# Nikolaos I Hatzidakis

### Quick Info

Berlin, Germany

Athens, Greece

**Nikolaos Hatzidakis**was a Greek mathematician, poet and patriot. He worked in differential geometry.

### Biography

**Nikolaos Hatzidakis**was the son of Ioannis N Hatzidakis and Penelope Lakonos. Ioannis Hatzidakis, who often transcribed his name as Hazzidakis, was born in Crete, studied at Syros, and then, from 1863, at the National and Kapodistrian University of Athens. Ioannis was awarded a Ph.D. in mathematics and then was awarded a scholarship which allowed him to study differential geometry in Paris followed by a time in Berlin studying under Karl Weierstrass. Ioannis was married to Penelope Lakonos, the sister of the Professor of Mathematics at the University of Athens, Vassilios Lakonos, from Kea (Tzia). It was while Ioannis and Penelope Hatzidakis were in Berlin that their son Nikolaos, the subject of this biography was born. Let us note that Ioannis Hatzidakis had a brother Georgios Nicolaou Hatzidakis (1843-1941) who became a linguist and Professor of Linguistics at the University of Athens.

At this point we record that this biography is based on [2], Melissa Iacovidou's translation of various Greek documents relating to Nikolaos Hatzidakis.

The school education of Nikolaos took place in Athens. He did not attend elementary school, but instead was home-schooled. He attended the Private School I Simopoulos in Athens for the first three years of his secondary education and then transferred to the Third Municipal Lyceum of Athens where spent his final school year. He graduated from the Third Municipal Lyceum in 1888. At the start of the next academic year, 1888-89, he enrolled in the Mathematics Department of the School of Philosophy at the University of Athens and in 1893 he received his degree with the highest honours. According to the tradition of that time he became a Doctor of Philosophy in Mathematics.

Following the same pattern that his father had followed, Hatzidakis went to Paris for graduate studies. There he attended courses given by Henri Poincaré, Émile Picard, Gaston Darboux, Paul Appell, Louis Raffy and other leading mathematicians. He cut short his visit, however, because of the unrest which had broken out in Crete.

There had been unrest on Crete for some time with rebellions by the majority Greek population against their Ottoman rulers which arose in 1886, 1888 and 1889. Renewed clashes in 1896 saw Greek volunteers arrive on the island to support the Greek population. Among these volunteers was Hatzidakis and his uncle who had, as a young man, fought for the Greeks in 1866 in a similar uprising at the side of his own father (the grandfather of the subject of this biography). Greek troops arrived on Crete in February 1897 and declared that Crete was part of Greece. The Ottoman forces were victorious in the war which followed, however, and by September an armistice had been signed which was a humiliation for the Greeks. Hatzidakis left for Germany to continue his graduate studies, again following the same pattern as his father.

Hatzidakis spent two years in Germany, 1898-1900. He attended lectures by David Hilbert, Felix Klein and Arthur Schönflies at the University of Göttingen while, at the University of Berlin, he attended lectures by Hermann Schwarz, Lazarus Fuchs and Johannes Knoblauch (1855-1915). At this time Schwarz was lecturing on his collected works and Hatzidakis had for company at these lectures his fellow Greek, Constantin Carathéodory. Hatzidakis, however, did not receive any diplomas from these universities. His main area of study was differential geometry and his first paper, published in 1899, was

*Note sur une nouvelle formule de géométrie différentielle*Ⓣ. Two further papers appeared in 1899, namely

*Trois formules trés générates relatives aux courbes dans l'espace*Ⓣ and

*Sur les courbes gauches*Ⓣ. He published his impressive work on a generalisation of Darboux's theories to $n$ dimensions in 1900. This work used the concept of multiplicity which had been introduced by Poincaré in 1899.

For a list of papers by Hatzidakis, see THIS LINK.

After two years spent in Germany, he returned to Greece in 1900 where he was appointed as the Professor of Theoretical Mechanics and Astronomy at the Hellenic Military Academy. He taught there until 1904, when he resigned as he was appointed professor of Higher Mathematics at the University of Athens. At this time, in 1904, he married Henriette Olsen from Copenhagen, Denmark; they had two children, Sophia, born on 16 December 1905, and Ioannis, born on 12 December 1913, who became a chemist.

On 17 January 1910 he addressed the Students' Mathematical Association with

*Mathematics in intellectual life*and presented his ideas for the creation of "Mathematical Schools." The first part of the talk dealt with mathematics as a science, and the second part dealt with the current aspirations throughout the mathematical world. He explained how difficult it was to awaken an interest for mathematics in students since it is not at first glance attractive or useful in living life. A student studying mathematics does not get an immediate gain nor are they admired for mathematical achievements which remain known only within a very limited circle. But research offers, he explained, great spiritual satisfaction for anyone who seeks for themselves "the higher delights of this desire to study Mathematics above all."

