Karl Weierstrass | Weierstrass theorem | Weierstrass–Erdmann condition | Lindemann–Weierstrass theorem |
Other valuable treatises and memoirs have been written by Strauch (1849), Jellett (1850), Otto Hesse (1857), Alfred Clebsch (1858), and Carll (1885), but perhaps the most important work of the century is that of Weierstrass.
Cantor biographer Joseph Dauben argues that "local circumstances" refers to the influence of Leopold Kronecker, Weierstrass' colleague at the University of Berlin.
After qualifying as a teacher of mathematics and physics Vályi was awarded a scholarship to allow him to study for two years at the University of Berlin, where the remarkable mathematics team of Kummer, Borchardt, Weierstrass and Kronecker were lecturing.
He also helped devise the Weierstrass–Erdmann condition, which gives sufficient conditions for an extremal to have a corner along a given extrema, and allows one to find a minimizing curve for a given integral.
After Weierstrass and Runge, many mathematicians (in particular Walsh, Keldysh, and Lavrentyev) had been working on the same problem.
Under the influence of Weierstrass and Bernhard Riemann this concept and related questions were intensely studied at the end of the 19th century by Hermann Hankel, Paul du Bois-Reymond, Ulisse Dini, Cesare Arzelà and others.