Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Herman Schwarz worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem from the calculus of variations, namely surfaces of least area.
Schwarz studied chemistry at Berlin but Kummer and Weierstrass influenced him to change to mathematics. Schwarz attended Weierstrass's lectures on The integral calculus in 1861 and the notes that Schwarz took at these lectures still exists.
Schwarz received his doctorate in 1864 and was appointed to the University of Halle in 1867. In 1869 he was appointed to a chair at Zurich and in 1875 to chair at Göttingen. Schwarz succeeded Weierstrass at Berlin in 1892 teaching there until 1917.
Schwarz had interests outside mathematics, although his marriage was a mathematical one since he married Kummer's daughter. Outside mathematics he was the captain of the local Voluntary Fire Brigade and, more surprisingly, he assisted the stationmaster at the local railway station by closing the doors of the trains.
Schwarz worked on conformal mappings of polyhedral surfaces onto the spherical surface. His alternative procedure for solving the Dirichlet problem soon became a standard technique. He also worked on minimal surfaces (surfaces of least area), a characteristic problem of the calculus of variations.
His most important work is a Festschrift for Weierstrass's 70th birthday. Schwarz answered the question of whether a given minimal surface really yields a minimal area. The ideas in this work led Émile Picard to his existence proof for solutions of differential equations. It also contains the inequality for integrals now known as the 'Schwarz inequality'.
References elsewhere in this archive:
Tell me about Schwarz's work on set theory
References:
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page History Topics Index Famous curves index Chronologies Birthplace Map Mathematicians of the day Anniversaries for the year Search Form Simple Search Form Search Suggestions