In 1912 he was sent as a representative of the National University of Athens to the 5th International Congress of Mathematicians held in Cambridge, England. He gave lectures at the conference and published two papers in the Proceedings, one in German and one in English, namely

*Rekreation Mathematik in den mittleren Schulen*Ⓣ, and

*On pairs of Frenet'ian trihedra*. He also attended the International Congress of Mathematicians in 1920 in Strasbourg, where he gave the lecture

*Sur quelques formules de géométrie cinématique*Ⓣ, and the 1928 International Congress of Mathematicians in Bologna where he gave the lecture

*Due proposte per l'insegnamento medio*Ⓣ.

In 1913 Hatzidakis served as dean of the School, and in that capacity he proposed the establishment of a Mathematical Journal, in which he could present his work to those who were not members of the university community. He also proposed the introduction of Sunday courses by the teachers of the Foundation and the setting up of Mathematical Schools. In the same year he published his famous book,

*Analytical Surface Theory*(Greek).

Hatzidakis was the first professor at the University who achieved close contact with his students. This effort was greatly appreciated from his students, who all seemed to adore him. Together with his colleague Georgios Remoundos he was a pioneer in creating special research seminars in the University in 1918, in which they taught - for the few students wishing to become research mathematicians - special branches of mathematics and the latest achievements of that science. Thus, the material and the spirit of presentation of the leading universities were brought to Greece as well. This activity resulted in the presentation of original works by Greek researchers who also received doctorates from the University of Athens. The initiative taken at this time was continued by the subsequent professors of the Mathematics Department.

He also organised free mathematics lectures, aimed at a broader audience, delivered at the University's premises. In these lectures he taught the history of mathematics, its relation to other disciplines, and mathematical games and paradoxes. These lectures were not only attended by students, but also by many scientists from other fields.

Several important initiatives in the development of mathematics in Greece were undertaken by Hatzidakis in collaboration with two of his colleagues, Georgios Remoundos and Panagiotis Zervos. In the year 1918, these three mathematicians founded the Hellenic Mathematical Society. Hatzidakis served as the first President of the Society having this role from 1918 to 1925. As president of the Hellenic Mathematical Society he worked with great zeal to consolidate the Society and increase its international visibility through the publication of the scientific journal "The Bulletin of the Greek Mathematical Society" which began publication during his second year of office, namely 1919. In the first issues of the journal, Hatzidakis published some remarkable work. As part of his role as president, he also gave a series of lectures on a diverse range of material. He also contributed greatly towards the creation of technical secondary schools.

Hatzidakis was the person who, following on from the beginnings by his father, brought the study of differential geometry to Greece. Most of his research papers were on differential geometry, but the particular branch of this topic that he was very keen to cultivate was kinematics. His most important contributions were based on Darboux's kinetic method. As he said "kinematics is a rugged intellectual, but very important, path, which is far away from analytical geometry." He taught a course on the kinetic theory of curves at the University but this was very much his own speciality and the course ceased being taught at the University after he retired. He also taught the theory of elliptical functions and several courses on function theory.

Hatzidakis was not only interested in mathematics and, having a multifaceted and extremely competent mind, he systematically dealt with other disciplines such as linguistics, geography, and literature. He was given a deep understanding of linguistics by his father's brother, Georgios Hatzidakis, a famous linguist, with whom, however, he disagreed with on basic linguistic issues. He published many articles on linguistics in the Greek Circular Dictionary, and according to his son Ioannis, he received twice as much remuneration as other lecturers for these articles.

Hatzidakis was also an excellent geographer. His knowledge of the various regions of the Earth was extraordinary. He used his wide knowledge to write a two-volume book about geography, which was owned by his son. But the field of activity, which he loved equally with the field of Mathematical Science, was Literature. His literary work is also quite rich, perhaps equal to his mathematical work in extent, but it does not appear to be nearly as highly rated as his mathematical contributions. His poetic work is divided into two distinct parts:

- Original lyrical work, which he published in several literary magazines, in various newspapers, and in the literary calendar "New Life" which he wrote on his own and published in 1906.
- Translations from most European languages, part of which was published in a book called "Foreign Flowers" in 1940. The second volume of the book remained unpublished and after his death was in the hands of his son, who was a chemist.

