; hydrostatics and capillarity theory; theory of space curves and surfaces; analytic mechanics; potential theory and spherical harmonics; celestial mechanics; the theory of the map projections; hydrodynamics; and the partial differential equations of mathematical physics.
Wangerin was honoured with election to the German Academy of Scientists Leopoldina in 1883. He served as President of the Academy from 1906 until he resigned in 1921. He received an honorary degree from the University of Upsala in Sweden in 1907, and several medals, including the Cothenius medal from the German Academy of Scientists Leopoldina in 1922.
Article by: J J O'Connor and E F Robertson