Gheorghe Țițeica (; 4 October 1873 – 5 February 1939) publishing as George or Georges Tzitzéica) was a

Romania Romania ( ; ro, România ) is a country located at the crossroads of Central, Eastern, and Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, Serbia to the southwest, Moldova to the east, and ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who made important contributions in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

. He is recognized as the founder of the Romanian school of differential geometry.

Education

He was born in

Turnu Severin Drobeta-Turnu Severin (), colloquially Severin, is a city in Mehedinți County, Oltenia, Romania, on the northern bank of the Danube, close to the Iron Gates. "Drobeta" is the name of the ancient Dacian and Roman towns at the site, and the modern ...

, western

Oltenia Oltenia (, also called Lesser Wallachia in antiquated versions, with the alternative Latin names ''Wallachia Minor'', ''Wallachia Alutana'', ''Wallachia Caesarea'' between 1718 and 1739) is a historical province and geographical region of Romania ...

, the son of Anca (née Ciolănescu) and Radu Țiței, originally from Cilibia, in

Buzău County Buzău County () is a county (județ) of Romania, in the historical region Muntenia, with the capital city at Buzău. Demographics In 2011, it had a population of 432,054 and the population density was 70.7/km2. * Romanians – 97% * Roma ...

. His name was registered as Țițeica–a combination of his parents' surnames. He showed an early interest in science, as well as music and literature. Țițeica was an accomplished violinist, having studied music since childhood: music was to remain his hobby. While studying at the Carol I High School in Craiova, he contributed to the school's magazine, writing the columns on mathematics and studies of literary critique. After graduation in 1892, he obtained a scholarship at the preparatory school in

Bucharest Bucharest ( , ; ro, București ) is the capital and largest city of Romania, as well as its cultural, industrial, and financial centre. It is located in the southeast of the country, on the banks of the Dâmbovița River, less than north of ...

, where he also was admitted as a student in the Mathematics Department of

University of Bucharest The University of Bucharest ( ro, Universitatea din București), commonly known after its abbreviation UB in Romania, is a public university founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princel ...

's Faculty of Sciences. His teachers there included David Emmanuel,

Spiru Haret Spiru C. Haret (; 15 February 1851 – 17 December 1912) was a Romanian mathematician, astronomer, and politician. He made a fundamental contribution to the ''n''-body problem in celestial mechanics by proving that using a third degree approx ...

, Constantin Gogu, Dimitrie Petrescu, and Iacob Lahovary. In June 1895, he graduated with a

Bachelor of Mathematics A Bachelor of Mathematics (abbreviated B.Math or BMath) is an undergraduate academic degree awarded for successfully completing a program of study in mathematics or related disciplines, such as applied mathematics, actuarial science, computational ...

. In the summer of 1896, after a stint as a substitute teacher at the Bucharest theological seminary, Țițeica passed his exams for promotion to a secondary school position, becoming teacher in Galați. In 1897, on the advice of teachers and friends, Țițeica completed his studies at a preparatory school in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

. Among his mates were

Henri Lebesgue Henri Léon Lebesgue (; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of ...

and

Paul Montel Paul Antoine Aristide Montel (29 April 1876 – 22 January 1975) was a French mathematician. He was born in Nice, France and died in Paris, France. He researched mostly on holomorphic functions in complex analysis. Montel was a student of Émile ...

. After ranking first in his class and earning a second undergraduate degree from the

Sorbonne Sorbonne may refer to: * Sorbonne (building), historic building in Paris, which housed the University of Paris and is now shared among multiple universities. *the University of Paris (c. 1150 – 1970) *one of its components or linked institution, ...

in 1897, he was admitted at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, S ...

, where he took classes with Paul Appell,

Gaston Darboux Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician. Life According this birth certificate he was born in Nîmes in France on 14 August 1842, at 1 am. However, probably due to the midnigh ...

Édouard Goursat Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his ''Cours d'analyse mathématique'', which appeared in the first decade of the twentieth century. It se ...

Charles Hermite Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Hermi ...

, Gabriel Koenigs,

Émile Picard Charles Émile Picard (; 24 July 1856 – 11 December 1941) was a French mathematician. He was elected the fifteenth member to occupy seat 1 of the Académie française in 1924. Life He was born in Paris on 24 July 1856 and educated there at t ...

, Henri Poincaré, and

Jules Tannery Jules Tannery (24 March 1848 – 11 December 1910) was a French mathematician, who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard. Tannery's theorem on interchange of limits and series is named after him. He ...

. Țițeica chose Darboux to be his thesis advisor; after working for two years on his doctoral dissertation, titled ''Sur les congruences cycliques et sur les systèmes triplement conjugués'', he defended it on 30 June 1899 before a board of examiners consisting of Darboux (as chair), Goursat, and Koenigs.

Career

Upon his return to Romania, Țițeica was appointed assistant professor at the

. He was promoted to full professor on 3 May 1903, retaining this position until his death in 1939. He also taught mathematics at the

Polytechnic University of Bucharest Politehnica University of Bucharest ( ro, Universitatea Politehnica din București) is a technical university in Bucharest, Romania. 200 years of activity have been celebrated lately, as the university was founded in 1818.member of the Romanian Academy, replacing Spiru Haret. Later he was appointed in leading roles: in 1922, vice-president of the scientific section, in 1928, vice-president and in 1929 secretary general. Țițeica was also president of the , of the Romanian Association of Science, and of the Association of the development and the spreading of science. He was a vice-president of the Polytechnics Association of Romania and member of the High Council of Public Teaching. Țițeica was the president of the geometry section at the International Congress of Mathematicians (ICM) in

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the anch ...

