Константин Каратеодори. Constantine Caratheodory

CONSTANTINE CARATHEODORY (in greek - Konstantinos Karatheodoris)
(Berlin 13.09.1873 – Munich 02.02.1950)

GREAT MODERN GREEK MATHEMATICIAN HEIR OF THALES OF MILETUS

STUDIES and UNIVERSITY CAREER
Caratheodory studied engineering in Belgium at the Royal Military Academy, where he was considered a charismatic and brilliant student.
1900 Studies at University of Berlin. 1902 Completed graduation at University of Gottingen (1904 Ph.D, 1905 Habilitation) 1908 Dozent at Bonn. 1909 Ordinary Professor atHannover Technical High School. 1910 Ordinary Professor at Breslau Technical High School. 1913 Professor following Klein at University of Gottingen. 1919 Professor at Universty of Berlin.
1919 Elected to Prussian Academy of Science. 1920 University Dean at Ionian University of Smyrna and later,University of Aegean. 1922 Professor at University of Athens. 1922 Professor at Athens Polytechnic. 1924 Professor following Lindeman at University of Munich. 1938 Retirement from Professorship. Continued working from Bavarian Academy of Science.Caratheodory had about 20 doctoral students among these being Hans Rademacher, known for his work on analysis and number theory, and Paul Finsler known for his creation of Finsler space. Caratheodory's contacts in Germany were many and included such famous names as: Minkowsky, Hilbert, Klein, Einstein, Schwarz, Fejer. During the difficult period of World War II his close associates at the Bavarian Academy of Sciences were Perron and Tietze.
While in Germany Caratheodory retained numerous links with the Greek academic world about which detailed information may be found in Georgiadou's book. He was directly involved with the reorganization of Greek universities. An especially close friend and colleague in Athens was Nicolaos Kritikos who had attended his lectures at G;ttingen, later going with him to Smyrna, then becoming professor at Athens Polytechnic.With Caratheodory he helped the famous topologist Christos Papakyriakopoulos take a doctorate in topology at Athens University in 1943 under very difficult circumstances. While teaching in Athens University Caratheodory had as undergraduate student Evangelos Stamatis who subsequently achieved considerable distinction as a scholar of ancient Greek mathematical classics.

WORKS
In his doctoral dissertation Caratheodory originated his method based on the use of the Hamilton-Jacobi equation to construct a field of extremals. The ideas are closely related to light propagation in optics. The method became known as the royal road to the calculus of variations. More recently the same idea has been taken into the theory of optimal control.The method can also be extended to multiple integrals.
He proved an existence theorem for the solution to ordinary differential equations under mild regularity conditions.Theory of measure : He is credited with the Caratheodory extension theorem which is fundamental to modern set theory. Later Caratheodory extended the theory from sets to Boolean algebras.
In 1909, Caratheodory published a pioneering work "Investigations on the Foundations of Thermodynamics" in which he formulated the Laws of Thermodynamics axiomatically. It has been said that he was using only mechanical concepts and the theory of Pfaff's differential forms. But in reality he also relied heavily on the concept of an adiabatic process. The physical meaning of the term adiabatic rests on the concepts of heat and temperature. Thus, in Bailyn's survey of thermodynamics, Caratheodory's approach is called "mechanical", as distinct from "thermodynamic". Caratheodory's "first axiomatically rigid foundation of thermodynamics" was acclaimed by Max Planck and Max Born. In his theory he simplified the basic concepts, for instance heat is not an essential concept but a derived one. He formulated the axiomatic principle of irreversibility in thermodynamics stating that inaccessibility of states is related to the existence of entropy, where temperature is the integration function. The Second Law of Thermodynamicks was expressed 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." In this connexion he coined the term adiabatic accessibility.
Caratheodory's work in optics is closely related to his method in the calculus of variations. 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. In his later work he gave the theory of the Schmidt Telescope.

