The article « Vulnerable Paul Valéry Between Poetry and Mathematics » has appeared in the Antioch Review (Fall 2018, Volume 76, No. 4). At the same time, a shorter French version of the same essay has appeared in the volume Paul Valéry et les écrivains (Éditions Fata Morgana, 2018). The opening passage:
« Having been in the early 1970s a well-behaved math major (who subsequently wandered off into the wilds of poetry and foreign languages), I remain curious about poets, both contemporary and classic, who are similarly drawn to algebra, topology, and the foundations of mathematics. I mention these more abstract fields (and let’s add set theory) because, when I meditate on the ways mathematics and poetry might enter into dialogue, I mostly exclude “computation,” that is, formal approaches such are practiced by the French Oulipo group (Ouvroir de littérature potentielle), who set down mathematical “constraints” according to which a literary text can be composed. This said, the Oulipean poet Jacques Roubaud (who was long a professor of mathematics), once evoked an autobiographical memory that rings a deep bell in me. In his memoir Mathématique: —and that colon in the title resonates—he admits that he could not bear sitting in on classes about poetry when he was a student because poetry mattered too much to him. So he switched majors and signed up for mathematics. Poetry was also my secret passion when I was studying mathematics and I preferred watching proofs unfolding on a blackboard than listening to a well-meaning English professor explicate Emily Dickinson.
« I’m thus thinking of how a poet might face up to, even reach out towards mathematics as a “language,” as a fountainhead of unusual images and ideas (which might or might not exist in “reality”), and as a kind of “beauty” that derives from the “elegance” of a proof combining concision, astuteness, resourcefulness, and novelty. These latter qualities are also, of course, literary. And so are questions such as “what is reality?” or “to what extent is language, mathematical or not, real?” When I mentioned this topic many years ago to Yves Bonnefoy, who had also studied mathematics before turning to art history and poetry, he told me that the symbolism and syntax of mathematical proofs, especially in their “purest” forms, were analogous to the ways by which some poets, such as himself, constructed and revised poems (which otherwise, to his mind, stemmed from the unconscious, without which no “presence” in the poem would arise).
« I have started wondering again about poetry and mathematics because I have been invited to read my poems at the “Journées Paul Valéry” festival in Sète, France. The organizer had asked each of us to begin our reading by devoting about ten minutes to explaining our relationship to Valéry’s poetry. This is an intimidating requirement. Will I be able to come up with anything to say in front of several Valéry scholars who will also be present? I perused Valéry’s poetry some forty years ago and it has exerted, as far as I can tell, no influence on mine. By the way, Bonnefoy somewhat conspicuously did not recognize any debt to Valéry’s poetry, even calling for it to be “forgotten”—although he later expressed regret about his harshness. In an essay collected in L’improbable, he considers Valéry to speak “of the clarity of the mind when he has consented, in his body and heart, to be a shade” and judges the poetry to be “that mixture of divertimento and knowledge, that game of chess that one never stops playing with ideas or their echoes.”
« Now I have done some in-house investigating. On a low bookshelf in the “V” section of my bookcases (and this section lies in a rather dark corner of my study), I have come across my old copy of a paperback selection of Valéry’s essays in translation: The Art of Poetry (translated by Denise Folliot, Vintage Books, 1961). The book goes back to my student years. T. S. Eliot was the prefacer. Like Eliot, Valéry seeks to understand how essential philosophical questions can be dealt with in poetry. As a math major drawn to algebra and topology (and Valéry relished algebra, geometry, and the first revolutionary developments in topology as laid down by Bernhard Riemann in the nineteenth century), those essays made me realize that I was fascinated by the same kind of issues involving poetry, philosophy, and—but was there a connection?—the deeper currents of mathematics.
« In his poem “The Soul and the Dance,” Valéry notably asks: “How can the unreal and the intelligible be blended and combined in accordance with the possibilities of the Muses?” It is mathematics, arguably, that made this interlocutor of Albert Einstein, Henri Poincaré, Émile Borel, and Louis de Broglie sensitive to such questions about the real, the unreal, the imaginary, the perceptible, and the intelligible. He would record his thoughts about such topics every morning in his Notebooks, which contain countless remarks about mathematics, philosophical questions, and, last but not least, poetry. [. . .] »
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