Dan Barbilian
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Ion Barbu (,
pen name A pen name, also called a ''nom de plume'' or a literary double, is a pseudonym (or, in some cases, a variant form of a real name) adopted by an author and printed on the title page or by-line of their works in place of their real name. A pen na ...
of Dan Barbilian; 18 March 1895 –11 August 1961) was a
Romania Romania ( ; ro, România ) is a country located at the crossroads of Central Europe, Central, Eastern Europe, Eastern, and Southeast Europe, Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, S ...
n
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 ...
and
poet A poet is a person who studies and creates poetry. Poets may describe themselves as such or be described as such by others. A poet may simply be the creator ( thinker, songwriter, writer, or author) who creates (composes) poems (oral or writte ...
. His name is associated with the
Mathematics Subject Classification The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. ...
number 51C05, which is a major posthumous recognition reserved only to pioneers of investigations in an area of mathematical inquiry.


Early life

Born in Câmpulung-Muscel,
Argeș County Argeș County () is a county ('' județ'') of Romania, in Muntenia, with the capital city at Pitești. Demographics On 20 October 2011, it had a population of 612,431 and the population density was 89/km2. * Romanians – 97% * Roma (Gypsi ...
, he was the son of Constantin Barbilian and Smaranda, born Șoiculescu. He attended elementary school in Câmpulung,
Dămienești Dămienești is a commune in Bacău County, Western Moldavia, 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, ...
, and
Stâlpeni Stâlpeni is a commune in Argeș County, Muntenia, Romania. It is composed of seven villages: Dealu Frumos, Livezeni, Ogrezea, Oprești, Pițigaia, Rădești, and Stâlpeni. Natives * Ilie Baicu (born 1974), footballer *Liviu Hapaină Liviu ...
, and for secondary studies he went to the Ion Brătianu High School in
Pitești Pitești () is a city in Romania, located on the river Argeș. The capital and largest city of Argeș County, it is an important commercial and industrial center, as well as the home of two universities. Pitești is situated in the historical re ...
, the Dinicu Golescu High School in Câmpulung, and finally the Gheorghe Lazăr High School and the
Mihai Viteazul High School Mihai () is a Romanian given name for males or a surname. It is equivalent to the English name Michael. A variant of the name is Mihail. Its female form is Mihaela. As a given name *Mihai I of Romania (1921–2017), King of Romania until 1947 *Miha ...
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 ...
. During that time, he discovered that he had a talent for mathematics, and started publishing in ''Gazeta Matematică''; it was also then that he discovered his passion for
poetry Poetry (derived from the Greek ''poiesis'', "making"), also called verse, is a form of literature that uses aesthetic and often rhythmic qualities of language − such as phonaesthetics, sound symbolism, and metre − to evoke meanings i ...
. Barbu was known as "one of the greatest Romanian poets of the twentieth century and perhaps the greatest of all" according to Romanian literary critic Alexandru Ciorănescu. As a poet, he is known for his volume ''Joc secund'' ("Mirrored Play"). He was a student at the University of Bucharest when
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
caused his studies to be interrupted by military service. He completed his degree in 1921. He then went to the
University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
to study
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
with Edmund Landau for two years. Returning to Bucharest, he studied with
Gheorghe Țițeica Gheorghe Țițeica (; 4 October 1873 – 5 February 1939) publishing as George or Georges Tzitzéica) was a Romanian mathematician who made important contributions in geometry. He is recognized as the founder of the Romanian school of differentia ...
, completing in 1929 his thesis, ''Canonical representation of the addition of hyperelliptic functions''.


