Hermann Schwarz  

Karl Hermann Amandus Schwarz  
Born  
Died  30 November 1921  (aged 78)
Residence  Germany, Switzerland 
Nationality  Prussian 
Alma mater  Gewerbeinstitut 
Known for  Cauchy–Schwarz inequality 
Scientific career  
Fields  Mathematician 
Institutions  University of Halle Swiss Federal Polytechnic Göttingen University 
Doctoral advisor  Karl Weierstrass Ernst Kummer 
Doctoral students  Lipót Fejér Harris Hancock Gerhard Hessenberg Paul Koebe Leon Lichtenstein Heinrich Maschke Robert Remak Theodor Vahlen Ernst Zermelo 
Karl Hermann Amandus Schwarz (German: [ˈhɛʁman ˈʃvaʁts]; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
YouTube Encyclopedic

1/3Views:6 08343611 086

✪ Cauchy Schwarz Inequality Proof

✪ Cauchyschwarz3

✪ Cauchy Schwarz Inequality Proof new
Transcription
Contents
Life
Schwarz was born in Hermsdorf, Silesia (now Jerzmanowa, Poland). On 30 June 1912 he married Marie Kummer, who was the daughter to the mathematician Ernst Eduard Kummer^{[1]} and Ottilie née Mendelssohn (a daughter of Nathan Mendelssohn's and granddaughter of Moses Mendelssohn). Schwarz and Kummer had six children, including his daughter Emily Schwarz.^{[1]}
Schwarz originally studied chemistry in Berlin but Ernst Eduard Kummer and Karl Theodor Wihelm Weierstrass persuaded him to change to mathematics.^{[2]} He received his Ph.D. from the Universität Berlin in 1864 and was advised by Ernst Kummer and Karl Weierstraß.^{[3]} Between 1867 and 1869 he worked at the University of Halle, then at the Swiss Federal Polytechnic.^{[4]} From 1875 he worked at Göttingen University,^{[4]} dealing with the subjects of complex analysis, differential geometry and the calculus of variations. He died in Berlin.
Work
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,^{[5]} 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.^{[6]} His work on the latter allowed Émile Picard to show solutions of differential equations exist (the Picard–Lindelöf theorem).^{[2]}
In 1892 he became a member of the Berlin Academy of Science and a professor at the University of Berlin, where his students included Lipót Fejér, Paul Koebe and Ernst Zermelo. In total, he advised 20 Ph.D students.^{[3]}
His name is attached to many ideas in mathematics,^{[1]} including:
 Additive Schwarz method
 Schwarz alternating method
 Schwarzian derivative
 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 map
 Cauchy–Schwarz inequality.
Publications
 Schwarz, H. A. (1871), Bestimmung einer speziellen Minimalfläche, Dümmler
 Schwarz, H. A. (1972) [1890], Gesammelte mathematische Abhandlungen. Band I, II, Bronx, N.Y.: AMS Chelsea Publishing, ISBN 9780828402606, MR 0392470
Notes
 ^ ^{a} ^{b} ^{c} Agarwal, Ravi; Sen, Syamal (20141111). Creators of Mathematical and Computational Sciences. Springer. pp. 297–298. ISBN 9783319108704.
 ^ ^{a} ^{b} O'Connor, J. J.; Robertson, E. F. "Schwarz biography". wwwgap.dcs.stand.ac.uk. The MacTutor History of Mathematics. Retrieved 20160522.
 ^ ^{a} ^{b} "The Mathematics Genealogy Project  Hermann Schwarz". www.genealogy.math.ndsu.nodak.edu. Retrieved 20160522.
 ^ ^{a} ^{b} Chang, Sooyoung (20110101). Academic Genealogy of Mathematicians. World Scientific. pp. 77–78. ISBN 9789814282291.
 ^ Bottazzini, Umberto (20030430). "Algebraic truths vs geometric fantasies: Weierstrass' Response to Riemann". arXiv:math/0305022.
 ^ Schwarz, Hermann Amandus (1884). "Proof of the theorem that the ball has less surface area than any other body of the same volume". News of the Royal Society of Sciences and the GeorgAugustUniversität Göttingen. 1884: 1–13.
External links
Wikimedia Commons has media related to Hermann Schwarz. 
 O'Connor, John J.; Robertson, Edmund F., "Hermann Schwarz", MacTutor History of Mathematics archive, University of St Andrews.
 Hermann Schwarz at the Mathematics Genealogy Project