Born in Câmpulung-Muscel, Arge? County, he was the son of Constantin Barbilian and Smaranda, born ?oiculescu. He attended the Ion Br?tianu High School in Pite?ti and the Gheorghe Laz?r High School in Bucharest. During that time, he discovered that he had a talent for mathematics, and started publishing in Gazeta Matematic?; it was also then that he discovered his passion for poetry. 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 Cior?nescu. As a poet, he is known for his volume Joc secund ("Mirrored Play").
In 1934, Barbilian published his article describing metrization of a region K, the interior of a simple closed curveJ. Let xy denote the Euclidean distance from x to y. Barbilian's function for the distance from a to b in K is
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. Ciuc? and Bogdan Suceav? write in the 2000s about "Barbilian's metrization procedure". Barbilian indicated in his paper Asupra unui principiu de metrizare that he prefers the term
"Apollonian metric space", and articles from Alan F. Beardon, Frederick Gehring and Kari Hag, Peter A. Häströ, Zair Ibragimov and others use that term.
A systematic study of projective planes over large classes of associative rings was initiated by D. Barbilian. His very general approach in [1940 and 41] remained 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 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 ...
1956: Teoria aritmetic? a idealelor (în inele necomutative), Editura Academiei, Bucharest, Romania
1960: Grupuri cu operatori: Teoremele de descompunere ale algebrei, Editura Academiei, Bucharest, Romania
As a mathematician, Barbilian authored 80 research papers and studies. His last two papers, written in collaboration with Nicolae Radu, appeared posthumously, in 1962.
Barbu was mostly apolitical, with one exception: around 1940 he became a sympathizer of the fascist movement The Iron Guard (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.
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 - ISBN1-58498-050-8
Testament - Anthology of Modern Romanian Verse / Testament - Antologie de Poezie Român? Modern? - Bilingual Edition English & Romanian - Daniel Ionita (editor and translator) with Eva Foster and Daniel Reynaud - Minerva Publishing 2012 and 2015 (second edition) - ISBN978-973-21-1006-5
Testament - Anthology of Romanian Verse - American Edition - monolingual English language edition - Daniel Ionita (editor and principal translator) with Eva Foster, Daniel Reynaud and Rochelle Bews - Australian-Romanian Academy for Culture - 2017 - ISBN978-0-9953502-0-5