The mathematician Dan Barbilian, aka the poet Dan Barbu

Steliu Lambru, 19.01.2025, 14:00

There are few personalities who manage to perform at a high level in different, even opposite, fields, as was the case of the mathematician Dan Barbilian, aka the poet Ion Barbu, who is remembered for having excelled at both mathematics and literature. Dan Barbilian was gifted with a unique talent for the science of mathematics and the art of poetry, but he worked hard to put it to good use.

Dan Barbilian was born in 1895 in Câmpulung Muscel into a family of magistrates and died in 1961 in Bucharest. He had been passionate about mathematics ever since primary school, and during high school he published in the magazine “Gazeta Matematica”, a mathematics magazine where we also find the most important Romanian mathematicians. His passion for poetry also dates from around this time, but it wasn’t until 1919 that he made his literary debut, in the magazine “Sburătorul”. He first studied mathematics at the University of Bucharest and, after the end of the First World War, between 1921 and 1924, he went to Germany, to study in Göttingen, Tübingen and Berlin.

In 1929, he earned his doctoral degree in mathematics under his Bucharest teacher, the mathematician Gheorghe Țițeica, and embarked on a busy scientific career,  taking part in many international congresses. He became a professor of algebra at the Faculty of Sciences in Bucharest where he taught algebra, geometry, number theory, group theory and axiomatics. He also taught courses at universities in the German-speaking world. A metrization procedure will be named after him, known as the “Barbilian spaces”, and another of his contributions paved the way for research in the geometry of rings. He also contributed to the standardization of algebraic geometry.

Mathematician and writer Bogdan Suceava told us more about the educational opportunities enjoyed by a very talented young man like Dan Barbilian in a country that was building itself up by borrowing from the European models: “Dan Barbilian wins the Gazeta Matematica competition in 1912 and, interestingly, I even found a mention of his name in the American Mathematical Society database. You really had to be someone to be mentioned there in a chapter on mathematics. Barbilian is related to 51C05, which is something from ring geometry. He introduced the spaces now named after him in 1934, but at the beginning he worked as a math solver for the magazine. He won the magazine’s competition in 1912, and later he studied in Göttingen with David Hilbert, Emmy Noether and Edmund Landau, but also produced interesting literary work. He has very important contributions in the field of algebra and is the author of an axiomatic approach to mechanics published in 1943, which went largely unnoticed. He was, creator of mathematics of the highest order, with his formative years being linked to the Gazeta Matematica.”

At the same time, mathematician Dan Barbilian wrote poetry under the name Ion Barbu, which was a return to the family’s original name. He was in the entourage of literary critic Eugen Lovinescu and his literary circle “Sburătorul”. Another literary critic, Tudor Vianu, a friend of Barbu since high school, is the author of a volume in which he analyzes the mathematician’s poetry. Thus, according to Vianu, Barbu’s poetic work is divided into several periods: the Parnassian period inspired by French Parnassian poetry until 1925, the period of the oriental ballad after 1925, inspired by Romanian authors like Anton Pann or writings whose hero was Nastratin Hogea, and the hermetic period. The last period was named as such due to the encryption of poetic meanings that Barbu makes.

Two poems from Barbu’s poetic work are very well-known today, “Riga Crypto and Enigel the Lapp” and “After the Snails”, the latter being the title of a folk song composed by Nicu Alifantis in 1979. Reading Dan Barbilian’s notes, Bogdan Suceavă was pleasantly surprised to discover a powerful literary description of the mathematician’s memories related to important moments in his life: “About the 1912 competition, he wrote in the 1950s: ‘The problem bears the seal of Ion Banciu, a member of the algebra commission, dear, unforgettable, great professor.’ Barbilian is sentimental when he wants to be. ‘Besides my father, have I met anyone who believed in me and helped me as much? Țițeica did not have Banciu’s enthusiasm, warmth, generosity. I want to remain Banciu’s student and then Felix Klein’s and Richard Dedekind’s, nobody else’s.’ Here he is a bit unfair because Țițeica helped him a lot, but I don’t think he comforted him. He gave him deadlines and Barbilian did not like deadlines. ‘What will I have written in the thesis? Țițeica’s very good appreciation of algebra surprised me. Did I manage to come out of so many numerical calculations? If the detail of the thesis escapes me, the atmosphere of that dusty hall of the School of Bridges and that almost Nordic afternoon, with polarized light, I find again. The geometry thesis passed in the morning still feels like a lived moment today. The algebra thesis remains somewhat hypnotic.’ Let’s not forget they gave them on the same day. I wouldn’t do that today. This atmosphere, that you forget yourself and that it seems like a hypnotic atmosphere while you have a competition, this yes, we can understand. That’s how it was in 1912, that’s how it was later, that’s how it is always. This intensity of a mathematics thesis remains. What’s interesting is something else: how he describes this experience four decades later, it is something remarkable. These are problems he returns to at old age and analyzes from an advanced perspective.”

Mathematician Dan Barbilian and poet Ion Barbu showed that the boundaries between fields are not fixed and that passions can be complementary. And that the human being is both reason and sentiment.