**Nicolae Abramescu**, the son of a priest, was born at Târgoviște in March 1884. Târgoviște, the ancient capital of Wallachia, is on the Ialomita river about 70 km north east of Bucharest. Nicolae attended primary and secondary school in his home town of Târgoviște before going to the high school in Ploiești. He graduated from the high school with his licence in mathematics in 1901. Already Abramescu had become fascinated by mathematics and, while a high school student, he had avidly read the

*Gazeta Matematica*(The Mathematical Gazette) and began to make contributions to this publication.

After graduating from the Ploiești High School, Abramescu entered the Mathematics programme in the Faculty of Science of the University of Bucharest. There he was a fellow student of Traian Lalescu (1882-1929) who also went on to become an important mathematician working mainly on integral equations. Abramescu graduated from the University of Bucharest in 1904 and, later that year, he was appointed as a substitute teacher in the secondary school in Ploiești. While he was teaching mathematics in this school he wrote his first book, *Lectures in Analytical Geometry for Eighth Grade Students* which was published a few years later in 1907. The book ran to several editions. One of the students he taught while at this school was Aurel Angelescu who was in the eighth grade when Abramescu gave the course that became his book. Abramescu went from Ploiești to Botoșani where again he was a substitute teacher. In Botoșani, at the school August Treboniu Laurian, he gave an algebra course which he published as a book for eighth grade students. First published in 1907, it ran to eight editions between 1907 and 1943. Having passed the necessary examinations, these two appointments completed his training to become a secondary school teacher. He left Botoșani when he was named as professor of mathematics at the school V Alecsandri in Galați taking up his appointment on 1 October 1907. He continued to teach there until September 1919. While in Galați he wrote the book *Formulas for the geometry of the triangle* and produced two manuals, *Mechanics for seventh grade students* and *Trigonometry for sixth grade students*. These school textbooks were renowned for the clarity of their style and the depth of ideas that they presented. They were used in secondary schools in Romania for around forty years.

In November 1919 Abramescu was appointed as an Associate Professor at the University of Cluj, following the recommendation of Gheorghe Țițeica. This appointment means that he was a founder member of the Faculty of Science of the University of Cluj. Here, together with Aurel Angelescu and Gheorghe Bratu, he formed a strong and valuable kernel around Dimitrie Pompeiu, the Director of the Mathematical Seminar. He worked on his doctoral dissertation and, in July 1921, he was awarded his Ph.D. in Mathematics from the University of Bucharest with a dissertation on the *Theory of the systematization of the orthogonal polynomials*. His thesis was not published. On 15 September 1921 he was appointed as a lecturer at the Polytechnic School of Bucharest. He held this position until early in the year 1923.

On 15 February 1923, after an examination, he was appointed Professor of Analytical Geometry in Cluj. At the same time, he was given the position the substitute teacher of descriptive geometry at Cluj. On 1 October 1926, Abramescu was appointed full professor of Descriptive and Infinitesimal Geometry at the University of Cluj, a position that he kept until the end of his career. Gheorghe Țițeica sent him a letter a few days after his appointment to the chair at Cluj giving him some advice (see for example [2]):-

World War II caused major disruptions for those teaching at Cluj and in particular it caused huge problems for Abramescu. To understand the difficulties we need to look at the history of universities in Cluj.I think that in Cluj you will find a serene academic atmosphere to continue your work. You owe it as a true soldier to hold up the flag. Keep in touch with other countries, I can say you should publish your work in foreign places as well. It is good that our country is known for science. It is the best, most serious and most reliable propaganda. However, you should publish only serious things.

