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

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

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, mathematical structure, structure, space, Mathematica ...

who made important contributions in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

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

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

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. It is one of six Romanian county seats lying on the river Danube. "Drobeta" is the name ...

, western

Oltenia Oltenia (), also called Lesser Wallachia in antiquated versions – with the alternative Latin names , , and between 1718 and 1739 – is a historical province and geographical region of Romania in western Wallachia. It is situated between the Da ...

, 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 regions of Romania, 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/km ...

. 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 The Carol I National College () is a high school located in central Craiova, Romania, on Ioan Maiorescu Street. It is one of the most prestigious secondary education institutions in Romania. Between 1947 and 1997 it operated under the name of Nic ...

Craiova Craiova (, also , ) is the largest city in southwestern Romania, List of Romanian cities, the seventh largest city in the country and the capital of Dolj County, situated near the east bank of the river Jiu River, Jiu in central Oltenia. It i ...

, 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 ( , ; ) is the capital and largest city of Romania. The metropolis stands on the River Dâmbovița (river), Dâmbovița in south-eastern Romania. Its population is officially estimated at 1.76 million residents within a greater Buc ...

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

University of Bucharest The University of Bucharest (UB) () is a public university, public research university in Bucharest, Romania. It was founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princely Academy of Bucharest, P ...

'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 Iacob N. Lahovary (; 16 January 1846 – 7 February 1907) was a member of the Romanian aristocracy, a general, politician and diplomat who served as the Minister of War and Minister of Foreign Affairs of the Kingdom of Romania. Life and care ...

. In June 1895, he graduated with a

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

. 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 Galați ( , , ; also known by other #Etymology and names, alternative names) is the capital city of Galați County in the historical region of Western Moldavia, in eastern Romania. Galați is a port town on the river Danube. and the sixth-larges ...

. 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, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

. Among his mates were

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

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 in 1897, he was admitted at the

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

, where he took classes with

Paul Appell Paul may refer to: People * Paul (given name), a given name, including a list of people * Paul (surname), a list of people * Paul the Apostle, an apostle who wrote many of the books of the New Testament * Ray Hildebrand, half of the singing duo P ...

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

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 s ...

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. Hermite p ...

, 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 th ...

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

, 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. H ...

. Țițeica chose Darboux to be his thesis advisor; after working for two years on his

doctoral A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

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 () is a technical university in Bucharest, Romania 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 The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

(ICM) in

Toronto Toronto ( , locally pronounced or ) is the List of the largest municipalities in Canada by population, most populous city in Canada. It is the capital city of the Provinces and territories of Canada, Canadian province of Ontario. With a p ...

(1924),

Zürich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

(1932), and

Oslo Oslo ( or ; ) 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 of 1,064,235 in 2022 ...

(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 Liège ( ; ; ; ; ) is a City status in Belgium, city and Municipalities in Belgium, municipality of Wallonia, and the capital of the Liège Province, province of Liège, Belgium. The city is situated in the valley of the Meuse, in the east o ...

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 hono ...

'' of the

University of Warsaw The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well ...

. In 1926, 1930, and 1937 he gave a series of lectures as titular professor at the Faculty of Sciences in Sorbonne. He also gave many lectures at the Free University of Brussels (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 list of members of the Romanian Academy, titular member of the Romanian Academy. His research was mainly in the fields of mathemati ...

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 mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordi ...

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

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 Șerban is a common name in Romania. It may be phonetically transcribed as Sherban or written without diacritics as Serban. It is also used by the Aromanians. Persons named Șerban include: Surname * Alina Șerban, Roma actress and writer * Andre ...

(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 Sector 1 is an administrative unit of Bucharest located in the northern part of the city. It contains also the northwestern districts of Băneasa and Pipera. Sector 1 is thought to be the wealthiest sector in Bucharest. Like each of Bucharest sec ...

of Bucharest; Țițeica moved there around 1913, when he was elected to the academy. A

commemorative plaque A commemorative plaque, or simply plaque, or in other places referred to as a historical marker, historic marker, or historic plaque, is a plate of metal, ceramic, stone, wood, or other material, bearing text or an image in relief, or both, ...

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. T ...

. A high school in

Drobeta-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. It is one of six Romanian county seats List of cities and towns on the river Danube, lyin ...

and a gymnasium in

bear his name, and so does a street in Sector 2 of Bucharest. The

Romanian Academy The Romanian Academy ( ) 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 bylaws, the academy's ma ...

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. It is widely regarded as the most prestigious mathematical competition in the wor ...

, 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 Scott may refer to: Places Canada * Scott, Quebec, municipality in the Nouvelle-Beauce regional municipality in Quebec * Scott, Saskatchewan, a town in the Rural Municipality of Tramping Lake No. 380 * Rural Municipality of Scott No. 98, Sas ...

#1415); he also figures on a 2 lei stamp from 1945 commemorating the founding of ''Gazeta Matematică'' in 1895 (

#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 Romanian 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 Academic staff of the University of Bucharest Academic staff of the Politehnica University of Bucharest Burials at Bellu Cemetery Romanian schoolteachers