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Carathéodory, considered to be the greatest modern Greek mathematician, made significant contributions to the calculus of variations, the theory of point set measure, and the theory of functions of a real variable.Carathéodory entered the University of Berlin in May 1900 where Frobenius and Schwarz were professors. He attended Frobenius's lectures but benefited most from a twice monthly colloquium run by Schwarz who was lecturing on his collected works. He also became close friends with Fejér while at Berlin.
Carathéodory received his Ph.D. in 1904 from the University of Göttingen, where he worked under Hermann Minkowski. After lecturing in Hanover, Breslau, Göttingen and Berlin, at the request of the Greek government, he took up a post at the University of Smyrna.
The Turks attacked Smyrna in 1922 and Carathéodory was able to save the university library which he moved to Athens. He taught at Athens at the university and technical school until 1924 when he moved to Munich where he remained for the rest of his academic career.
Carathéodory made significant contributions to the calculus of variations, the theory of point set measure, and the theory of functions of a real variable. He added important results to the relationship between first order partial differential equations and the calculus of variations.
He contributed important results to the theory of functions of several variables. He examined conformal representations of simply connected regions and he developed a theory of boundary correspondence. He wrote many fine books including Funktionentheorie , a 2 volume work published in 1950.
Carathéodory also made contributions in thermodynamics, the special theory of relativity, and geometrical optics.
References (6 books/articles)
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