Everything about Constantin Carath Odory totally explained
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 can't be approached arbitrarily close through adiabatic changes of state." Carathéodory coined the term
adiabatic accessibility. 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've 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.
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.
(External Link
) (External Link)
Published Works
Further Information
Get more info on 'Constantin Carath Odory'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://constantin_carath__odory.totallyexplained.com">Constantin Carathéodory Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
