Constantin Carathéodory

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Constantin Carathéodory (ca.1920)

Constantin Carathéodory ( Greek Κωνσταντίνος Καραθεοδωρή Konstantínos Karatheodorí ; born September 13, 1873 in Berlin ; † February 2, 1950 in Munich ) was a mathematician of Greek origin. In the literature, the surname is also found as Karatheodori , Caratheodory or Carathéodori .


Carathéodory was born the son of Stephanos Carathéodory, a Greek diplomat in the service of the Ottoman Empire . The Carathéodory family has a long diplomatic tradition and several family members have held important government posts in Constantinople . A great uncle, Alexander Carathéodory Pascha , who was also the father of his wife Euphrosyne, had represented the High Porte at the Berlin Congress in 1878 as Foreign Minister . The family originally comes from the village of Vosnochori (Βοσνοχώρι) today Nea Vyssa (Νέα Βύσσα) near Orestiada .

Carathéodory grew up in Brussels , where his father was ambassador from 1875. Already in his youth, his mathematical talent became evident and he won various school awards. Twice he won first prize in mathematics at the Concours généreaux of all high schools in the country. In 1891 he passed the Belgian Abitur and entered the École Militaire de Belgique in Brussels as élève étranger . He completed his engineering studies at this cadet school after four years.

As a civil engineer with officer rank, he went to Mytilene (Lesbos) in the Ottoman Empire in 1895 to help build the road network there. The Greco-Turkish War of 1896/97 prevented further construction projects . Carathéodory went to London to work a little later for a British company on the Suez Canal . In Assiout he worked for two years as an assistant engineer for the Nile regulation. In his free time he was engaged in mathematics and studied the works of Jordan . He took measurements in the entrance of the Great Pyramid of Cheops , which he also published. Here, to the great surprise of his family, he made the decision to focus exclusively on mathematics in the future.

Carathéodory attended the universities of Berlin (1900–1901) and Göttingen (1902–1904). For his doctorate at the University of Göttingen , which at that time enjoyed an excellent reputation worldwide for its outstanding mathematicians, he chose the topic of Discontinuous Solutions in the Calculus of Variations . In Göttingen talent Carathéodory was recognized and even the day before the viva joined Felix Klein at him with the proposal approach, to habilitate in Göttingen. He obtained his doctorate on October 1, 1904. His doctoral supervisor was Hermann Minkowski . In March of the following year he received the venia legendi , the license to teach. His habilitation thesis was submitted without notice. He worked as a private lecturer in Göttingen for three years. In 1908 he moved to Bonn , a year later, in 1909, he became a full professor at the Technical University of Hanover . The following year he was appointed to the newly founded Technical University of Wroclaw . In 1913 he returned to Göttingen to succeed Felix Klein. In 1918 he followed the call to Berlin. Together with Albert Einstein he was accepted into the Prussian Academy of Sciences in 1919 . When Carathéodory was admitted, none other than Max Planck gave the laudatory speech. In the same year he was elected a corresponding member of the Göttingen Academy of Sciences .


In 1920 he received the call of the University of Smyrna , today's Izmir , which appointed him president. He made a significant contribution to its construction, but his work ended in ruin when the Turks invaded in 1922 . Carathéodory was able to get his family - wife, son and daughter - to safety on the island of Samos in time to return to Smyrna alone. There he organized the rescue of valuable documents from the university, which he had transported to Greece on boats. Afterwards Carathéodory found refuge with his family in Athens . He taught here until 1924.

In 1924 he succeeded Ferdinand Lindemann at the University of Munich . In 1925 he was elected as a full member of the math and science class of the Bavarian Academy of Sciences . Alfred Pringsheim co-signed the application for his admission . In 1927, Carathéodory was a co-signer of the application of this class, Albert Einstein, with whom he used regular letter contact, to be accepted as a corresponding member. At the academy, Carathéodory was jointly responsible for the publication of the works of Johannes Kepler . He and his colleagues Oskar Perron and Heinrich Tietze were referred to as the “Munich triad of mathematics”.

In 1928 Carathéodory stayed for a long time in the United States . He has given guest lectures at the University of Pennsylvania , Harvard , Princeton , as well as the University of Texas at Austin and the University of Texas at San Antonio .

