H. A. Schwarz
| Hermann Schwarz | |
|---|---|
Karl Hermann Amandus Schwarz
|
|
| Born |
25 January 1843 Hermsdorf, Silesia, Prussia |
| Died | 30 November 1921 (aged 78) Berlin, Germany |
| Residence | Germany, Switzerland |
| Nationality | Prussian |
| Fields | Mathematician |
| Institutions |
University of Halle Swiss Federal Polytechnic Göttingen University |
| Alma mater | Gewerbeinstitut |
| Doctoral advisor |
Karl Weierstrass Ernst Kummer |
| Doctoral students |
Friedrich Busse Lipót Fejér Richard Fuchs Otto Fulst Harris Hancock Robert Haußner Viktor Henry Gerhard Hessenberg Heinrich Karstens Paul Koebe Leon Lichtenstein Heinrich Maschke Hans Meyer Chaim Müntz Robert Remak Carl Schilling Friedrich Steinbacher Theodor Vahlen Ernst Wendt Ernst Zermelo |
| Known for | Cauchy–Schwarz inequality |
Karl Hermann Amandus Schwarz (25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
Schwarz was born in Hermsdorf, Silesia (now Jerzmanowa, Poland). He was married to Marie Kummer, who was the daughter to the mathematician Ernst Eduard Kummer and Ottilie née Mendelssohn (a daughter of Nathan Mendelssohn's and granddaughter of Moses Mendelssohn). Schwarz and Kummer had six children.
Schwarz originally studied chemistry in Berlin but Ernst Eduard Kummer and Karl Theodor Wihelm Weierstraß persuaded him to change to mathematics. He received his Ph.D. from the Universität Berlin in 1864 and was advised by Ernst Kummer and Karl 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, dealing with the subjects of complex analysis, differential geometry and the calculus of variations. He died in Berlin.
Schwarz's works include Bestimmung einer speziellen Minimalfläche, which was crowned by the Berlin Academy in 1867 and printed in 1871, and Gesammelte mathematische Abhandlungen (1890).
Among other things, Schwarz improved the proof of the Riemann mapping theorem, 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).
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