## Summary

Konstantinos Karatheodoris (Berlin, 13 September 1873 – Munich, 2 February 1950) was a Greek mathematician who distinguished himself on a world level. Karatheodoris was known outside Greece as Konstantin Carathéodory and is often referred to as Karatheodoris. His scientific work extended to many areas of mathematics, physics and archaeology. He made significant contributions particularly in the fields of real analysis, functional analysis and measure and integration theory. He wrote most of his works in German.

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## His childhood

Karatheodoris” father, Stefanos Karatheodoris, was a lawyer from Constantinople, originally from Bosnochori or Vyssa (today moved to Nea Vyssa in the Prefecture of Evros) in Western Thrace. He worked as a diplomat for the Ottoman Empire, first as a secretary and then as the Sultan”s ambassador to Brussels, St. Petersburg and Berlin. Karatheodoris” mother, Despina née Petrokokkinou, was originally from Chios.

His mother died when Constantine was only six years old and the young Karatheodoris was brought up by his grandmother, Euthalia Petrokokkinou. He grew up in a European, scientific and aristocratic environment. He spent his childhood in Brussels, where his father had been ambassador to the High Gate since 1875, and as a result his native language was Greek and Flemish. Before he even entered his teens he spoke Turkish and German.

From 1883 to 1885 he attended schools on the Riviera and in San Remo. For one year he attended a secondary school in Brussels, where in the course of geometry he felt his love and inclination for mathematics. In 1886 he enrolled at the gymnasium Atene Royale in Brussels, from which he graduated in 1891. In Belgium at that time there was a mathematics competition in which his class was invited to compete for two years in a row, and Karatheodoris took first place both years.

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## The youthful years

From 1891 to 1895, he studied civil engineering at the Belgian Military School in Brussels. Upon his graduation in 1895, he accepted the invitation of his uncle, Alexandros Stephanos Karatheodoris, who was the general commander of Crete, to visit him in Chania. There he met Eleftherios Venizelos. He then went to Lesvos, where he participated in the construction of road works, and in 1898 he went to Egypt to work as an engineer for the British company that was building the dam in Aswan. In Egypt he continued to study mathematical writings, and also made measurements at the central entrance to the pyramid of Cheops, which he published.

In Egypt, Karatheodoris realised how much fascination and influence Mathematics had on him and realised that the job of an engineer was not what his restless spirit was looking for. So in 1900, the now 27-year-old Karatheodoris, much to the surprise of his family, decided to give up the engineering profession and go to Germany to study Mathematics. For two years he attended mathematics courses at the University of Berlin.

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## The first scientific steps

In Berlin, Karatheodoris had the good fortune to attend lessons from great mathematicians such as Herman Schwarz, Georg Frobenius, Erhard Schmidt and Lazarus Fuchs. Schmidt left for Göttingen University in the autumn of 1901 and motivated Karatheodoris to decide to settle there as well. So in 1902, Karatheodoris transferred to Göttingen University to do a doctoral thesis under the supervision of Hermann Minkowski.

Göttingen at that time was considered the greatest centre of mathematics and two famous professors, David Hilbert and Felix Klein, taught there. These two great mathematicians had a great influence on his life and career as a mathematician. Karatheodoris was awarded a doctorate at the University of Göttingen in 1904 and immediately afterwards asked to work in Greece. But the authorities replied that he had hopes of being appointed only as a teacher in schools in the province. He then returned to Germany, where the following year (March 1905) he was appointed lecturer in mathematics at Göttingen University. At the same university he taught until 1908. In the same year he married the then 24-year-old Euphrosyne, with whom he had two children, Stefanos and Despina.

The relationship that linked Karatheodoris with Albert Einstein was particularly special. The two men met in 1915 and maintained a scientific relationship based on mutual respect and appreciation.

In 1911, at the invitation of Eleftherios Venizelos, Karatheodoris participated in the selection committee for the University of Athens. In 1913 he became professor of the first chair of mathematical science at the University of Göttingen, a position he held until 1918. In 1920, again at the invitation of Venizelos, he undertook to organize the Ionian University in Smyrna.

Karatheodoris remained in Smyrna until the collapse of the Asia Minor front in August 1922. When the Turks invaded the city, the 49-year-old Karatheodoris managed to save the library and many of the laboratory instruments of the Ionian University and transferred them to the University of Athens. The Karatheodoris donation is still in the Museum of Natural Sciences of the University of Athens. In 1922 he was appointed professor at the University of Athens and in 1923 he was appointed professor at the National Technical University of Athens.

