C. CARATHEODORY
The greatest Greek mathematician since antiquity
Athanasios Lipordezis
Constantin Caratheodory was a rare figure in the history of science. His exceptional scientific oeuvre was congruous to Caratheodory himself, a devoted family man, a modest and responsible citizen of patriotic sentiment and a selfless visionary.
The constitution of such a strong character, combined with an unravelling ambition which had its foundations in his talent and brilliant mind, could only prescribe a bright trajectory, a blazing star with a burning Greek and universal light which illuminates us even to this day, continually making us proud.
He was the offspring of a powerful and well-off family with roots in Adrianople in Eastern Thrace.
Ο Κων/νος Καραθεοδωρή με τον πατέρα του Στέφανο. Πίνακας του Richter (Βρυξέλλες 1880).
The head of the Caratheodory family, Stefanos Caratheodory (1789-1867) was a physician, scholar and mathematician. He was the founder of the Imperial Medical School of Constantinople, where he taught as a professor for forty years. He was also the sultan’s personal physician and an advisor to the Ministry of Education. He introduced and imposed many scientific terms of Greek origin into the Turkish language. He spoke and wrote seventeen languages. In general, the Caratheodory family occupied highly sought-out offices in the Ottoman Empire, as ministers, ambassadors, island rulers and diplomatic officials.
With this power at play, they managed to serve national interests by handing over trade, arts and sciences to Greek hands, without being exposed to the Ottoman Empire.
Michael Anastasiadis, a professor at the University of Athens stated at a memorial service for C. Caratheodory “it was the fault of the Greeks who did not think of following the wise policy of the Caratheodory family a hundred years ago. It would have been possible for the Ottoman Empire to become Greek. Instead, they pleaded their case in the Sultan’s harems and argued over who would become ruler in the Danubian lands so that they could be a tyrant on behalf of the tyrants.”
Constantin Caratheodory was born in Berlin on the 13th of September 1873. His grandfather was the nephew of the martyred Patriarch Cyril VI, while his mother Despina Petrokokkinou came from Chios. The Petrokokkinou family played an important role in Greek modern history Moreover, his father Stefanos Caratheodory, born in Constantinople in 1834, was a diplomat in Belgium and a member of the Brussels Academy of International Law.
Η μητέρα του, Δέσποινα Καραθεοδωρή
Η γιαγιά του, Ευθαλία Πετροκοκκίνου
Although he lost his mother at the tender age of six, he was raised by his grandmother, Evthalia Petrokokkinou, a woman of the Aegean with all the principles of the housekeepers of the time. In the summers, the Caratheodory families gathered in Chios, giving Constantin the opportunity to spend unforgettable summers with his cousins.
The incipience of his range is found in his school notebooks. We read in a note which was written by Jules Verne: To Mr. Kostia Caratheodory, I am overjoyed that I was able, passing through Brussels, to leave this testimony of all my sympathy towards you (24-9-1887).
In another notebook, his professor Bourgaults writes: To my young friend Kostia , who will become, if he continues like this, a modern Euclid !!! May 1st, 1888.
While Legrand, the famous Hellenist notes: “Human language, with its infinite varieties, is the most convincing proof of our freedom.”
Constantin’s first distinctions came at the age of sixteen, when he won first prize in a national mathematics competition in Belgium for two consecutive years.
His first studies began at the Belgian military engineering school, followed by further studies in Paris and London. In 1898, he was put in charge of major irrigation projects on the Nile, a promising position with many prospects, such as the Assiut and Aswan dams and Cheops pyramid.
Στη Σχολή Ευελπίδων στο Βέλγιο
One evening, while he was preoccupied with his beloved Mathematics, Constantin tried to find the solution to a problem which had arisen. The following day, he would go to his regular job where he had to make some measurements on the pyramid of Cheops. But his mind was transfixed in the search for the solution to the problem. At that moment, he realized at last his great fascination for mathematics. He made a life-altering decision. To give up his engineering profession in order to study the science of mathematics. This was the most important turning point in the life of Constantin Caratheodory, one he described as followed in his autobiographical notes:
“My family, my old friends, Dimitrios Vikelas and Markos Dragoumis, found my plan to leave a secure position with many prospects for the future more than ridiculous. I myself was not at all convinced that this plan would succeed and bear fruit. But I could not resist this compulsive thought that only the uninhibited pursuit of mathematics would give my life meaning.”
