# Gheorghe Țițeica

### Quick Info

Turnu-Severin, Oltenia, Austro-Hungarian Empire (now Romania)

Bucharest, Romania

**Gheorghe Țițeica**was a Romanian mathematician who worked in geometry. He was a founder of the Romanian school of differential geometry.

### Biography

**Gheorghe Țițeica**published under this version of his name and also under the version

**Georges Tzitzeica.**When he was young his interests included science, literature and especially music. He learnt to play the violin when he was young and this remained one of his pleasures throughout his life. He showed his many talents during his years in primary school in Turnu Severin. By 1885 when he was admitted to the prestigious secondary school "Carol I" National College in Craiova (today named Nicolae Balcescu College) his parents knew that they had a remarkably talented son.

In Craiova he continued to achieve top grades, and he also spent time in pursuing his musical interests as a relaxation. The city, situated near the Jiu River, 185 km west of Bucharest, was a good centre for music and the arts which suited Țițeica very well. He graduated from secondary school in Craiova in 1882 and was awarded a scholarship to train to become a teacher at the Training College in Bucharest. He went to Bucharest where, in addition to studying at the Training College, he attended mathematics lectures at the University. Among his lecturers were David Emmanuel, Spiru Haret, O Gogu, Dimitrie Petrescu and Iacob Lahogary. He graduated with a bachelor's degree in mathematics in June 1895 and in the autumn of that year he began teaching at the theological seminary in Bucharest while continuing his studies for his "capability examination".

He qualified as a secondary school teacher of mathematics in 1896 and later that year was appointed to the 'Vasile Alecsandri' secondary school in Galati. The city is an inland port 190 km northeast of Bucharest. Teachers at the school, and Țițeica's friends, all encouraged him to go to Paris and study further mathematics, and this he did in 1897 when he entered the École Normale Superieure. There he made friends with two other students, Henry Lebesgue and Paul Montel. Among his lecturers were a whole host of leading mathematicians including Darboux, Picard, Poincaré, Appell, Goursat, Hadamard, and Borel. After Țițeica left Paris, his close friend Lebesgue wrote about Țițeica in a letter to one of his friends (see [9]):-

I was thrilled to find him again happy, vivid, delighted to talk to me about his home, with that magnificent moral health radiating from his luminous yet thorough look in his eyes. ... I understood then, that inside himself, laid an everlasting union between the sense of the duty to be achieved and the euphoria rising from the conscience of the fulfilled duty ... and I discovered that our friendship for him was always shaded by an even greater respect.Țițeica flourished in Paris having teachers and friends with outstanding mathematical abilities who inspired him to produce excellent research. He published three papers in 1898, namely

*Sur un theoreme de M Cosserat; Sur les systemes orthogonaux*Ⓣ and

*Sur les systemes cycliques*Ⓣ. In the following year he published seven papers including his doctoral dissertation

*Sur les congruences cycliques et sur les systemes triplement conjugues*Ⓣ. His thesis was presented to the Faculty of Science and was examined on 30 June 1899 by a committee headed by Gaston Darboux.

Returning to Romania, Țițeica was appointed as an assistant professor at the University of Bucharest where he taught the course on differential and integral calculus. He was promoted to professor of Analytical Geometry at Bucharest University on 4 May 1900. He remained there until his death in 1939.

Țițeica's research contributions were mainly in geometry, in particular affine differential geometry. The author of [17] writes:-

In 1908 Țițeica showed that for a surface in Euclidean 3-space the ratio of the Gaussian curvature to the fourth power of the distance from a fixed point to the tangent plane is invariant under an affine transformation fixing O. He defined an S-surface to be any surface for which this ratio is constant. These S-surfaces turn out to be what are now called proper affine spheres with centre at O.His book