Rather disappointed by the miserable state of Greek universities, he left Greece in 1924 to take up a professorship at the University of Munich, which at that time was the second largest university in Germany and was taught by leading names. In November 1926, he became a member of the newly founded Academy of Athens for the class of Sciences. In 1928, responding to an invitation from Harvard University and the American Mathematical Society, he visited the United States with his wife for almost a year to lecture at various American universities, including Princeton University, the University of Pennsylvania, the University of Texas at Austin, and others.

In 1930, again at the invitation of Eleftherios Venizelos, he assumed the duties of government commissioner at the University of Athens and the University of Thessaloniki to assist in the reorganization of the former and the organization of the (newly established) latter.

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## In recent years

In 1932, he returned to his headquarters in Munich and remained in the city even during the difficult years of the Second World War. His role during the Third Reich and his attitude towards the Nazi regime is controversial, while other scientists were critical of Hitler. He was a commissioner of the Church of the Saviour in Munich, appointed by the Nazi regime. In 1945, several American universities invited him to settle and teach in the United States, but he preferred to stay in Germany, since he was elderly and had already lost his partner.

In December 1949 he gave his last lecture in Munich. He died two months later. His body was interred in the Waldfriedhof Cemetery in Munich.

Karatheodoris started writing scientific studies already from the time he was working as an engineer in Egypt. His researches, which he published mainly in German, make up a huge and multifaceted body of work, which ranks him among the greatest mathematicians.

He first worked on the Calculus of Variations and his doctoral thesis (Göttingen, 1904) is entitled “On discontinuous solutions in the Calculus of Variations”. Subsequently, he dealt with almost all branches of mathematics: theory of real functions, theory of complex functions, differential equations, set theory and differential geometry, conformal representations, etc.

His mathematical proofs are characterized by “elegance and simplicity”, but also by a rigor that gives absolute certainty to the conclusions that are drawn. With his contribution to the calculus of variations he helped develop the General Theory of Relativity, arousing the admiration of Einstein himself:

“If you want to take the trouble to explain even the normal transformations to me, you will find a grateful and conscientious listener. But if you also solve the problem of the closed lines of time, I will stand before you with crossed arms. Behind it there is hidden something worthy of the sweat of the best.” – Einstein”s letter to Karatheodoris, 1916

His contribution to theoretical physics was essential to the mathematical foundations of areas of physics such as thermodynamics, geometric optics, mechanics and relativity.

In 1909 he published a paper entitled “Research on the Foundations of Thermodynamics” in the journal Mathematische Annalen. This paper only became widely known in physics circles in 1921 through an article on it by Max Born in the Physikalische Zeitschrift. The 1909 paper also contains the famous Karatheodoris Principle

“in every thermodynamic equilibrium state of a system there are some infinitely neighbouring equilibrium states that cannot be reached by adiabatic changes”.

With simple axioms and assumptions, Karatheodoris managed to arrive at the definition of fundamental thermodynamic quantities such as entropy, without any reference to thermodynamic cycles, etc.

He was a member of the academies of Berlin (1919), Göttingen (1920), Munich (1925), Cologne (1926), Athens (1927) and Rome (1929).

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## Children

His mathematical work (books, articles, etc.) was carefully collected by his son, Stefanos, and published in German in 1957. His daughter, Despina Karatheodoris-Rodopoulou, edited the recent edition of his biography in Greek. He was born in 1909 and grew up in Germany. She married the politician, president of the parliament and minister, Konstantinos Rodopoulos, with whom she had one child, Stefanos. In 1950, on her return from Germany, she lived on an estate in Skotina Beach in Pieria, writing books on her famous father, such as Konstantinos Karatheodoris the Wise Hellene of Munich (with Despina Vlahostergiou-Vasvateki). She died in November 2009. With her death the family name evolved.

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## Conferences and honours in his memory

In 1973, the Hellenic Mathematical Society organised an international symposium on the 100th anniversary of the birth of Karatheodoris, while in 2000 the Democritus University of Thrace organised a World Congress of Mathematics on the 50th anniversary of the death of the great scientist.

His memorials have been erected in Komotini – on the initiative of the local branch of the Hellenic Mathematical Society – and in Peristeri, Attica. His bust was erected at the University of the Aegean, while many streets in Greek cities have been named after Konstantinos Karatheodoris.

The Association of Greek Scientists of Berlin, the Administration Building of the Aristotle University of Thessaloniki, the Gymnasium of Paleo Psychiko, the 4th Lyceum of Galatsiou, the 30th Gymnasium of Thessaloniki and the Greek Lyceum of Munich bear the name “Konstantinos Karatheodoris”.

The Karatheodoris Museum was founded and operates in Komotini and exhibits books, handwritten letters from and to Einstein, Rosenthal, Kneser, original documents, photographs of the Karatheodoris family, etc.

**Sources**