So at the age of twenty-seven, he made the greatest decision of his life, accompanied by an equally great one: to study mathematics in Berlin and then in Göttingen, the world’s leading mathematical centre in the world.
Caratheodory himself talked about this decision saying ”it was the greatest decision, in terms of consequences, that I have ever made in my life”.
Besides, many great scientists in the future referred in their speeches and notes to this important decision of Caratheodory, which was destined to offer so much to science, thus making him one of the most eminent scientists of the twentieth century.
Unsurprisingly, his progress was rapid and his rise to the ranks of the scientific community unimpeded. A shining star in the sky of science, his brilliance was palpable right through the title of his doctoral dissertation “On discontinuous solutions in the calculus of variations” which was accompanied by praise that read “the ingenuity of his invention is conspicuous”.
His supervisor, Professor Minkowski in his evaluation wrote: “The paper is among the best mathematical dissertations submitted to the school.”
Felix Klein, even before Constantin had been assessed for his doctorate, suggested that he should consider a post-doctoral degree and, at David Hilbert’s suggestion, before the prescribed dates, he acquired the right “to teach”.
So great are the three mathematicians mentioned above and even greater are the precursors of his theory, such as Bernoulli, Euler and Gauss that thanks to their evaluation of Caratheodory’s thesis, it was deemed highly prestigious and of the greatest value.
αραθεοδωρή να αποκτά πολύ μεγάλο κύρος και ύψιστη αξία.
Meinem Vater | In memory of my father
COMMENT:
Such was the impression made by his doctoral thesis that it was considered by Klein, the so-called professor of mathematics, to be a work of exceptional gallantry and was proposed to him, in derogation of the standard, as a direct post-doctoral degree.
Constantin Caratheodory was immediately given an important position in Göttingen, the renowned mathematical centre of Europe. Nevertheless, when the patriotic Greek sought recognition in his homeland, his merit was ignored and he was offered a teaching position in a school in Macedonia, as a language teacher and not as a mathematician. Thus, he set off on his bright scientific journey in Germany. At the same time, he created an amazing family. In 1908, at the age of thirty-five, he married the twenty-four-year-old Euphrosyne. The following year, Stefanos was born and later on his daughter Despina. As Despina herself informed us, as a family man he was exemplary, modest and discreet, since he never spoke to his children about the magnitude of the offices he held. Three years before his death, they were able to fully grasp his greatness as a mathematical genius. As a father, he pursued their ongoing education through trips and every Sunday after church, he made sure to take his children to museums, exhibitions and notable events.
He was devoted in spending quality time with his family. He constantly taught them to have values, ideals, to love work and above all, to love Greece. So, we learn that he raised his children with the traditions and principles that he was also raised on by his grandmother, the magnificent lady from Chios.
As a teacher, he left an indelible mark on the minds of his students, since, just like with his children, he knew how to combine love with pedagogical rigour. When he was to depart from Göttingen for Berlin, his students, who affectionately called him Cara, arranged a special ceremony, at which they wrote and recited a poem of thirty-eight stanzas, extolling the great virtues of their teacher and describing their sorrow for his parting.
The life and legacy of C. Caratheodory was characterized by continuous action, in harmony with his modesty, humility, selflessness and generosity, rather unique features which truly astounded the scientific community.
The photo of Euphrosyne, who was always by Constantin’s side until his death, with a dedication on the back and dated May 1906
His children Stefanos and Despina.
Throughout the course of his lustrous scientific career, his relationship with Einstein also stood out, since by way of the correspondence between these two men, which began in September 1916, the great contribution of Caratheodory to three issues Einstein encountered in formulating the general theory of relativity became apparent. Einstein acknowledged the help he received from C. Caratheodory, as is evident from the correspondence between the two scientists.
In one of these letters, a copy of which is in the archives of the museum, C. Caratheodory wrote:
“Dear colleague!
I find your derivative wonderful.
At first, I had trouble with a small typo that was on the second page. But now I understand everything. You should have published the theory in this form in Αnnalen der Physik, because physicists usually know nothing about this subject, as do Ι. I must have appeared to you in my letter like that Berliner who has only just discovered Grunewald and asks whether there have ever been people there.
And if you were willing to take the trouble to develop the normal transformations for me, you will find in me a grateful and conscious listener. And if you also solve the problem of closed time lines, then I will bow to you. There is something here and it is worth the attention of the best in science.
