**Constantin Carathéodory**'s father, Stephanos Carathéodory, was an Ottoman Greek who had studied law in Berlin and then served as secretary in the Ottoman embassies in Berlin, Stockholm and Vienna. Stephanos had married Despina Petrocochino, who came from a Greek family of businessmen who had settled in Marseille. At the time of Constantin's birth, the family were in Berlin since Stephanos had been appointed there two years earlier as First Secretary to the Ottoman Legation.

The Carathéodory family spent 1874-75 in Constantinople, where Constantin's paternal grandfather lived, while Stephanos was on leave. Then in 1875 they went to Brussels when Stephanos was appointed there as Ottoman Ambassador. In Brussels, Constantin's younger sister Loulia was born. The year 1895 was a tragic one for the family since Constantin's paternal grandfather died in that year, but much more tragically, Constantin's mother Despina died of pneumonia in Cannes. Constantin's maternal grandmother took on the task of bringing up Constantin and Loulia in his father's home in Belgium. They employed a German maid who taught the children to speak German. Constantin was already bilingual in French and Greek by this time.

Constantin began his formal schooling at a private school in Vanderstock in 1881. He left after two years and then spent time with his father on a visit to Berlin, and also spent the winters of 1883-84 and 1884-85 on the Italian Riviera. Back in Brussels in 1885 he attended a grammar school for a year where he first began to become interested in mathematics. In 1886 he entered the high school Athénée Royal d'Ixelles and studied there until his graduation in 1891. Twice during his time at this school Constantin won a prize as the best mathematics student in Belgium.

At this stage Carathéodory began training as a military engineer. He attended the École Militaire de Belgique from October 1891 to May 1895 and he also studied at the É d'Application from 1893 to 1896. In 1897 a war broke out between Turkey and Greece. This put Carathéodory in a difficult position since he sided with the Greeks, yet his father served the government of the Ottoman Empire. Since he was a trained engineer he was offered a job in the British colonial service. This job took him to Egypt where he worked on the construction of the Assiut dam until April 1900. During periods when construction work had to stop due to floods, he studied mathematics from some textbooks he had with him, such as Jordan's *Cours d'Analyse* and Salmon's text on the analytic geometry of conic sections. He also visited the Cheops pyramid and made measurements which he wrote up and published in 1901. He also published a book *Egypt* in the same year which contained a wealth of information on the history and geography of the country.

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. After hearing excellent reports of mathematics research at Göttingen, he decided to continue his studies there and enrolled for the summer semester of 1902. Carathéodory was indeed impressed with Göttingen, describing it as the [3]:-

... seat of an international congress of mathematicians permanently in session.

He worked on the calculus of variations and was much influenced by both Hilbert and Klein. He received his doctorate in 1904 from Göttingen University for his thesis *Über die diskontinuierlichen Lösungen in der Variationsrechnung* which he submitted to Hermann Minkowski. His oral examination was held on 13 July when he was also examined in his subsidiary subjects of applied mathematics and astronomy by Klein and Schwarzschild. He remained at Göttingen to write his habilitation thesis *Über die starken Maxima und Minima bei einfachen Integralen* which he submitted on 5 March 1905. He then lectured as a Privatdozent at Göttingen until 1908.

Carathéodory had spent time in Brussels with his father Stephanos over the summer of 1907. After a few months of deteriorating health Stephanos died in late 1907. Study, at Bonn, had proposed Carathéodory as Furtwängler's successor and, after serious thought as to whether he should leave Göttingen, Carathéodory went to Bonn where he became a Provatdozent on 1 April 1908. At Bonn he collaborated with Study on isoperimetric problems. On 5 February 1909 he married Euphrosyne Carathéodory in Constantinople. In marrying Euphrosyne, who was his aunt and eleven years his junior, Carathéodory was following a family tradition of marrying close relatives.

After a year at Bonn, Carathéodory was appointed as Professor of higher Mathematics at the Technical University of Hanover, so becoming Stäckel's successor. Again it was not long before he moved on and on 1 October 1910 he was appointed to the Chair of Higher Mathematics at the Technical University of Breslau. This time he held the chair for two and a half years before being appointed professor at Göttingen from 1 April 1913. The years of World War I were difficult ones for Carathéodory and his family. Most of his colleagues and students served in the military and he was isolated in Göttingen. The famine of 1917 hit hard but Carathéodory continued to give lecture courses at the university.