Achievements in mathematics


Apollonian metric

In 1934, Barbilian published his article describing metrization of a region ''K'', the interior of a
simple closed curve In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior ...
''J''. Let ''xy'' denote the
Euclidean distance In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefor ...
from ''x'' to ''y''. Barbilian's function for the distance from ''a'' to ''b'' in ''K'' is :d(a,b) = \log \underset (pa/pb) + \log \underset (qb/qa) . At the
University of Missouri The University of Missouri (Mizzou, MU, or Missouri) is a public university, public Land-grant university, land-grant research university in Columbia, Missouri. It is Missouri's largest university and the flagship of the four-campus Universit ...
in 1938
Leonard Blumenthal Leonard Mascot Blumenthal (February 27, 1901 – August 1984) was a Jewish American mathematician. He received his Ph.D. in 1927 from Johns Hopkins University, under the supervision of Frank Morley; his dissertation was titled ''Lagrange Reso ...
wrote ''Distance Geometry. A Study of the Development of Abstract Metrics'', where he used the term "Barbilian spaces" for
metric space In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general settin ...
s based on Barbilian's function to obtain their
metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathema ...
. And in 1954 the
American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an e ...
published an article by Paul J. Kelly on Barbilian's method of metrizing a region bounded by a curve. Barbilian claimed he did not have access to Kelly's publication, but he did read Blumenthal's review of it in
Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...
and he understood Kelly's construction. This motivated him to write in final form a series of four papers, which appeared after 1958, where the metric geometry of the spaces that today bears his name is investigated thoroughly. He answered in 1959 with an article which described "a very general procedure of metrization through which the positive functions of two points, on certain sets, can be refined to a distance." Besides Blumenthal and Kelly, articles on "Barbilian spaces" have appeared in the 1990s from Patricia Souza, while Wladimir G. Boskoff, Marian G. Ciucă and
Bogdan Suceavă Bogdan Suceavă (born September 27, 1969) is a Romanian-American mathematician and writer. Biography He was born in Curtea de Argeș, Romania. Growing up, Suceavă spent his holidays with his maternal grandparents at Nucșoara, a remote communit ...
wrote in the 2000s about "Barbilian's metrization procedure". Barbilian indicated in his paper ''Asupra unui principiu de metrizare'' that he preferred the term "
Apollonian The Apollonian and the Dionysian are philosophical and literary concepts represented by a duality between the figures of Apollo and Dionysus from Greek mythology. Its popularization is widely attributed to the work ''The Birth of Tragedy'' by Fri ...
metric space", and articles from
Alan F. Beardon Alan Frank Beardon (April 16, 1940) is a British mathematician. Education and career Beardon obtained his doctorate at Imperial College London in 1964, supervised by Walter Hayman. In 1970 he was appointed as a lecturer in the Department of Pu ...
,
Frederick Gehring Frederick William Gehring (7 August 1925 â€“ 29 May 2012) was an American mathematician who worked in the area of complex analysis (quasi-conformal mappings). Personal life Both of Fred Gehring's parents graduated from the University o ...
and Kari Hag, Peter A. Häströ, Zair Ibragimov and others use that term. According to Suceavă, "Barbilian's metrization procedure is important for at least three reasons: (1) It yields a natural generalization of Poincaré and Beltrami-Klein's hyperbolic geometries; (2) It has been studied in the context of the study of Apollonian metric; (3) Provides a large class of examples of Lagrange generalized metrics irreducible to Riemann, Finsler, or Lagrange metrics."


Ring geometry

Barbilian made a contribution to the
foundations of geometry Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but t ...
with his articles in 1940 and 1941 in
Jahresbericht der Deutschen Mathematiker-Vereinigung The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathe ...
on projective planes with coordinates from a
ring Ring may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell :(hence) to initiate a telephone connection Arts, entertainment and media Film and ...
. According to Boskoff and Suceavă, this work "inspired research in ring geometries, nowadays associated with his, Hjelmslev's and Klingenberg's names." A more critical stance was taken in 1995 by Ferdinand D. Velkamp: :A systematic study of projective planes over large classes of associative rings was initiated by D. Barbilian. His very general approach in 940 and 41remained rather unsatisfactory, however, his axioms were partly of a geometric nature, partly algebraic as pertaining to the ring of coordinates, and there were a number of difficulties which Barbilian could not overcome. Nevertheless, in 1989 John R. Faulkner wrote an article "Barbilian Planes" that clarified terminology and advanced the study. In his introduction, he wrote: :A classical result from projective geometry is that a
Desarguesian In projective geometry, Desargues's theorem, named after Girard Desargues, states: :Two triangles are in perspective ''axially'' if and only if they are in perspective ''centrally''. Denote the three vertices of one triangle by and , and tho ...
projective plane is coordinatized by an associative division ring. A Barbilian plane is a geometric structure which extends the notion of a projective plane and thereby allows a coordinate ring which is not necessarily a division ring. There are advantages ...


Works

* 1956: , Bucharest. * 1960: , Bucharest.