Best wishes
Yours, A. Einstein.”
In another letter, Einstein pleaded with Caratheodory: “Would you be interested in thinking more about time? Here lies the core of this hitherto unsolved problem of space-time.
Your very own A. Einstein salutes you.”
As expected, Caratheodory immediately and very informatively replied to Einstein and when he ultimately published his paper on the Axioms of the Special Theory of Relativity, the first congratulatory telegram he received was from Einstein. It read “DEAR COLLEAGUE I AM IN AWE”.
His stature was magnified by his work, which placed him among the stars of the mathematical science firmament.
Of Caratheodory’s work, Professor Lars of Harvard noted: “Constantin Caratheodory will always remain one of the leading mathematicians, who in the first half of the 20th century, laid the foundation for the future development of mathematics that was in danger of stagnating.”
Professor Hantrix Tietze wrote: “His conception that the content of science is not only the supervision of results, but first and foremost the construction of a sound theoretical edifice, motivated Caratheodory to develop the structure of thermodynamics in a way that allows a clear view of the fundamental principles”.
His friend, professor Erhard Schmidt, often stressed at the meetings of the professors that Caratheodory was a man, free of the passions prevalent in the field of scientists, while he said of his work “thanks to his deep and extensive work on the calculus of variations and its adjacent areas, which were developed in his eponymous work on this subject, Caratheodory was able to penetrate into geometric optics, of which his theory of the mirror telescope of B. Schmidt, which is even numerically sound, is the prime example.
Furthermore, we must also consider his contribution to theoretical physics, so fruitful for the clarification of the logical foundations, which Caratheodory offered with his work on the fundamental principles of thermodynamics and the axioms of the special theory of relativity. We must also remember his justification of Poincare’s recurrence theorem, unsurpassed in clarity and simplicity.
The anthology of acclaimed reviews for the work of the great Greek mathematician is large and written by the greatest scientists of the 20th century.
We will conclude our favourite picks with the opinion of a Greek professor, Michael Stephanidis, without this meaning of course that his is superior to the critics of professors N. Kritikos, Dem. Hondros, Nilos Sakellariou, G. Joakimoglou, I. Kalitsounakis and many others.
“The scientific works of Caratheodory, which mainly focus on mathematical analysis and geometry, the calculus of variations and mathematical representation, as well as thermodynamics and geometric optics, set theory and the theory of relativity, are regarded as fundamental research of excellent inspiration, which makes him one of the few in the world of science who deserve the accolades of pioneers of mathematical intellect”.
On the one hand, Caratheodory’s reach is proven and highlighted by his great scientific papers which were included in the most renowned scientific journals of Europe and on the other hand, by his relationship and correspondence with the best scientists in the world of mathematical science.
In 1919, the Greek army liberated the ancient region of Ionia and the Greek authorities settled in Smyrna. Eleftherios Venizelos invited C. Caratheodory to his house in order to entrust him with the organization of its university.
At the time, C. Caratheodory was among approximately fifty of the world-class scientists of their era, such as Max Plank, Albert Einstein, Herman Schwarz, George Fobenius, Erhard Schmit, Arnold Sommerfeld, Felix Klein, Hermann Minkowski, Arthur Rosenthal, David Hilbert and many other important people.
However, the fervent Greek, characterized by his strong patriotic sentiment and Christian ideals and values, would not let the sweet aroma of victory, generalised joy and national enthusiasm go to his head. He decided to abandon his brilliant career, his enviable position as a professor at the University of Berlin and without hesitation, accepted the invitation of the Greek Prime Minister. Venizelos invited him to his house and while waving his right index finger, with great animation and exuberance, he said to Caratheodory: “You will go to Smyrna and there you will be provided with all the necessary accommodation. Your work is important, Greece must civilize Asia Minor.
To Mr C. Caratheodory, the distinguished Professor
of Mathematics and wise Organizer of the first
Greek University in the liberated capital of
Greek Asia Minor.
Chrysostomos, Metropolitan bishop of Smyrna
1920.
Thus, the high-minded philanthropist and great scientist conceived the vision for the creation of the university which, as he emphasized, would be the “LIGHT FROM THE EAST”. With great enthusiasm, the scientist worked diligently and tirelessly night and day to organize and equip the university.
