Hermann Schwarz

Karl Hermann Amandus Schwarz (; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.

Life Schwarz was born in Hermsdorf, Silesia (now Sobieszów, Poland). In 1868 he married Marie Kummer, who was the daughter to the mathematician Ernst Eduard Kummer and Ottilie née Mendelssohn (a daughter of Nathan Mendelssohn and granddaughter of Moses Mendelssohn). Schwarz and Kummer had six children, including his daughter Emily Schwarz. He received his Ph.D. from the Universität Berlin in 1864 and was advised by Kummer and Weierstrass. Between 1867 and 1869 he worked at the University of Halle, then at the Swiss Federal Polytechnic. From 1875 he worked at Göttingen University, developed a special case of the Cauchy–Schwarz inequality, and gave a proof that the ball has less surface area than any other body of equal volume. His work on the latter allowed Émile Picard to show solutions of differential equations exist (the Picard–Lindelöf theorem).

His name is attached to many ideas in mathematics, including the following:

Abstract additive Schwarz method Additive Schwarz method Schwarz alternating method

Schwarzian derivative Schwarz function Schwarz lantern Schwarz lemma Schwarz's list Schwarz minimal surface Schwarz theorem (also known as Clairaut's theorem) Schwarz integral formula Schwarz–Christoffel mapping Schwarz–Ahlfors–Pick theorem Schwarz reflection principle Schwarz triangle Schwarz triangle function Cauchy–Schwarz inequality Theorem of Pohlke and Schwarz

Publications