Constantinos Caratheodory

Constantin Carathéodory (or Constantine Karatheodoris) (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.

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. He is credited with the authorship of the Carathéodory conjecture that a closed convex surface admits at least two umbilic points. To this day, this conjecture is open 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.

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.

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.

Letter from Einstein to Carathéodory

Letter from Einstein to Carathéodory dated September 6, 1916.

Letter from Carathéodory to Einstein dated December 16, 1916.

From

Life and Work

http://www-m2.ma.tum.de/Veroeffentli.../Caratheodory/.

http://74.125.77.132/search?q=cache:...lnk&cd=1&gl=gr

by

Roland Bulirsch and Michael Hardt

Guest lecture held at Vissa Orestiada, Greece in honor of Constantin Carathéodory

September 1-4, 2000

also...

http://www.fs.lmu.de/gaf/einstein/wi...e_0405/07_cara