But this dream of his, for which he had made so many sacrifices, he would not be able to see realized. It was turned to ashes by the events of 1922. There are written and non-written testimonies of that time which state that Constantin Caratheodory left literally at the last minute and risked his own life, in order to board a ship together with items which he had so painstakingly transported from Europe to the University of Smyrna
The University of Smyrna on the hill of Bahri Baba. “Light from the East”
When disaster stroke, he was one of the last to be rescued. From the relevant Greek testimonies that exist about the event, Th. Danilides wrote in his personal diary:
“I was about to set sail in a crowded boat when I saw the professor on the quay. I beckoned him to come but he was trying to comfort an old lady. Almost completely standing up, I took him with my boat. He never ceased to have his head turned towards Smyrna, silent and tearful.”
Christos Angelomatis, 40 years after the event and in the newspaper “Estia”, in an article entitled “A short chronicle of the great tragedy” would write: ‘’Caratheodory too, the organiser of the University of Smyrna, risked falling into the hands of the Turks. This brilliant Greek man stayed at the University until the very last minute in order to save the laboratory material, which had been brought from Germany shortly before the catastrophe.
In the following years he was appointed professor at the University of Athens, where he experienced the existing conditions, otherwise unknown to him but widespread in the scientific community, as well as the ingratitude of Greece, something that would later force him to return to Munich as a professor. In 1928, responding to an invitation from the University of Harvard and the Mathematical Society, Caratheodory arrived in the USA with his wife on the 25th of January 1928.
At Harvard, Massachusetts, he taught for a full semester and continued for two months at the University of California. He also gave a series of lectures at 20 universities around America, including Cambridge, Berkley in San Francisco, Los Angeles, Washington, New Orleans, New York etc.
He was greeted with great enthusiasm and during his lectures he was listened to with awe and in complete silence.
At the International Mathematical Conference in New York he was given the honorary chair.
Once again in 1929, Venizelos summoned C. Caratheodory, this time from Munich, for the organization of the Aegean, Athens and Thessaloniki universities. Although his colleague and friend, professor Joakimoglou would advise him “not to put a crown of thorns on his head all over again for Greece”, the fervent patriot, lover of the ancient Greek ideal and visionary of a great and glorious Greece, could not help but put himself at its disposal. Shortly before the meeting of the Hellenic Parliament in December 1929, the then Minister of Education, Georgios Papandreou, would mention C. Caratheodory with the following words “we consider it a happy event for the universities of Athens and Thessaloniki, and a third one which may be the Aegean University with its seat in Mytilene or Chios, that the Greek scientist, who honours his Greek name in foreign lands, has returned to offer his immense knowledge to his homeland”.
At the same meeting, Prime Minister Eleftherios Venizelos would say the following: “As you know, Mr. Caratheodory is not only a great Mathematical exaltation, but also the eminent organizer of higher education in Europe as a whole. I ought to tell you that Germany entrusted him with the organization of the Breslau Polytechnic University.”
In the next 2 years he worked as Government Commissioner with the rank of Rector for the organization of the universities of Athens and Thessaloniki. Under this regulation, the universities operated for 50 years until 1982. Greece, which so enthusiastically elected C. Caratheodory, in a disappointing manner and with a document bearing the signature of a third class secretary, removed him from this position. He thus returned to his headquarters in Munich. So instead of Greece, in 1932 he represented Germany at the International Mathematical Congress in Zurich as its leading mathematician. In 1934, at the Session of the First Inter-Balkan Congress, he was unanimously elected by selected foreign scientists as honorary president and the professor of the University of Iasi Constantin Popovici stated during his speech: “The Greek people granted this wise man to the science of mathematics, the world famous C. Caratheodory”. In the spring of 1935, he went to the University of Pisa in Italy together with his daughter, where he gave four lectures.
In 1936 he travelled to America, invited by the Universities of Harvard and Massachusetts. At an event celebrating the 200th anniversary of the founding of the mathematical society in America, Caratheodory’s presence attracted a large and enthusiastic audience and a special event was held in his honour. Upon his return from America to Munich, he went straight to Oslo, where the Fields Award for mathematics was established. The prestige of this prize and its contribution to the development of mathematical science is internationally recognised. The Fields prize is awarded every four years during an international conference and eligible recipients are considered mathematicians under the age of forty. The evaluation committee is composed by a team of leading mathematicians of recognised standing.
