Constantin Carathéodory

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Constantin Carathéodory
Constantin Carathéodory
Born	September 13, 1873(1873-09-13) Berlin, Germany
Died	February 2, 1950 (aged 76)
Nationality	Greek
Fields	Mathematics
Alma mater	University of Berlin University of Göttingen
Doctoral advisor	Hermann Minkowski
Known for	Carathéodory theorems Carathéodory conjecture

Constantin Carathéodory (or Constantine Karatheodori) (Greek: Κωνσταντίνος Καραθεοδωρή) (September 13, 1873 – February 2, 1950) was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory. His work also includes important results in conformal representations and in the theory of boundary correspondence. In 1909, Carathéodory pioneered the Axiomatic Formulation of Thermodynamics along a purely geometrical approach.

Contents 1 Origins 2 Studies 3 Works 4 Books 5 The Smyrna years 6 Linguistic talent 7 Legacy 8 Published works 9 See also 10 Notes 11 References 11.1 Books 11.2 Articles (journals) 11.3 Encyclopaedias — reference 11.4 Lectures 12 External links

[edit] Origins

Constantin Carathéodory was born in Berlin to Greek parents and grew up in Brussels, where his father served as the Ottoman ambassador to Belgium. The Carathéodory family was well-established and respected in Constantinople, and its members held many important governmental positions.

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 École 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 on Egypt in the same year which contained a wealth of information on the history and geography of the country.

[edit] Studies

Carathéodory studied engineering in Belgium at the Royal Military Academy, where he was considered a charismatic and brilliant student. In 1900 he entered the University of Berlin. In the years 1902-1904 he completed his graduate studies in the University of Göttingen under the supervision of Hermann Minkowski. During the years 1908-1920 he held various lecturing positions in Bonn, Hannover, Breslau, Göttingen and Berlin.

[edit] Works

He is credited with the theories of outer measure, and prime ends, amongst other mathematical results. He is credited with the authorship of the Carathéodory conjecture claiming that a closed convex surface admits at least two umbilic points. As of 2007, this conjecture remained unproven despite having attracted a large amount of research.

In 1909, Carathéodory published a pioneering work "Investigations on the Foundations of Thermodynamics" (Untersuchungen ueber die Grundlagen der Thermodynamik, Math. Ann., 67 (1909) p. 355-386) in which he formulated the Laws of Thermodynamics axiomatically, using only mechanical concepts and the theory of Pfaff's differential forms. He expressed the Second Law of Thermodynamics via the following Axiom: "In the neighbourhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state." Carathéodory coined the term adiabatic accessibility.^[1] This "first axiomatically rigid foundation of thermodynamics" was acclaimed by Max Planck and Max Born.

[edit] Books

Conformal Representation, London, 1932

Elementare Theorie des Spiegeltelescops von B. Schmidt (Elementary Theory of B. Schmidt's Reflecting Telescope), Leipzig and Berlin, 1940

Functionentheorie , Basel 1950. English translation: Theory of Functions of a Complex Variable, New York, Chelsea Publishing Company, 1954

Geometrische Optik, Berlin, 1937

Mass und Integral and Ihre Algebraisierung, Basel 1956. English translation, Measure and Integral and their Algebraisation, New York, Chelsea Publishing Company, 1963

Reelle Funktionen, Leipzig, 1939. English Translation, Real Functions, New York, Chelsea Publishing Company, 1946

Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Leipzig, 1935. English translation, Calculus of Variations and Partial Differential Equations of the First Order, New York, Chelsea Publishing Company, 1965.

Vorlesungen Ueber Reelle Funktionen (Lectures on Real Functions), Leipzig, 1918. American edition, (in German): New York, Chelsea Publishing Company, 1948

All of Caratheodory's books are written in a beautiful and lucid style; they have been studied by generations of mathematicians, and still being studied to great benefit. Carathéodory's books are unusual in the extent to which geometry is used in the exposition.

[edit] The Smyrna years

On 20 October 1919 he submitted a plan for the creation of a new University in Greece, to be named Ionian University. This university never actually admitted students due to the War in Asia Minor in 1922, but the present day University of the Aegean claims to be a continuation of Carathéodory's original plan.^[2]

In 1920 Carathéodory accepted a post in the University of Smyrna, invited by Prime Minister Eleftherios Venizelos. He took a major part in establishing the institution, but his efforts ended in 1922 when the Greek population was expelled from the city during the War in Asia Minor.

Having been forced to move to Athens, Carathéodory brought along with him some of the university library, thus saving it from destruction. He stayed at Athens and taught at the university and technical school until 1924.

In 1924 Carathéodory was appointed professor of mathematics at the University of Munich, and held this position until his death in 1950.

Carathéodory formulated the axiomatic principle of irreversibility in thermodynamics in 1909, stating that inaccessibility of states is related to the existence of entropy, where temperature is the integration function.

In 1926 he gave a strict and general proof, that no system of lenses and mirrors can avoid aberration, except for the trivial case of plane mirrors.

[edit] Linguistic talent

Carathéodory excelled at languages, much like many members of his family did. Greek and French were his first languages, and he mastered German with such perfection, that his writings composed in the German language are stylistic masterworks. Carathéodory also spoke and wrote English, Italian, Turkish, and the ancient languages without any effort. Such an impressive linguistic arsenal enabled him to communicate and exchange ideas directly with other mathematicians during his numerous travels, and greatly extend his fields of knowledge.