(1924),

Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco Zürich ...

(1932), and

Oslo Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population ...

(1936). With 5 invited ICM talks (1908, 1912, 1924, 1932, and 1936), he is in a tie for 7th place among mathematicians with the most invited ICM talks. He was elected correspondent of the Association of Sciences of Liège and ''

doctor honoris causa An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad ho ...

'' of the

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields o ...

. In 1926, 1930, and 1937 he gave a series of lectures as titular professor at the Faculty of Sciences in

. He also gave many lectures at the

Free University of Brussels University of Brussels may refer to several institutions in Brussels, Belgium: Current institutions * Université libre de Bruxelles (ULB), a French-speaking university established as a separate entity in 1970 *Vrije Universiteit Brussel (VUB), a D ...

(1926) and the University of Rome (1927). His Ph.D. students include Dan Barbilian and

Grigore Moisil Grigore Constantin Moisil (; 10 January 1906 – 21 May 1973) was a Romanian mathematician, computer pioneer, and titular member of the Romanian Academy. His research was mainly in the fields of mathematical logic ( Łukasiewicz–Moisil algebra ...

Scientific work

Țițeica wrote about 400 articles, of which 96 are scientific projects, most addressing problems of differential geometry. His bibliography includes over 200 published papers and books, which appeared in many editions. Carrying on the researches of the American geometer of German origin Ernest Wilczynski, Țițeica discovered a new class of

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

s and a new class of curves which now carry his name. His contributions represent the beginning of a new chapter in mathematics, namely,

affine differential geometry Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name ''affine differential geometry'' follows from Klein's Erlangen program. The basic difference between aff ...

. He also studied webs in

n-dimensional In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...

space, defined through Laplace equations. He investigated what is now known as the Tzitzeica equation, which was further generalized by

Robin Bullough Robin K. Bullough (21 November 1929 – 30 August 2008) was a British mathematical physicist known for his contributions to the theory of solitons, in particular for his role in the development of the theory of the optical soliton, now commonl ...

and Roger Dodd (the Tzitzéica–Bullough–Dodd equation). He is also known for a result on the geometry of circles and triangles in the plane, referred to as Țițeica's , a problem he proposed (and solved) at the ' contest in Galați in 1908. The problem was posed independently by Roger Arthur Johnson in 1916, and the resulting configuration is also referred to as the

Johnson circles In geometry, a set of Johnson circles comprises three circles of equal radius sharing one common point of intersection . In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): th ...

Private life and legacy

Țițeica married Florence Thierin (1882–1965) and the couple had three children — Radu (1905–1987), Gabriela (1907–1987), and

Șerban Şerban is a common name in Romania. It may be phonetically transcribed as Sherban or written without diacritics as Serban. Persons named Şerban include: Surname * Alina Serban, Alina Șerban, Roma actress and writer * Andrei Șerban, Romanian- ...

(1908–1985) — all of whom pursued careers in academia; the youngest one became a renowned quantum physicist. The family lived in a 19th-century house on Dionisie Lupu Street, close to Lahovari Plaza, in Sector 1 of Bucharest; Țițeica moved there around 1913, when he was elected to the academy. A commemorative plaque was affixed to the house by the city administration in 1998. He died in 1939 in Bucharest and was buried in the city's

Bellu Cemetery Șerban Vodă Cemetery (commonly known as Bellu Cemetery) is the largest and most famous cemetery in Bucharest, Romania. It is located on a plot of land donated to the local administration by Baron Barbu Bellu. It has been in use since 1858. Th ...

. A high school in Drobeta-Turnu Severin and a gymnasium in Craiova bear his name, and so does a street in

Sector 2 Sector 2 ( ro, Sectorul 2) is an administrative unit of Bucharest. Demographics Sector 2 is the city's most multicultural sector. In particular, it contains Romania's largest community of Chinese people, who mainly live in the districts of C ...

of Bucharest. The

Romanian Academy The Romanian Academy ( ro, Academia Română ) is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 active members who are elected for life. According to its byl ...

offers an annual "Gheorghe Țițeica Prize" for achievements in mathematics. The logo of the 40th

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

, held in Bucharest in 1999, was inspired by Țițeica's 5 lei coin problem. In 1961,

Poșta Română CN Poșta Română SA is the national operator in the field of postal services in Romania. It is the sole supplier of universal service in any point on the Romanian territory. Poșta Română is active on the free market of value added postal ...

issued a 1.55 lei stamp in his honor ( Scott #1415); he also figures on a 2 lei stamp from 1945 commemorating the founding of ''Gazeta Matematică'' in 1895 ( Scott #596).

Publications

* * * * * *

References

{{DEFAULTSORT:Titeica, Gheorghe 1873 births 1939 deaths People from Drobeta-Turnu Severin 19th-century Romanian mathematicians 20th-century Romanian mathematicians Differential geometers Geometers Science communicators Romanian scientists Romanian inventors Carol I National College alumni University of Bucharest alumni University of Paris alumni École Normale Supérieure alumni Titular members of the Romanian Academy University of Bucharest faculty Politehnica University of Bucharest faculty Burials at Bellu Cemetery