His poems dealt with love, the childish soul, Crete, Greece, nature and the beauty of the Greek land. It is difficult, of course, to do justice to his poetry in translation to English but, more to show his love for nature, which he wanted to pass on to his readers, we give this example:

Love the flowers! Love the forests!He had a beautiful garden around his house, which he took care of himself, and had a vast collection of flowers. When the weather permitted, he sat in his garden and learnt foreign languages or read poetry. In fact he could speak and write in twelve foreign languages: 1) French, 2) German, 3) Italian, 4) English, 5) Danish, 6) Swedish, 7) Norwegian, 8) Dutch, 9) Finnish, 10) Spanish, 11) Portuguese, and 12) Romanian. He was also a member of the organising committee for the first Trans-Balkan Mathematical Convention in Athens in 1934, where he worked hard for its success. The 2nd Convention was held in Bucharest in 1937, where he took part and spoke in Romanian, which surprised the delegates.

Every pure flower, every green leaf,

you won't find a better one created

or a more loyal friend.

.......................................................................

When the water murmurs through the forests

and the breeze whispers sweetly in the foliage,

our miserable soul breathes and hopes

-- it doesn't see everything so dark ...

He admired the Arabic Language, which he said is a beautiful language, but regretted he had no time to learn it. At the time of his death he had begun to learn Russian, Serbian, Hungarian, and Turkish but was quick to say that he had yet to perfect his knowledge of them. He knew the ancient Greek language very well, so he spent a lot of time studying the ancient Greek authors, especially Homer. He could recite many passages from the ancient Greek writers which he knew by heart.

Hatzidakis inherited many qualities from his father, and amongst those being his genuine Cretan character. He remained adamant in his beliefs and did not compromise easily. The gentleness and sweetness of his character, a quality inherited from his mother, meant that his character had two sides which were not always reconcilable.

He was a patriot so he had strong feelings against the enemies of Greece. We have seen an example of this above with his participation as a volunteer fighter in the Cretan Revolution of 1897 against the Turks. Another example came in a letter, which he sent before the war of 1940 between Greece and Italy, to the Italian ambassador in Athens, when he was invited to attend a ceremony for the opening of the 'Italian Institute of Higher Education'. In this letter he thanked the ambassador for his kind invitation but said that he was unable to attend since Italy "had yet to make the gesture of 'true higher education', namely to return the Dodecanese islands to Greece".

Hatzidakis was a member of various foreign mathematical societies including the German Mathematical Society, the Swiss Mathematical Society and the Mathematical Circle of Palermo. He was honoured in his own country with the award of the silver cross of the Knights of the Order of the Redeemer.

It was the events of World War II which led to his death. The Italian army invaded Greece in October 1940 but were pushed back by the Greek army. Germany intervened to help the Italians in April 1941 and by May of that year Greece was defeated and occupied by Germany, Italy and Bulgaria. The occupying forces plundered the fuel supplies, food and industry. The situation was made worse by an Allied naval blockage of Greece, aimed at weakening the military efforts of the occupying forces but had the effect of cutting of all food imports. The lack of food was serious by the summer of 1941 and by the winter of 1941-42 had turned into a major famine with large numbers of Greeks starving to death. Although Hatzidakis spoke German and Italian fluently, there was no way he would socialise with the occupying forces and he starved to death in January 1942.

Hatzidakis's children Sophia and Ioannis survived and inherited his large library, which consisted of about eight hundred volumes of foreign books and a great number of manuscripts with his own work. His children donated these books to various local institutions and libraries as well as to libraries in universities abroad. His large collection of Higher Mathematics works was donated by Sophia and Ioannis to the University of Athens in 1946 in memory of their father. They also donated his books to the public libraries of Athens, Thessaloniki and various other cities in Greece, as well as to the Student's Unions at the Universities of Athens and Thessaloniki.

### References (show)

- C P Fili, Panagiotis Zervos (1878-1952) - Georgios Remoundos (1878-1928) - Nikolaos Hatzidakis (1872-1942): Fundamentals of mathematics in Greece in the 20th century (Greek),
*The News*(14 January 2000), N14. - M Iacovidou, Nikolaos Hatzidakis (1872-1942), Translation of various Greek documents concerning Hatzidakis,
*University of St Andrews*(July 2018). - M Kassiouras, Nikolaos Hatzidakis (1872-1942),
*Euclid***4**(7) (1971). - M Kassiouras, Nikolaos Hatzidakis (1872-1942),
*Euclid***8**(7) (1971).

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Written by J J O'Connor and E F Robertson

Last Update January 2019

Last Update January 2019