Constantin Carathéodory

Studies and university career

Carathéodory studied engineering in Belgium at the Royal Military Academy, where he was considered a charismatic and brilliant student.

University career

• 1900 Studies at Humboldt University of Berlin.
• 1902 Completed graduation at University of Göttingen (1904 Ph.D., 1905 Habilitation)
• 1908 Dozent at University of Bonn
• 1909 Ordinary Professor at Hannover Technical High School.
• 1910 Ordinary Professor at Breslau Technical High School.
• 1913 Professor following Klein at University of Göttingen.
• 1919 Professor at Humboldt University of Berlin
• 1919 Elected to Prussian Academy of Science.
• 1920 University Dean at Ionian University of Smyrna (later, University of the Aegean).
• 1922 Professor at University of Athens.
• 1922 Professor at Athens Polytechnic.
• 1924 Professor following Lindemann at Ludwig-Maximilians-Universität München (LMU).
• 1938 Retirement from professorship. Continued working at Bavarian Academy of Science

Doctoral students

Carathéodory 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.

Academic contacts in Germany

Carathéodory had numerous contacts in Germany. They included such famous names as Hermann Minkowski, David Hilbert, Felix Klein, Albert Einstein, Edmund Landau, Hermann Amandus Schwarz, and Lipót Fejér. During the difficult period of World War II, his close associates at the Bavarian Academy of Sciences were Perron and Tietze.

Einstein, then a member of the Prussian Academy of Sciences in Berlin, was working on his general theory of relativity when he contacted Carathéodory for clarifications on the Hamilton-Jacobi equation and canonical transformations. He wanted to see a satisfactory derivation of the former and the origins of the latter. Einstein told Carathéodory his derivation was "beautiful" and recommended its publication in the Annalen der Physik. Einstein employed the former in a 1917 paper titled Zum Quantensatz von Sommerfeld und Epstein (On the Quantum Theorem of Sommerfeld and Epstein). Carathéodory explained some fundamental details of the canonical transformations and referred Einstein to E.T. Whittaker's Analytical Dynamics. Einstein was trying to solve the problem of "closed time-lines" or the geodesics corresponding to the closed trajectory of light and free particles in a static universe, which he introduced in 1917.

Landau and Schwarz stimulated his interest in the study of complex analysis.

Academic contacts in Greece

While in Germany, Carathéodory retained numerous links with the Greek academic world, details of which can 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 Göttingen, later going with him to Smyrna, then becoming professor at Athens Polytechnic. Kritikos and Carathéodory helped the Greek topologist Christos Papakyriakopoulos take a doctorate in topology at Athens University in 1943 under very difficult circumstances. While teaching at Athens University, Carathéodory had Evangelos Stamatis as an undergraduate student, who subsequently achieved considerable distinction as a scholar of ancient Greek mathematical classics.

The University of Smyrna

At the time, Athens was the only major educational centre in the wider area and had limited capacity to sufficiently satisfy the growing educational needs of the eastern part of the Aegean Sea and the Balkans. Carathéodory, who was a professor at the University of Berlin at the time, proposed the establishment of a new university - the difficulties regarding the establishment of a Greek university in Constantinople led him to consider three other cities: Thessaloniki, Chios and Smyrna.

At the invitation of the Greek Prime Minister Eleftherios Venizelos, he submitted a plan on 20 October 1919 for the creation of a new university at Smyrna in Asia Minor, to be named Ionian University of Smyrna. In 1920 Carathéodory was appointed dean of the university and took a major part in establishing the institution, touring Europe to buy books and equipment. The university, however, never actually admitted students, due to the War in Asia Minor which ended in the Great Fire of Smyrna. Carathéodory managed to save books from the library and was only rescued at the last moment by a journalist who took him by rowboat to the battleship Naxos which was standing by. Carathéodory brought to Athens some of the university library and stayed there, teaching at the university and technical school until 1924.

In 1924, Carathéodory was appointed professor of mathematics at the Ludwig-Maximilians-Universität München (LMU), and held this position until retirement in 1938. He later worked at the Bavarian Academy of Sciences until his death in 1950.

The new Greek university in the broader area of the Southeast Mediterranean region, as originally envisioned by Carathéodory, finally materialised with the establishment of the Aristotle University of Thessaloniki in 1925.

Linguistic and oratorical talents

Carathéodory excelled at languages, much like many members of his family. 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 extended 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 and professor of ancient languages, Kurt von Fritz, praised Carathéodory on the grounds that from him one could learn an endless amount about the old and new Greece, the old Greek language, and Hellenic mathematics. Von Fritz conducted numerous philosophical discussions with Carathéodory.

The mathematician sent his son Stephanos and daughter Despina to a German high school, but they also obtained daily additional instruction in Greek language and culture from a Greek priest, and at home he allowed them to speak Greek only.

Carathéodory was a talented public speaker, and was often invited to give speeches. In 1936, it was he who handed out the first ever Fields Medals at the meeting of the International Congress of Mathematicians in Oslo, Norway.

Legacy

In 2002, in recognition of his achievements, the LMU Munich named one of the largest lecture rooms in the mathematical institute the Constantin-Carathéodory Lecture Hall.

In the town of Nea Vyssa, Caratheodory's ancestral home, a unique family museum is to be found. The museum is located in the central square of the town near to its church, and includes a number of Karatheodory's personal items, as well as letters he exchanged with Albert Einstein. More information is provided at the original website of the club, http://www.s-karatheodoris.gr.

At the same time, Greek authorities had long since intended to create a museum honoring Karatheodoris in Komotini, a major town of the northeastern Greek region, more than 200 km away from his home town above. On 21 March 2009, the "Karatheodoris" Museum (Καραθεοδωρής) opened its gates to the public in Komotini.

The coordinator of the museum, Athanasios Lipordezis (Αθανάσιος Λιπορδέζης), has noted that the museum provides a home for original manuscripts of the mathematician running to about 10,000 pages, including correspondence with the German mathematician Arthur Rosenthal for the algebraization of measure. At the showcase, visitors are also able to view the books " Gesammelte mathematische Schriften Band 1,2,3,4 ", "Mass und ihre Algebraiserung", " Reelle Functionen Band 1", " Zahlen/Punktionen Funktionen ", and a number of others. Handwritten letters by Carathéodory to Albert Einstein and Hellmuth Kneser, as well as photographs of the Carathéodory family, are on display.

Efforts to furnish the museum with more exhibits are ongoing.