Bohdan Suchava’s recently published research – “The depth of this peace grows – Erlangen program and poetics The second game” [1] explores the connections between the set of ideas on which poetics is built The second game Ion Barbu and the set of ideas on which the mathematical work of Dan Barbilian is built. Understanding these connections is conditional (1) on knowledge of the chronology of Dan Barbilian’s mathematical, poetic and existential experiences in the 20s of the last century and (2) on knowledge, at least qualitatively, of Felix Erlangen Klein’s program.

(1) Let’s take a look at the timeline first:

In the autumn of 1920, Barbilian graduated from the Faculty of Natural Sciences of the University of Bucharest with some delay caused by the interruption of his studies due to the war. He will soon receive a scholarship from the Ministry of Education to study in Germany. Against the advice of Gheorghe Shiteica to choose Hamburg to work with one of the geometers who had the most intensive creative activity in the period immediately after the World War, namely Blaschke, Barbilian chooses Göttingen, fascinated by the prospect of learning from the great Hilbert. – which then intended to enter a marked decline. Arrival in Germany, admiration Crairs... overcomes his fascination with mathematics, and Barbilian’s German journey ends disappointingly.

Even in a situation where his success as a mathematician seemed doubtful and his success as a poet obvious (1927), Barbilian states:

I consider myself more of a practitioner of mathematics and less of a poet, and only so long as poetry resembles geometry. As contradictory as these two terms may seem at first glance, somewhere in the high realm of geometry is a bright spot where it meets poetry.

Returning to the country, Barbilian’s career, which is seriously threatened by academic failures, is saved by Gheorghe Siceik, who invites him to join the doctoral program; he defended his thesis in 1929 and with this success entered a new stage of his life as a mathematician.

Also in 1929, Barbilian sends poems to be composed for publication The second game; in 1930, the volume received the poetry prize of the Society of Romanian Writers.

Thus, 1929 is the year Dan Barbilian begins his career as a mature mathematician, in which Jon Barbu prepares a highly successful editorial debut and also abandons poetry. Since then, his creative valences seem to be better appreciated by mathematics than by poetry. The new universe created by mathematics seems to have more concreteness, more radiation in the spiritual world, and is more comprehensible than the one created by poetry [2].

(2) Now let’s turn to the Erlangen program:

In 1872, 23-year-old Felix Klein was appointed professor of mathematics at the University of Erlangen. [3]. The inaugural conference he presented at his installation, in accordance with the customs of higher education in Germany at the time, went down in the history of mathematics as the Erlangen Program. The real name of the conference Comparative considerations about the latest geometric studies.

“Program…” appears about two generations after the creation of non-Euclidean geometries by Lobachevsky, Bolyai and Gauss. These new geometries were the product of the inspiration of brilliant minds, not the result of a specific research strategy. The shortcoming of this approach is eliminated by Klein in his “Program”: the novelty lies in the definition of geometry not on a plane or in ordinary space. [4]but on some diversity [5]. Namely, geometry was defined by Klein by properties of invariance of a manifold with respect to a group of transformations [6]. According to Klein, the study of what does not change, what remains invariant, regardless of what transformations it undergoes, is important for understanding mathematical space.

The Erlangen program represents for geometry a principle with an ordering power analogous to the periodic table of elements for chemistry, argued Richard Courant. It brings clarity, brevity, and order to the jungle of mathematical objects.

For the Romanian reader, a monograph important for understanding the Erlangen Program is a happy coincidence, namely Lectures on the development of mathematics in the 19th centuryby Felix Klein [7], arrived in bookstores a few months before Bohdan Suchava’s book. The translation is by the late Mircea Iosifescu, a well-known specialist in the mathematical fields developed in Klein’s book from the perspective of their application to quantum physics. In addition, the humanist culture of the translator allowed him to develop a complex critical apparatus, in which historical events, biographical aspects, epistolary sources contained in the huge correspondence of great mathematicians of the 19th century and often mentioned by Klein, make up a matrix in which purely scientific aspects appear not as rigid statements of mathematical results, and as voices in a seductive polyphony. Because, lectures In part, Klein’s books can be extremely useful reading even for people without special mathematical training.

(3) What is the connection of the above with the poetry of Ion Barbu?

The central statement proposed by Bohdan Suchava is that the poems of The second game to extend to poetics the research of the general approach that was announced in mathematics by the Erlangen program… It is important for the transfer of the mathematical approach to poetry that “the idea of ​​invariant is connected with the idea of ​​beauty: it is so aesthetic and substantive describe in a poem what does not change: invariant,remainder. Thus, poetry becomes a game of imagination and intellect; Isn’t the discovery of an invariant an act of maximum intelligence and essentialization of the world?”

The way in which the world can be mathematized and the way in which the world can be poeticized follow the same rules of brevity, according to our author. Therefore, both the poetry of Ion Barbu and the mathematics of Dan Barbilian are extremely difficult to access, and this is not because of the frivolous search for hermeticism, but because of the consequence of following a distillation of form that is Gaussian in origin. “It doesn’t matter how many contemporaries know, the important truth is that few people reach anyway,” Barbilian says, referring to one of his courses he teaches to mathematics students.

The poetic part and the mathematical part of the work of Barbu/Barbilyan “cannot be separated, but they must be thought together. Not only do they belong to different branches of human creativity, but they also contain ideas of great depth and complexity, and the task we assume is to throw light on the connection that unites this field of ideas. The second game we can understand the poetics of the most interesting author of Romanian modernism, a unique case that is difficult to repeat in the history of literature.” [8]

To explain this duality, Bohdan Suchava’s essay can be considered, in my opinion, one of the most important editorial events of 2022. Read the whole article and comment on Contributors.ro