Constantine Karatheodori (September 13, 1873 – February 2, 1950) was a Greek mathematician known for his contributions to real and complex analysis, the calculus of variations, and measure theory. He is considered to be the greatest Greek mathematician since antiquity.

Karatheodori spent most of his professional career in Germany. His mathematical works were varied and extensive. He explored topics as diverse as convex geometry, real analysis, complex analysis, and thermodynamics, among many more.

Karatheodori enjoyed extensive contacts in European academia and rubbed shoulders with many of the early 20th century’s greatest mathematicians and scientists. He corresponded with Albert Einstein, whom he helped with his theory of general relativity.

### Early life of Constantine Karatheodori

Constantine Karatheodori – also spelled Constantin Carathéodory – was born on September 13, 1873, in Berlin, then the capital of the German Empire. His father, Stephanos, was an ambassador for the Ottoman Empire to Belgium, Russia, and Germany. His mother, Despina, née Petrokokkinos, was from the island of Chios.

Between 1874 and 1875, the Karatheodori family lived in Constantinople, then the capital of the Ottoman Empire. During the late 19th century, many Greeks still lived there before subsequent population exchanges and expulsions in the 20th century. Many members of the Karatheodori family held government positions in the city and they were well respected.

Then, in 1875, the family went to Brussels when Stephanos was appointed ambassador to Belgium. In 1879, tragedy struck and Despina died from pneumonia. Constantine Karatheodori was then raised by his maternal grandmother.

In 1881, the young Karatheodori began his education at a private school in Vanderstock. However, it was in 1885 at a grammar school in Brussels that he first developed an interest in mathematics. Between 1886 and 1889, he studied at the Athénée Royal d’Ixelles in Brussels, where he was twice recognized with an award as the best mathematics student in Belgium.

After his schooling, Karatheodori attended the École Militaire de Belgique from October 1891 to May 1895, where he trained to become a military engineer. He also studied at the École d’Application from 1893 to 1896.

Karatheodori was then offered a job with the British Colonial Service as an engineer. This occupation brought him to Egypt where he worked on the construction of the Assiut dam until April 1900. There were often delays caused by the floods, which gave Karatheodori time to pursue his passion for mathematics.

Whilst in Egypt, he also visited the Great Pyramid of Giza, which he decided to measure. He published his findings in 1901, as well as a book on the geography and history of Egypt.

### University education

After his stint in Egypt as an engineer, Karatheodori enrolled at the University of Berlin in May 1900. He attended lectures by the mathematicians Ferdinand Georg Frobenius and Hermann Amandus Schwarz. He also became a close friend of Lipót Fejér, a prominent Hungarian mathematician.

Karatheodori continued his studies at Göttingen University in 1902. He was greatly impressed by this academic institution and described it as the “seat of an international congress of mathematicians permanently in session.”

At Göttingen University he devoted his time to the study of the calculus of variations. The calculus of variation is used to “find the path, curve, surface, etc., for which a given function has a stationary value (usually a maximum or minimum).”

In 1904, he received his doctorate from Göttingen. His thesis was titled *On discontinuous solutions in the calculus of variations*. He stayed on at Göttingen to complete his post-doctoral thesis, *On strong maxima and minima in simple integrals*. He then lectured at the university as a Privatdozent (un-salaried lecturer) until 1908.

### University career

In 1908, Karatheodori was appointed as a Privatdozent at Bonn. Here, he worked on isoperimetric problems with Eduard Study. In 1909, he became a Professor of Higher Mathematics at the Technical University of Hanover.

After just a year at Hannover, Karatheodori again moved on to another institution. This time he was appointed Chair of Higher Mathematics at the Technical University of Breslau. He remained at Breslau for two and a half years before returning to Göttingen on April 1, 1913, this time as a professor. He lectured at Göttingen throughout the First World War.

After five years, Karatheodori took up a new position at the University of Berlin in 1918. However, he was not here for long. In 1919, he complied with a request by the Greek government to establish a second university at Smyrna.

Once in Greece, Karatheodori required a university position before he could begin work on establishing a new institution at Smyrna, so he was appointed Professor of Analytical and Higher Geometry at the University of Athens on June 2, 1920.

In the summer of 1920, Karatheodori was officially appointed as organizer of the Ionian University in Smyrna and also as a Professor of Mathematics at the new institution. He spent the latter half of 1921 disseminating books and materials across Europe for the new university.

The university project was thrown into disarray when the Turks attacked Smyrna in September 1922. Karatheodori managed to escape, together with most of the books he had gathered over the six months or so he spent in Europe. He was evacuated by a battleship to Athens where he took up posts at the National University and the National Technical University until 1924.

Karatheodori left Greece and took up a new position at the University of Munich where he remained until his retirement in 1938. During this time, he also acted as a visiting lecturer at Harvard and the American Mathematical Society. He was also offered a position at Stanford but decided to remain in Munich.

### Work with Albert Einstein

Constantine Karatheodori collaborated with many great mathematicians, scientists, and scholars over the course of his career, but the most famous by far was Albert Einstein.

Einstein was at the Prussian Academy of Sciences in Berlin when he contacted Karatheodori. He wanted assistance with his general theory of relativity and asked Karatheodori for clarifications on the Hamilton-Jacobi equation and canonical transformations.

Karatheodori provided Einstein with a satisfactory derivation of the Hamilton-Jacobi equation and the origins of canonical transformation. Einstein called Karatheodori’s derivation “beautiful” and recommended it for publication in the *Annalen der Physik*.

Karatheodori passed away on February 2, 1950. He is remembered as arguably the greatest Greek mathematician since antiquity. One of the largest lecture rooms at the University of Munich was named after him in 2002.

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