A very important fact for all Greeks is that C. Caratheodory was the chairman of the jury at the first award, although no Greek has ever won the Fields Prize. This demonstrates the unsurpassed prestige of the great Greek mathematician. Other judges were Eli Cartan (a friend of Caratheodory), George Brikhoff, Francesco Severi and Teigi Takagi.
In 1937, he returned to Greece where he gave a lecture at the Technical University for the celebration of the 100th anniversary of the founding of the Archaeological Society. This resulted in an original study entitled “On the curves of the Parthenon’s Pillar”, a scientific research documenting the architectural curves of the Parthenon. In the same year, his daughter Despina would marry Theodoros Skoutaris, a civil engineer, in the Church of St. George in Kifisia. The following year, he would retire from the University of Munich due to the university’s age limit. Something that proves once again the unsurpassed pinnacle of his scientific entity is the fact that his chair remained vacant for six years because a worthy replacement could not be found. In the end, Eberhand Hopf was elected as his successor in 1944.
Few mathematicians have known and seen as much in their lives as Caratheodory. He participated in numerous meetings with experts in their fields and in the most important world conferences of science. He was an editor or contributor to the most renowned writings and scientific journals. As the Munich academic Professor H. Tiezze stated: ‘‘He was highly respected everywhere and appreciated for his value as a mathematician, but also because of his personal qualities, thus he was repeatedly invited to receive honorary invitations’’. The article dedicated to Caratheodory in the Hamburg Foreign Journal on the 13th of September 1943, the day of his seventieth birthday, was in the same spirit: ‘‘He was a multifaceted individual, dominant in all fields of science, who contributed greatly to the enrichment of Mathematical Physics. Mathematics owes a great deal to the keen, deep and clear thinking of the sage of Munich for the enlightenment and clarification of problems, which had previously only just been clarified, for the simplification, generalization and therefore easier solution of other difficult and complex questions …”.
On July 7, 1944, at its meeting, the Department of Mathematics and Natural Sciences of the Bavarian Academy of
Sciences (Academy of Munich) drew up a plan to publish all the mathematical publications of C. Caratheodory.
In 1945, three American universities, including Harvard, offered him a place, but he was already 72 years old, and life in Germany after the capitulation had become very difficult. Nevertheless, just as he began his career with the unexpected twist of starting to study mathematics at the age of 27, he ended his career by writing critical and remarkable papers, up to 7 days before his death at the age of 77! A truly unprecedented, admirable and unique individual.
On February 2nd 1950, his death was officially announced at the plenary session of the Academy of Athens. The then president of the Academy would say, among other things: “An outstanding figure of international science has passed away”.
On February 2nd 1950, his death was officially announced at the plenary session of the Academy of Athens. The then president of the Academy would say, among other things: “An outstanding figure of international science has passed away”.
The academic Ioannis Kalitsounakis, among others, said the following: “…The loss of C. Caratheodory is a loss for Greece and for international science. He honoured Greece abroad during his long stay, he honoured Greece as a civilised man, as a scientist and as a Greek patriot. His academic and friend George Joakimoglou would deliver a speech for the late adamant of science: “Whatever came, it has passed and will never return again. But with a glow so strong, it will keep on shining forever”.
In his telegram of condolence to his son he wrote, among other things: ‘‘I then had the opportunity to get to know this great scientist, a perfect man and true Greek patriot. During our many meetings in Athens and Munich in the years before the war, I always admired the man’s rare qualities’’.
The late Professor Nilos Sakellariou wrote about the man Caratheodory was: “Caratheodory’s upbringing and family education were truly Greek. Although he lived in Germany, where he received and held the office of regular University Professor, Academician and Geheimrat (Privy Counselor), he maintained his admiration and love for his Immortal Greece, which he greatly honoured with his personal merit and ability. I came to realise all this through my own eyes and personal understanding’’.
The academic of the Bavarian Academy of Sciences Oscar Perron, when informed of his death, said: “One of the brightest mathematicians, he has substantially enriched and decisively influenced Science. A man of unusual and broad education, as a part of the Greek nation, with his high spirits and unceasing pursuit of knowledge, he continued the tradition and heritage of Classical Greece.”
This is Constantin Caratheodory and such role models are what students and children need, to galvanize their dreams, their goals and lives.
Athanasios Lipordezis, Mathematician –
Author