In 1930 the Greek government asked him to organize the reorganization of the Universities of Athens and Thessaloniki. Carathéodory accepted this request, although colleagues from Munich such as Arnold Sommerfeld tried to persuade him to stay. During this time he also wrote a contribution on mathematics for the great Greek encyclopedia. On the Acropolis he examined the Parthenon . After completing this assignment, he will return to Munich. In 1938 he retired . He spent the time of National Socialism withdrawn as the Church Council of the Greek Church to the Redeemer at Salvatorplatz in Munich , where he held a lecture on potential theory after a one-year break. In the summer of 1946, after a serious illness, he gave his first lecture at the Mathematical Colloquium in Munich on the subject of "About length and surface". At the end of January 1950, his health deteriorated again. He died on February 2nd of his ailment. Carathéodory is buried in the Munich forest cemetery. His wife Euphrosyne had already died on July 29, 1947.


Carathéodory was heavily influenced by David Hilbert . He provided fundamental results in many areas of mathematics, especially in the theory of partial differential equations , function theory (Carathéodory's metric) and measure and integration theory.

His contributions to the calculus of variations , function theory, geometric optics , thermodynamics and theoretical physics influenced many well-known mathematicians. From the correspondence with Albert Einstein it emerges that Carathéodory was able to give him important mathematical explanations for his foundation of the theory of relativity . The new field concept that Carathéodory introduced into the calculus of variations was to have great consequences. Carathéodory derived an inequality from this that 20 years later caused a sensation in the mathematical world under other names as Bellman's equation or inequality and became the basis for the principle of dynamic optimization , and since then has radiated far beyond mathematics.

His investigations into simple integrals in the calculus of variations were not limited to the plane, but he developed them further for space. He also worked on variational problems of multiple integrals. As a member of the academy, he also devoted several treatises to optics, mechanics and planetary motion. However, thermodynamics took a special place. His 1909 publication in this area ( “First axiomatically strict justification of thermodynamics” ) received great attention from Planck and Max Born .

In the theory of functions , Carathéodory's theorem is his result, proven in 1913, that a conformal mapping of the unit disk onto an area bounded by a Jordan curve has a continuous, bijective continuation to the edge of the unit circle. Furthermore, his result, found in 1912, is named after him, that the locally uniform convergence of a sequence of conformal images of the unit disk corresponds to the core convergence of the image areas. In differential geometry , Carathéodory's conjecture is ascribed to him, which postulates the existence of at least two umbilical points on every smooth, closed and convex surface (the conjecture is open).

In 1926 he provided the general proof that no system of lenses and mirrors without optical aberrations exists, with the exception of the trivial case for plane mirrors. In 1940, together with Bernhard Schmidt, he published a theory of a mirror telescope on the theory of the Schmidt telescope , the first copy of which he had built in Hamburg-Bergedorf . B. followed on Mount Palomar . In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (On the analytical mapping through functions of several variables).

He discovered various other mathematical theorems, including the maximum principle . The Carathéodory's extension theorem is still the subject of numerous mathematical investigations.

In 2002, in recognition of its achievements, the Ludwig Maximilians University of Munich named one of the largest lecture halls of the Mathematical Institute the Constantin Carathéodory Lecture Hall at a ceremony . His daughter Despina Rodopoulou-Carathéodory was among the guests.

Carathéodory enjoyed high esteem far beyond his field because of his extraordinary analytical mind and his professional competence, but also because of his personal integrity. In addition to his numerous merits in mathematics , Carathéodory is also known for his extraordinary talent for languages. His mother tongues were Greek and French. In addition, he published most of his work in German and was fluent in English, Italian and Turkish.