*Géométrie différentielle projective des réseaux*Ⓣ (1923) consisted mostly of Țițeica's own results. The paper [18] is devoted entirely to looking at the mathematical contents of this important work. It describes the work he did on the lattice of mutually conjugated lines on a surface and the Laplace sequence of such lattices [18]:-

Țițeica was led to these studies starting from deep research concerning deformation theory of surfaces in three dimensional Euclidean space.Further investigations of such structures led Țițeica to develop further beautiful theory which he set out in his book

*The projective differential geometry of lattices*(1927). He published

*Introduction to Differential Projective Differential Geometry of Curves*in 1931. An interesting insight into his ideas about the nature of mathematical research is given in [19]. This paper, written by Țițeica's daughter Gabriela, illustrates his thoughts on such matters by quoting passages from his notebooks.

As well as being famed for this geometrical research, Țițeica also gave a famous geometry course at Bucharest University over many years. Mihaileanu [8] reports on the topics covered by Țițeica in this course and shows how he covered different areas every year. Among these many topics were surfaces of constant curvature, ruled surfaces, metrical properties of space, minimal surfaces, Weingarten congruencies, conformal representation, and conformal geometry. One of his students, who went on the become a university professor of mathematics, wrote of his teaching (see for example [9]:-

After Tzitzeica's courses one would have left home bearing the teaching in his mind. But this is an understatement. It is hard to express in words the internal harmony of Tzitzeica's courses. Each course left you with a strong feeling of delightfulness; the one you would have expresses when being confronted with a painting. One would have left the courses of this apostle of geometry abiding by both his example of dignity and straightness that he was for his entire life and by the optimistic belief the mathematics, in general, and, especially, geometry have a high and admirable educational value for young people.Another important contribution made by Țițeica was his work with the

*Journal of Mathematics*, which published research contributions, and

*Natura*, a magazine he co-founded which published popular scientific articles. D Barbilian, at one time assistant to Țițeica, wrote of these different aspects of his contributions [9]:-

This man's life is split between the faculty, where his Analytical Geometry course flows like a river of clarity whose waters cannot be seen twice, the two magazines, and his scientific work. Unlike ours, his life passes, aside from worries, equally and exemplary.In [16] Rimer describes Țițeica's contributions to mathematics education in Romania. He notes in particular the non-parochial emphasis Țițeica placed on learning about, and incorporating, the experiences of other countries, while at the same time keeping in mind their relevance to Romanian national spirit and culture.

Many trips abroad allowed him to sample the best educational practices of other countries. He gave lecture courses at the Sorbonne in Paris in 1926, 1930 and 1937. In particular the 1930 course covered the research topics for which he achieved international distinction at that time, namely webs and congruencies. He also taught courses in Brussels in 1926 and Rome in 1937.

Țițeica was elected a corresponding fellow of the Maryland Academy of Science in 1930, a fellow of the Royal Society of Science in Liège in 1934 and, in the same year, he was awarded an honorary degree by the University of Warsaw. He was elected a corresponding member of the Romanian Academy of Sciences in May 1909, then a full member in 1913 on the death of Spiru Haret. He became vice-president of the scientific section in 1922, becoming vice-president of the Academy in 1928 as well as general secretary the following year. He also served as president of the Romanian Mathematical Society (Societatea de Stiinte Matematice din Romania) (several times) and of the Romanian Association of Science. He was honoured for his work on the promoting science by election as President of the Association for the Development and Spreading of the Sciences.