CARATHEODORY and EINSTEIN
We all know about Albert Einstein, the founder of the theory of relativity but how about the person who taught him and showed him the way to a bright scientific journey which would change the world? That was his teacher, Konstantinos Karatheodoris. During one of his last pubic appearance Albert Einstein said, “You ask me to answer to all sorts of questions, but noone has ever wanted to know who was my teacher, who showed me the way to the higher mathematical science, thought and research. I simply say that my teacher was the unrivalled Greek Konstantinos Karatheodoris,to who we owe everything…” Indeed, it was a Greek from Thrace. He has not only been in touch with Einstein but has also hepled him to complete the theory of relativity. The world’s mathematical community acknowledges the  major offering and contrubution of  “Kara” , as they name him when it comes to the research of higher mathematics. He started his studies at the age of 27 and until the last days of his life he kept writing critics and scientific studies. His cooperation and communication with Einstein  for the theory of relativity is imprinted in the letters they exchanged, which know are  exhibited in the museum “Karatheodoris ” in Komotini. Below is an excerpt:

“I consider your derivative as excellent.. at first I was misleaded by a slight error in  the second page. But know, I understand everything. You should publish the theory in this form in ;nnalen der Physik since physicists know  nothing on this subject, neighter do I. [...] If you would  like to unfold regular transformations, I would be  a concious and grateful listener. If you could also solve the problem of  closed timelines, then I would kneel to you. [...] A.Einstein”

В 1916 году, когда Константинос Каратеодори преподавал в университете Гёттингена, в «Мекке математики»,  он  получил по случаю анализа теории Гамильтона-Якоби  письмо от Альберта Эйнштейна:

Дорогой  коллега!
Я считаю вашу производную чудесной.  Вначале маленькая ошибка,  которая была найдена на  второй  странице, причинила  мне  некоторые затруднения. Но теперь я всё понимаю. Вы должны опубликовать теорию в этой  форме в «Анналах  физики», потому что учёные не сведущи в этом вопросе, как  впрочем и я. С моим письмом я для вас как берлинец, который  только что открыл Грюневальда и спросил: жили ли однажды там люди.  Если  вы  постараетесь,  чтобы позволить мне развиваться и дальше,  вы  сможете    найти в моём лице ещё одного благодарного и сознательного слушателя.  Если в дальнейшем решите и проблему замкнутых линий времени, то  я  буду стоять перед вами  со скрещенными руками. Здесь скрывается что-то такое, присущее лишь пытливым корифеям.
Мои наилучшие поздравления.

С уважением, А.Эйнштейн

[Это письмо, переписка между двумя великими учёными, как и целый частный архив Альберта Эйнштейна, хранится в Национальной библиотеке Израиля в городе Иерусалим.]

Академик Оскар Перрон сказал о нём:

Константинос Каратеодори – один из самых блестящих математиков – существенно обогатил науку и оказал дальнейшее влияние на её развитие. Человек необычайной и широкой образованности, принадлежащий к греческой нации, с высокой силой духа и неутомимыми поисками знаний, продолжающий наследовать традиции классической Греции.

Эйнштейн на пресс-конференции в 1955 году сказал о нём:

«...Господа, вы попросили ответить на тысячу вещей. Но никто не хочет спросить, кто мой учитель, который показал мне и открыл дорогу в высшую математическую науку к научным исследованиям. А чтобы не утомлять вас, я говорю просто, без подробностей, что великим моим учителем был непревзойдённый греческий учёный Константинос Каратеодори, которому я лично и  математическая наука, физика, мудрость нашего века,- мы обязаны все…»

НАЗВАННЫЕ В ЧЕСТЬ КАРАТЕОДОРИ:

Каратеодори     теорема о продолжении меры
Каратеодори  -  Якоби - Ли теорема
Каратеодори     уравнение
Каратеодори     внешняя мера
Каратеодори     класс регулярных   функций
Каратеодори     мера
Каратеодори     область
Каратеодори     расширение
Каратеодори     теорема для граничных элементов
Каратеодори     теорема о выпуклой оболочке
Каратеодори     теорема о конформном отображении
Каратеодори     теорема об интегралных представлениях
Каратеодори     теорема об односвязных областях
Каратеодори  -  Теплица теорема
Каратеодори  -  Фейера задача.

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