  • Collected Mathematical Writings. Beck, Munich 1956, 1957, 5 volumes
  • Calculus of Variations and First Order Partial Differential Equations. 2nd Edition. Teubner, 1956. (English translation Calculus of variations and partial differential equations of first order. American Mathematical Society 1999)
  • Function theory. 2 volumes. 2nd Edition. Birkhäuser, 1961. (English translation Theory of functions of a complex variable. 2 volumes. Chelsea Publ., 1954)
  • Measure and integral and their algebraization. Birkhäuser, 1956. (English translation: Algebraic theory of measure and integration. Chelsea 1963)
  • Conformal representations. Cambridge University Press, 1969.
  • Geometric optics. Springer, 1937.
  • Lectures on real functions. 2nd Edition. Teubner, 1927. (first 1918, reprint Chelsea 1948)
  • About the discontinuous solutions in the calculus of variations. Dissertation . Goettingen 1904.
  • Studies on the fundamentals of thermodynamics. In: Mathematical Annals. Volume 67, 1909, pp. 355-386. (Göttingen digitization center)
  • About a generalization of Picard's theorems. In: Meeting reports of the Prussian Academy of Sciences, Math.-Physics. Class. Berlin 1920, pp. 202-209. (and Collected Math. Writings, Volume 3, p. 45)
  • Over the range of variability of the coefficients of power series that do not take on given values. In: Mathematical Annals. Volume 64, 1907, pp. 95-115.
  • Over the range of variability of Fourier's constants of positive harmonic functions. In: RCMP (Rendiconti del Circolo Matematico di Palermo). Volume 32, 1911, pp. 193-217.

See also


  • Roland Z. Bulirsch : Greece in Munich. Constantin Carathéodory civil engineer and mathematician. (PDF; 1.7 MB). Lecture at the Bavarian Academy of Sciences on June 28, 2007. In: DMV Mitteilungen. 1999, No. 1, p. 4.
  • Maria Georgiadou: Constantin Carathéodory. Mathematics and Politics in Turbulent Times. Springer Verlag, 2004, ISBN 3-540-20352-4 .
  • Maria Georgiadou: Expert knowledge between tradition and reform. The Carathéodorys: a Neo-Phanariot Family in 19th Century Constantinople. In: Méropi Anastassiadou-Dumont (ed.): Médecins et ingénieurs ottomans à l'âge des nationalismes. Maisonneuve et Larose, Paris 2003, ISBN 2-7068-1762-6 , pp. 243-294 (English).
  • Ulf Hashagen: A foreign mathematician in the Nazi state: Constantin Carathéodory as a professor at the University of Munich. Munich: Deutsches Museum, 2010 (preprint; 1).
  • Ulf Hashagen: A Greek mathematician as a Bavarian professor in the Third Reich: Constantin Carathéodory (1873–1950) in Munich. In: Dieter Hoffmann and Mark Walker (eds.): "Foreign" scientists in the Third Reich: the Debye affair in context. Wallstein, 2011, pp. 151-181.
  • Monika Stoermer: Albert Einstein and the Bavarian Academy of Sciences. ( Memento from December 11, 2007 in the Internet Archive ) (PDF; 260 kB) In: Akademie Aktuell. 01/05.
  • Heinrich Tietze: In memory of C. Carathéodory. Obituary presented at the meeting of the mathematical and natural science class of the Bavarian Academy of Sciences on June 9, 1950, published in the 1950 yearbook of the BAdW, p. 85 ff.
  • Takis Chr. Tsonidis: The Caratheodory Family. Nea Orestias, Thessaloniki 1989, pp. 306-344.
  • Hermann Boerner : Carathéodory's input to the calculus of variations. In: Annual report DMV. 1953. online .
  • Heinrich Behnke : Constantin Caratheodory. In: Annual report DMV. Volume 75, 1974, pp. 151-165. online .

Web links

Commons : Constantin Caratheodory  - collection of images, videos and audio files

Individual evidence

  1. Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 56.
  2. Carathéodory's grave in the Munich forest cemetery (Grabfeld 303, location , pictures )
  3. C. Carathéodory: About the mutual relationship of the edges in the conformal mapping of the interior of a Jordan curve onto a circle. In: Mathematical Annals. Volume 73, 1913, pp. 305-320.
  4. C. Carathéodory: Investigations into the conformal mapping of fixed and changeable areas. In: Mathematical Annals. Volume 72, 1912, pp. 107-144.
  5. Constantin Carathéodory-Hörsaal (PDF; 1.8 MB), mathe-lmu, No. 7/2002, publisher. Friends of Mathematics in Business, University and School at the Ludwig-Maximilians-Universität München eV, p. 9.