### References (show)

- G Bantas and V Cruceanu, Gheorghe Țițeica (1873-1939),
*Mem. Sect. Stiint. Acad. Romana Ser. IV***20**(1997), 321-329. - D Barbillian, Gh Tzitzeica,
*Numerus***5**(1939), 27. - F T Campan, La vie et l'activité de Georges Țițeica (Tzitzéica),
*Noesis, II, Travaux Colloq., Comité Roumain d'Histoire Philos. Sci., Bucharest, 1973*(Editura Acad. R. S. R., Bucharest, 1974), 257-263. - N Cioranescu, Gh Tzitzeica - viatasi opera,
*Buletinul Social Politic din Romania***3**(2) (1939), 170-199. - Gh Th Gheorghiu, Obituary: George Țițeica,
*Gaz. Mat.***45**(1939), 169-173; 281-288; 339-344; 396-405. - Gh Th Gheorghiu, Gh Țițeica and the influence of his work on Romanian mathematicians (Romanian), in
*'Gheorghe Țițeica and Dimitrie Pompeiu' Symposium on Geometry and Global Analysis, Bucharest, 1973*(Romanian) (Editura Acad. R.S.R., Bucharest, 1976), 77-86. - Gh Gheorghiev and G Vrănceanu, On the scientific work of Gheorghe Țițeica (Romanian), in
*'Gheorghe Țițeica and Dimitrie Pompeiu' Symposium on Geometry and Global Analysis, Bucharest, 1973*(Romanian) (Editura Acad. R.S.R., Bucharest, 1976), 49-56. - N N Mihaileanu, Gheorghe Țițeica's lectures on geometry (Romanian), in
*'Gheorghe Țițeica and Dimitrie Pompeiu' Symposium on Geometry and Global Analysis, Bucharest, 1973*(Romanian) (Editura Acad. R.S.R., Bucharest, 1976), 71-75. - F Nicolescu and L Nicolescu, Gheorghe Tzitzeica - Romanian scientist of recognition,
*Balkan J. Geom. Appl.*10 (1) (2005), 6-10. - O Onicescu, Gheorghe Țițeica and Dimitrie Pompeiu (Romanian), in
*'Gheorghe Țițeica and Dimitrie Pompeiu' Symposium on Geometry and Global Analysis, Bucharest, 1973*(Romanian) (Editura Acad. R.S.R., Bucharest, 1976), 11-19. - O Onicescu and G Vrănceanu, La vie et l'oeuvre de Georges Țițeica,
*Bull. Math. Soc. Roumaine Sci.***43**(1941), 147-161. - N M Ostianu, The Romanian geometer Gheorghe Țițeica (on the hundredth anniversary of his birth) (Russian),
*Trudy Geometr. Sem.***6**(1974), 25-36. - G Pripoae, Sur les courbes de Tzitzeica,
*Revue Roumaine des Mathematiques Pures et Appliques***29**(1984), 589-591. - G Pripoae, Sur les sousvarietes de Tzitzeica,
*Bulletin Mathematique de la Societe des Sciences RSR***30**(1986), 257-263. - I Popa, Gheorghe Țițeica and the Iasi school of geometry (Romanian), in
*'Gheorghe Țițeica and Dimitrie Pompeiu' Symposium on Geometry and Global Analysis, Bucharest, 1973*(Romanian) (Editura Acad. R.S.R., Bucharest, 1976), 87-90. - D Rimer, The modernity of the pedagogical thought of Gh Țițeica (Romanian),
*Stud. Cerc. Mat.***31**(4) (1979), 479-482. - N Soare, Gheorghe Țițeica and affine differential geometry,
*Balkan J. Geom. Appl.*10 (1) (2005), 21-23. - K Teleman, On the mathematical work of Gheorghe Tzitzeica,
*Balkan J. Geom. Appl.*10 (1) (2005), 59-64. - G Țițeica, Recollections of my father (Romanian),
*Gaz. Mat. (Bucharest)***85**(1) (1980), 17-18. - G Țițeica, From the notebooks of Professor Gheorghe Țițeica (Romanian), in
*Gheorghe Țițeica and Dimitrie Pompeiu Symposium on Geometry and Global Analysis, Bucharest, 1973*(Romanian) (Editura Acad. R.S.R., Bucharest, 1976), 93-97.

### Additional Resources (show)

Other websites about Gheorghe Țițeica:

Written by J J O'Connor and E F Robertson

Last Update July 2007

Last Update July 2007