After five years Göttingen he was appointed to the University of Berlin in 1918 but after he had been there for a year, at the request of the Greek government, he ended his contract with Berlin on 31 December 1919 and travelled to Greece to undertake a new venture. By this time Constantin and Euphrosyne had two children, Stephanos born in Hanover on 7 November 1909 and Despina born on 13 October 1912. Carathéodory had also accepted editorial positions on the boards of two major mathematics journals, the *Rendiconti del Circolo Matematico di Palermo* from 1909 and the *Mathematische Annalen* from 1914.

The Greek government had asked Carathéodory to establish a second university in Smyrna. However, he also required a university post so he was appointed as Professor of Analytical and Higher Geometry at the University of Athens on 2 June 1920. On 14 July the Greek government published a bill setting up a Greek University in Smyrna and soon others were appointed at assist Carathéodory. On 28 July Carathéodory was officially appointed as organiser of the Ionian University in Smyrna and also Professor of Mathematics at the new university. In the second half of 1921 he travelled widely through Europe purchasing books and equipment for the new university. The Turks attacked Smyrna in September 1922 and so the planned opening of the university in October of that year became impossible. Carathéodory was able to save the university library, which he had worked so hard to establish, and most of the equipment which he had been purchased for the science departments, and escaped to Athens on a Greek battleship. He taught at Athens at the National University and the National Technical University until 1924 when he moved to Munich to fill the chair left vacant when Lindemann retired.

In 1928 Carathéodory became the first visiting lecturer of the American Mathematical Society. He sailed to the United States with his wife in January and after a lecture tour and time spent as a visiting professor at Harvard, returned to Munich in September. In the following year he received an offer of a post from Stanford university and was in fact appointed there in September 1929. However, he seems to have only been using this offer as a means of getting better salary and conditions from Munich, which indeed he managed to do.

On 30 January 1933 the National Socialist party led by Hitler came to power in Germany [3]:-

Carathéodory could hardly conceive how this could happen in a country with the cultural traditions of Germany. He initially tended to view the Hitler regime with a somewhat overconfident contempt, whereas later, when Hitler gained absolute power, he was incapable of resistance. His behaviour in the Nazi era was, in fact, identical with that of the ... educated bourgeois who, despite their humanistic background, in their overwhelming majority abstained from any opposition against Hitler's dictatorship, and especially Hitler's war, and thus dramatically failed to exercise their historic responsibility towards both Germany and humanity as a whole.

Carathéodory continued to hold his position in Munich until he retired in August 1938. However he certainly undertook many duties which took him to other places. In particular he continued to work on reorganising the Greek universities, particularly during 1930-32, with the aim of integrating Greece academically into Europe. In 1936-37 he made another visit to the United States, giving a lecture at the American Mathematical Society meeting to commemorate the tercentenary of Harvard University on 31 August 1936, then spending the winter semester at the University of Wisconsin as Carl Schurz Memorial Professor.

The World War II was a difficult time for Carathéodory. Georgiadou writes [3]:-

... during World War II he took part in the procedures of the Bavarian Academy of Sciences. He did not get involved in the movement for national socialism, but he did have connections with Nazi party members[particularly Hasse, Blaschke and Süss]. He never openly mentioned the holocaust or the Nazi crimes against Greece. ... kept silent in the face of crimes that violated any idea of human decency, accepted the authority of an illegal state, made his compromises and submitted to the expulsion of Jews from scientific institutions ... However, he took great pains to re-establish mathematics as an academic discipline in Germany after the war and thus to contribute to the reintegration of this country into the community of civilised nations.

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 also made contributions in thermodynamics, the special theory of relativity, mechanics, and geometrical optics.

Carathéodory wrote many fine books including *Lectures on Real Functions* (1918), *Conformal representation* (1932), *Calculus of Variations and Partial Differential Equations* (1935), *Geometric Optics* (1937), *Real functions Vol. 1: Numbers, Point sets, Functions* (1939), and *Funktionentheorie,* a 2 volume work published in 1950.

One might wonder why there is no *Real functions Vol. 2* in this list. In fact Carathéodory did write the second volume of this work but it was destroyed while at the publisher Teubner during the bombing of Leipzig in 1943.

Perron, writing in 1952, remarks that Carathéodory [8]:-

... had not published many of his ideas; they result in others works, especially in those of the numerous students who were introduced by him to the spirit and ways of scientific research and who partly themselves occupy university chairs today.

He supervised two doctoral students at Göttingen (Hans Rademacher and Paul Finsler), one at Berlin, and 17 at Munich.

**Article by:** *J J O'Connor* and *E F Robertson*

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