Much more than that, Carathéodory was a treasured conversation partner for his fellow professors in the Munich Department of Philosophy. The well-respected, German philologist, professor of ancient languages Kurt von Fritz praised Carathéodory, saying that from him one could learn an endless amount about the old and new Greece, the old Greek language, and Hellenic mathematics. Fritz had an uncountable number of philosophical discussions with Carathéodory. Deep in his heart, Carathéodory felt himself Greek above all. The Greek language was spoken exclusively in Carathéodory's house – his son Stephanos and daughter Despina went to a German high school, but they obtained daily additional instruction in Greek language and culture from a Greek priest. At home, they were not allowed to speak any other language.

[edit] Legacy

The Greek authorities intend to create a museum honoring Karatheodoris in Komotini, a major town of the northeastern Greek region where his family came from.

On December 19, 2005, Israeli officials along with Israel's ambassador to Athens, Ram Aviram, presented the Greek foreign ministry with copies of 10 letters between Albert Einstein and Constantin Carathéodory [Karatheodoris] that suggest that the work of Carathéodory helped shape some of Albert Einstein's theories. The letters were part of a long correspondence which lasted from 1916 to 1930. Aviram said that according to experts at the National Archives of Israel — custodians of the original letters — the mathematical side of Einstein's physics theory was partly substantiated through the work of Carathéodory. [1] [2]

[edit] Published works

[edit] See also

• Borel-Carathéodory theorem
• Carathéodory Conjecture
• Carathéodory's theorem (disambiguation)
• Carathéodory-Jacobi-Lie theorem
• Carnot-Carathéodory manifold
• Carathéodory metric

[edit] Notes

1. ^ adiabatic accessibility = adiabatische Erreichbarkeit; see also Elliott H. Lieb, Jakob Yngvason: The Physics and Mathematics of the Second Law of Thermodynamics, Phys. Rep. 310, 1-96 (1999) and Elliott H. Lieb, (editors: B. Nachtergaele, J.P. Solovej, J. Yngvason): Statistical Mechanics: Selecta of Elliott H. Lieb, 2005, ISBN 978-3540222972
2. ^ "University of the Aegean". University of the Aegean. http://www.aegean.gr/aegean/en/history.htm. Retrieved on 2006-10-07. 

[edit] References

[edit] Books

1. Maria Georgiadou, Constantin Carathéodory: Mathematics and Politics in Turbulent Times, Berlin-Heidelberg:Springer Verlag, 2004. ISBN 3-540-44258-8 MAA Book review
2. Themistocles M. Rassias (editor) (1991) Constantin Caratheodory: An International Tribute, Teaneck, NJ: World Scientific Publishing Co., ISBN 981-02-0544-9 (set)
3. Rassias, T. M. (editor) (1990) Constantin Caratheodory: An International Tribute: vol. 1, London: World Scientific Publishing Co., ISBN 981-02-0229-6
4. Rassias, T. M. (editor) (1990) Constantin Caratheodory: An International Tribute: vol. 2, London: World Scientific Publishing Co., ISBN 981-02-0230-X
5. Nicolaos K. Artemiadis; translated by Nikolaos E. Sofronidis [2000](2004), History of Mathematics: From a Mathematician's Vantage Point, Rhode Island, USA: American Mathematical Society, pp. 270-4, 281, ISBN 0-8218-3403-7

[edit] Articles (journals)

1. C. Carathéodory, Untersuchungen ueber die Grundlagen der Thermodynamik, Math. Ann., 67 (1909) p. 355-386.
2. H. Behnke, Carathéodorys Leben und Wirken, in A. Panayotopolos (ed.), Proceedings of C .Carathéodory International Symposium, September 1973, Athens (Athens, 1974), 17-33.
3. H. Boerner, Carathéodory und die Variationsrechnung, in A Panayotopolos (ed.), Proceedings of C. Carathéodory International Symposium, September 1973, Athens (Athens, 1974), 80-90.
4. O. Perron, Obituary: Constantin Carathéodory, Jahresberichte der Deutschen Mathematiker vereinigung 55 (1952), 39-51.
5. N. Sakellariou, Obituary: Constantin Carathéodory (Greek), Bull. Soc. Math. Grèce 26 (1952), 1-13.
6. A. Shields, Carathéodory and conformal mapping, The Mathematical Intelligencer 10 (1) (1988), 18-22.
7. H Tietze, Obituary: Constantin Carathéodory, Arch. Math. 2 (1950), 241-245.

[edit] Encyclopaedias — reference

1. Chambers Biographical Dictionary (1997), Constantine Carathéodory, 6th ed., Edinbourgh: Chambers Harrap Publishers Ltd, pp 270-1, ISBN 0-550-10051-2, * Also available online.
2. The New Encyclopaedia Britannica (1992), Constantine Carathéodory, 15th ed., vol. 2, USA: The University of Chicago, Encyclopaedia Britannica, Inc., pp 842, ISBN 0-85229-553-7 * New edition Online entry
3. H Boerner, Biography in Dictionary of Scientific Biography (New York 1970-1990).
4. O'Connor, John J.; Robertson, Edmund F., "Constantin Carathéodory", MacTutor History of Mathematics archive .

[edit] Lectures

1. Bulirsch R., Hardt M., (2000) Constantin Carathéodory: Life and Work, Lecture, Proceedings of International Congress: "Constantin Caratheodory", September 1-4, 2000, Vissa Orestiada, Greece. [Accessed: 19 January 2007]

[edit] External links

• (Greek) Web site dedicated to Carathéodory
• Constantin Carathéodory at the Mathematics Genealogy Project

Persondata
NAME	Carathéodory, Constantin
ALTERNATIVE NAMES
SHORT DESCRIPTION	Greek mathematician
DATE OF BIRTH	September 13, 1873
PLACE OF BIRTH	Berlin
DATE OF DEATH	February 2, 1950
PLACE OF DEATH