Now Cluj had, with the rest of Transylvania, been incorporated into Romania with the Treaty of Trianon in 1919. The University in Cluj, which had been named the Franz Joseph University since 1881, became a Romanian institution and was officially opened as such by King Ferdinand on 1 February 1920. The Hungarian university in Cluj moved first to Budapest, then to Szeged. The university in Cluj was, during these years between the two World Wars, named King Ferdinand I University. In August 1940, after the start of World War II, the north-west part of Romania (including Cluj) was surrendered to Hungary in the Vienna Dictate. This was a decision taken in Vienna under severe pressure from the German Third Reich. The Hungarian university was moved back from Szeged to Cluj, and the Romanian university in Cluj moved to Alba-Iulia, Turda, Sibiu and Timișoara. In fact the Faculty of Sciences was moved to Timișoara, while the rest of the faculties were moved to Sibiu. All of them began operating in November 1940. Abramescu was one of 26 professors who signed a petition protesting against this break-up of the University of Cluj. He spent the years 1941-43 partly in Cluj where he participated in the Mathematical Society, and partly in Timișoara. In 1945, following the end of World War II, the Romanian University returned to Cluj and was named Babeș University (after the Romanian natural scientist Victor Babeș). Abramescu did much work in restoring the mathematics library and teaching equipment. Parts of the Hungarian university in Cluj moved back to Szeged, while that part which remained in Cluj was named the Bolyai University (after the mathematician János Bolyai). It was given the building that had belonged to Queen Mary Grammar School for girls.

At the University of Cluj, Abramescu taught many different courses throughout his career. For example he taught courses on elementary geometry, analytic geometry, mechanics, higher algebra, descriptive geometry, pure infinitesimal geometry, pure higher geometry, non-Euclidean geometry, and vector geometry. We mentioned above some of the high school level texts that Abramescu wrote. He also wrote a number of undergraduate level texts which were very popular. Many of these were lithographed notes (in Romanian) of the courses he gave in Cluj such as *Analytical Geometry*, *Pure Infinitesimal Geometry*, *Non-Euclidean Geometries*, and *Descriptive Geometry*. In printed format he published *Lectures on Analytical Geometry*, which was subtitled *Introduction to Elementary Studies in Analytic and Non-Euclidean Geometry and Elementary Notes on Vector Geometry *(3 editions, 1927, 1937, 1944), and *Lessons on Pure Infinitesimal Geometry with Applications to Descriptive Geometry* (1 edition, 1930). The 1927 edition of *Lectures on Analytical Geometry* was dedicated to Gheorghe Țițeica. This edition had a Preface written by Țițeica who heaps praise on his former student Abramescu:-

In the second edition, published in 1937, Abramescu says that the work he has put into writing the book would be well rewarded if it helps students, fills them with enthusiasm and hope for the future. When the third edition appeared in 1944, Petre Sergescu wrote in a review [7]:-I met him first as an enthusiastic high school student, as a correspondent to the Mathematical Gazette, then as a student and high school teacher. I have rarely seen an example of someone with more perseverance and unwavering love of science. Nicholas Abramescu is an example of someone with titanic and rare will power who deserves to be known, so that his example can be followed. Having been a high school teacher for a long time, he made the heroic decision to prepare his doctoral thesis and to write papers which have led to him being today a professor.

The second of these books,It is a rich and valuable source of information for anyone who wants to delve deeper into the study of geometry, and can bring the greatest benefits to students of the Faculties of Science and Polytechnics. We strongly recommend it.

*Lessons on Pure Infinitesimal Geometry*, was dedicated to:-

Gino Loria wrote in a review of this book:-Maurice d'Ocagne, member of the Institute of France, professor at the École Polytechnique in Paris.

Nicolae Abramescu put a lot of effort in organising the Cluj Scientific Society, and the First Congress of Romanian Mathematicians which was held in Cluj from 9 - 12 May 1929. He was president of the Second Congress of Romanian Mathematicians held in Turnu Severin (now Drobeta-Turnu Severin) from 5 - 9 May 1932. He was on the organising committee of the Third Congress of Romanian Mathematicians held in Bucharest from 29 October to 3 November 1945. He was also a founder member of the Cluj journalWhat is special in this work is that Abramescu uses descriptive geometry methods in an analytical study of curves and surfaces in the neighbourhood of a point. In this way, he shows with elegance how easy it is to solve a pure infinitesimal geometry problem using methods of descriptive geometry.

*Mathematica*which began publishing in 1929.

Among the honours given to Abramescu we mention his election to the Romanian Academy of Sciences on 5 June 1943. He was also elected to the Cluj Scientific Society, the French Mathematical Society, the Mathematical Circle of Palermo, and the German Mathematical Society.

Abramescu died in February 1947 at Cluj.

**Article by:** *J J O'Connor* and *E F Robertson*

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