Dimitrie D. Pompeiu (; – 8 October 1954) 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, a ...

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 ...

, professor at the

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 Princ ...

, titular member of 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 by ...

, and President of the Chamber of Deputies.

Biography

He was born in 1873 in

Broscăuți Broscăuți is a commune in Botoșani County, Western Moldavia, Romania. It is composed of two villages, Broscăuți and Slobozia. The commune had 3450 people at the 2002 census; of these, 99.9% were ethnic Romanians and 99.4% were Romanian Orth ...

Botoșani County Botoșani County () is a county (județ) of Romania, in Western Moldavia (encompassing a few villages in neigbhouring Suceava County from Bukovina to the west as well), with the capital town ( ro, Oraș reședință de județ) at Botoșani. De ...

, in a family of well-to-do peasants. After completing high school in nearby

Dorohoi Dorohoi () is a city in Botoșani County, Romania, on the right bank of the river Jijia, which broadens into a lake on the north. History Dorohoi used to be a market for the timber and farm produce of the north Moldavian highlands; merchants fr ...

, he went to study at the Normal Teachers 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 ...

, where he had

Alexandru Odobescu Alexandru Ioan Odobescu (; 23 June 1834 – 10 November 1895) was a Romanian author, archaeologist and politician. Biography He was born in Bucharest, the second child of General Ioan Odobescu and his wife Ecaterina. After attending Saint Sava ...

as a teacher. After obtaining his diploma in 1893, he taught for five years at schools in

Galați Galați (, , ; also known by other 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 Danube River. It has been the only port for the most pa ...

and

Ploiești Ploiești ( , , ), formerly spelled Ploești, is a city and county seat in Prahova County, Romania. Part of the historical region of Muntenia, it is located north of Bucharest. The area of Ploiești is around , and it borders the Blejoi commun ...

. In 1898 he went to

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan ar ...

, where he studied mathematics at the

University of Paris The University of Paris (french: link=no, Université de Paris), Metonymy, metonymically known as the Sorbonne (), was the leading university in Paris, France, active from 1150 to 1970, with the exception between 1793 and 1806 under the French Revo ...

(the Sorbonne). He obtained his Ph.D. degree in mathematics in 1905, with thesis ''On the continuity of complex variable functions'' written under the direction of

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

. After returning to Romania, Pompeiu was named Professor of

Mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects ...

at the University of Iași. In 1912, he assumed a chair at the

. In the early 1930s he was elected to the

Chamber of Deputies The chamber of deputies is the lower house in many bicameral legislatures and the sole house in some unicameral legislatures. Description Historically, French Chamber of Deputies was the lower house of the French Parliament during the Bourbon ...

as a member of

Nicolae Iorga Nicolae Iorga (; sometimes Neculai Iorga, Nicolas Jorga, Nicolai Jorga or Nicola Jorga, born Nicu N. Iorga;Iova, p. xxvii. 17 January 1871 – 27 November 1940) was a Romanian historian, politician, literary critic, memoirist, Albanologist, poet ...

's Democratic Nationalist Party, and served as President of the Chamber of Deputies for a year. In 1934, Pompeiu was elected titular member of the Romanian Academy, while in 1943 he was elected to the Romanian Academy of Sciences. In 1945, he became the founding director of the Institute of Mathematics of the Romanian Academy. He died in Bucharest in 1954. A boulevard in the Pipera neighborhood of the city is named after him, and so is a school in his hometown of Broscăuți.

Research

Pompeiu's contributions were mainly in the field of

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

, complex functions theory, and

rational mechanics Rational mechanics may refer to: *'' mécanique rationelle'', a historical (19th century) term for classical mechanics *a school of thought within physics advocated by Clifford Truesdell in the 1960s See also * Newtonianism *Auguste Comte *''Archi ...

. In an article published in 1929, he posed a challenging

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1 ...

integral geometry In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformat ...

, now widely known as the

Pompeiu problem In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929, as follows. Suppose ''f'' is a nonzero continuous function defined on a Euclidean space, and ''K'' is a simply c ...

. Among his contributions to

real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include con ...

there is the construction, dated 1906, of non-constant, everywhere differentiable functions, with derivative vanishing on a dense set. Such derivatives are now called

Pompeiu derivative In mathematical analysis, a Pompeiu derivative is a real-valued function of one real variable that is the derivative of an everywhere differentiable function and that vanishes in a dense set. In particular, a Pompeiu derivative is discontinuou ...

Selected works

*. *. *.

Biographical references

* *

References

*. ("''Areolar derivative and functions of bounded variation''" is an important reference paper in the theory of areolar derivatives.) *. {{DEFAULTSORT:Pompeiu, Dimitrie 1873 births 1954 deaths People from Botoșani County University of Paris alumni 20th-century Romanian mathematicians Complex analysts Mathematical analysts Alexandru Ioan Cuza University faculty University of Bucharest faculty Titular members of the Romanian Academy Members of the Romanian Academy of Sciences Democratic Nationalist Party (Romania) politicians Presidents of the Chamber of Deputies (Romania)