Weierstrass and some members of his circle: Kovalevskaia, Fuchs, Schwarz, Schottky

Abstract

Karl Weierstrass (1815-1897) belongs to the outstanding mathematicians who have worked in Berlin. After 13 years as a Gymnasium teacher at remote locations in Prussia far away from the centers of mathematical research, Weierstrass came to Berlin in 1856 at the age of 41 (as professor extraordinarius; he was promoted to Ordinarius in 1864). This advancement in his career came after he solved one of the era’s challenging problems: the Jacobi inversion problem for hyperelliptic integrals, first formulated in 1832. Weierstrass published a preliminary version of his solution in 1854 in Crelle’s Journal,and his results served as the starting point for the emergence of the theory of Abelian functions. Weierstrass’s paper created a sensation, and from one day to the next his name became well known in mathematical circles. The aged A. von Humboldt (1769-1859) along with E. E. Kummer (1810-1893) emphatically supported his appointment, and in the years that followed he became one of the leading mathematicians of his time. Together with his colleagues Kummer and L. Kronecker (1823-1891), Weierstrass ensured Berlin’s reputation as a world-class mathematical center in the second half of the 19th century.