Academic career

In 1942, Barbilian was named professor at the University of Bucharest, with some help from fellow mathematician Grigore Moisil. As a mathematician, Barbilian authored 80 research papers and studies. His last paper, written in collaboration with Nicolae Radu, appeared posthumously, in 1962, and is the last in the cycle of four works where he investigates the Apollonian metric.


Political creed

Barbu was mostly apolitical, with one exception: around 1940 he became a sympathizer of the fascist movement
The Iron Guard The Iron Guard ( ro, Garda de Fier) was a Romanian militant revolutionary fascist movement and political party founded in 1927 by Corneliu Zelea Codreanu as the Legion of the Archangel Michael () or the Legionnaire Movement (). It was strong ...
(hoping to get a professorship if they came to power), dedicating some poems to one of its leaders, Corneliu Zelea Codreanu. In 1940, he also wrote a poem praising
Hitler Adolf Hitler (; 20 April 188930 April 1945) was an Austrian-born German politician who was dictator of Germany from 1933 until his death in 1945. He rose to power as the leader of the Nazi Party, becoming the chancellor in 1933 and then ...
.


Death and legacy

Ion Barbu died 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 ...
in 1961, and is buried at Bellu Cemetery. The Ion Barbu Theoretical High School in
Pitești Pitești () is a city in Romania, located on the river Argeș. The capital and largest city of Argeș County, it is an important commercial and industrial center, as well as the home of two universities. Pitești is situated in the historical re ...
, the Ion Barbu Technological High School in
Giurgiu Giurgiu (; bg, Гюргево) is a city in southern Romania. The seat of Giurgiu County, it lies in the historical region of Muntenia. It is situated amongst mud-flats and marshes on the left bank of the Danube facing the Bulgarian city ...
, and the
Dan Barbilian Theoretical High School Dan or DAN may refer to: People * Dan (name), including a list of people with the name ** Dan (king), several kings of Denmark * Dan people, an ethnic group located in West Africa **Dan language, a Mande language spoken primarily in Côte d'Ivoir ...
in
Câmpulung Câmpulung (also spelled ''Cîmpulung'', , german: Langenau, Old Romanian ''Dlăgopole'', ''Длъгополе'' (from Middle Bulgarian)), or ''Câmpulung Muscel'', is a municipality in the Argeș County, Muntenia, Romania. It is situated among t ...
are all named after him.


Presence in English language anthologies

* ''Born in Utopia - An anthology of Modern and Contemporary Romanian Poetry -'' Carmen Firan and Paul Doru Mugur (editors) with Edward Foster - Talisman House Publishers - 2006 - * ''Testament - Anthology of Romanian Verse - American Edition -'' monolingual English language edition - Daniel Ioniță (editor and principal translator) with Eva Foster, Daniel Reynaud and Rochelle Bews - Australian-Romanian Academy for Culture - 2017 - * T''estment – 400 Years of Romanian Poetry – 400 de ani de poezie românească'' – bilingual edition – Daniel Ioniță (editor and principal translator) with
Daniel Reynaud Daniel Reynaud (born 27 August 1958) is an Australian historian whose work on Australian war cinema and on Australian World War I soldiers and religion has challenged aspects of the Anzac legend, Australia’s most important national mythology ...
, Adriana Paul & Eva Foster – Editura Minerva, 2019 – * ''Romanian Poetry from its Origins to the Present'' – bilingual edition English/Romanian – Daniel Ioniță (editor and principal translator) with
Daniel Reynaud Daniel Reynaud (born 27 August 1958) is an Australian historian whose work on Australian war cinema and on Australian World War I soldiers and religion has challenged aspects of the Anzac legend, Australia’s most important national mythology ...
, Adriana Paul and Eva Foster – Australian-Romanian Academy Publishing – 2020 – ;


References

{{DEFAULTSORT:Barbu, Ion 1895 births 1961 deaths People from Câmpulung Gheorghe Lazăr National College (Bucharest) alumni University of Bucharest alumni University of Bucharest faculty Romanian avant-garde Romanian male poets 20th-century Romanian inventors Romanian textbook writers 20th-century Romanian mathematicians 20th-century Romanian poets 20th-century Romanian male writers Pseudonymous mathematicians Members of the Romanian Academy elected posthumously Members of the Romanian Academy of Sciences Burials at Bellu Cemetery Geometers 20th-century pseudonymous writers