[6]: 174  He then studied with Gheorghe Țițeica, completing in 1929 his Ph.D. thesis, Reprezentarea canonică a adunării funcțiilor ipereliptice (Canonical representation of the addition of hyperelliptic functions).

[11] In the summer of 1937, he served as president of the commission administering the Baccalaureate at the Gheorghe Lazăr High School in Sibiu, after which he issued a scathing report to the Ministry of Education.

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.

A more critical stance was taken in 1995 by Ferdinand D. Velkamp: Nevertheless, in 1989 John R. Faulkner wrote an article "Barbilian Planes"[22] that clarified terminology and advanced the study.

Barbu made his literary debut in 1918 in Alexandru Macedonski's magazine Literatorul [ro], and then started contributing to Sburătorul, where Eugen Lovinescu saw him as a "new poet".

[3][28] Ut algebra poesis [Ninei Cassian] La anii-mi încă tineri, în târgul Göttingen, Cum Gauss, altădată, sub curba lui alee — Boltirea geometriei astrale să încheie — Încovoiam poemul spre ultimul catren.

As Algebra, So Poetry [For Nina Cassian] In my young days I strolled the lanes of Göttingen - Where Gauss, beneath arched canopies of leaves, Sealed once for all the vaults of higher geometries - And curved a poem towards its last quatrain.

—translation by Sarah Glaz and JoAnne Growney[28] According to Loveday Kempthorne and Peter Donelan, Barbu "saw mathematics and poetry as equally capable of holding the answer to understanding and reaching a transcendental ideal.

[29] Barbu was mostly apolitical, with one exception: around 1940 he became a sympathizer of the fascist movement The Iron Guard (hoping to be promoted to full professor if they came to power), dedicating a poem to one of its leaders, Corneliu Zelea Codreanu.

[31][8] Suceavă attributes these moves to be opportunistic devices in a professional advancement plan and ignores Barbu’s own explanation, that he was attempting to deflect attention from the fact that he was hiding in his house his wife’s brother, a German citizen who eluded conscription by staying hidden in Romania.

[30] After the Communists came to power in the wake of World War II, his friend Alexandru Rosetti sought to convince Barbu to write poems praising the new regime.

Barbu reluctantly wrote in early 1948 one poem that can be interpreted as pro-communist, namely "Bălcescu living", but he never relapsed and kept his dignified demeanor until the end.