Constantin Carathéodory

Constantin Carathéodory (or Constantine Karatheodoris) (Greek: Κωνσταντίνος Καραθεοδωρής) (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.

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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.

Studies

Carathéodory studied engineering in Belgium, 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 1909-1920 he held various lecturing positions in Hannover, Breslau, Göttingen and Berlin.

Works

He is credited with the theories of outer measure, and prime ends, amongst other mathematical results.

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 und Max Born.

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

Geometrishe 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.

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.

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. Kurt von 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.

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]

Published Works

See also

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

References

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. Retrieved on 2006-10-07.

Sources

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

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.

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; Edmund F. Robertson "Constantin Carathéodory". MacTutor History of Mathematics archive.  

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]