Mathematics and Poetry: Some Impressions

I think I've always loved mathematics in my own ways.

True, given the kinds of options that were available in my high school, I enthusiastically opted for what was then called the "Humanities Group." But I enrolled in that group—and later majored in literature—not out of my fear or dislike of mathematics as such.

In fact, very early on in my life, I used to look at mathematical symbols—or, say, at certain mathematical "compositions"—as I would look at paintings or even poems with a sense of awe and wonder. The symbols arranged in certain order on a page—or for that matter, patterns rendered visible—simply looked beautiful to me. They still do. Once in my dream, a dream that I vividly recall, I saw how an entire Shakespearean sonnet morphed into a 14-line mathematical equation right under my eyes!

Indeed, way before I began to read the French philosopher Alain Badiou—whose love of mathematics is unmistakable—I had realized in my own way that mathematics is more than just logical proofs; that mathematics cannot always be reduced to conventional logic; and that mathematics at a certain level does not have to do with even computational accuracy but it surely involves the power of our imagination.

As I recall, I even told a mathematics teacher during my Dhaka University undergrad days that there's poetry in mathematics. He laughed out loud, thinking that I was crazy or even stoned out on pot.

But I was surely high on the poetry of mathematics itself.

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The more I read Dante's epic poetry on the one hand, and examine Bhaskaracharya's mathematical works on the other, the more I realize that there has always been some poetry in mathematics and some mathematics in poetry. Of course, poets have long mobilized mathematical imagery, ideas, and insights. Many mathematicians, on the other hand, are known for using poetic lines, images, metaphors. I find it both interesting and instructive that the earliest poet known by name is also the earliest mathematician known by name—Enheduanna. She was the chief priestess of the moon god Nana in the city of Ur and daughter of the Akkadian king Sargon, one who was known to govern the region of Sumer during the period between 2334 and 2279 BCE.

In their book Discovering Patterns in Mathematics and Poetry, Marcia Birken and Anna C. Koon rightly provide other examples of poet-mathematicians that history has witnessed: Eratosthenes of Greece (274-194 BCE), Omar Khayyam (1048-1131), Lewis Carroll (1832-1898), Piet Hein (1905-1996)), among others. All of them—their different styles and approaches notwithstanding—found striking and even stimulating parallels between poetry and mathematics, even anticipating Ezra Pound's crisp contention that poetry is a kind of inspired mathematics, among other things.

As Pound puts it: "Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions." But, then, it is also true that certain kinds of poems—variously known as typographical poems, concrete poems, prometa figurata, or visual poems, or carmen figuratum—directly provide those figures, triangles, and squares Pound speaks of. One can readily think of the French poet Guillaume Apollinaire and the American poet e. e. cummings and even—before them—the great French poet Stéphane Mallarmé, among numerous others, who produced typographical poems, attesting to their geometrical imagination.

We discuss some of their poems in a course called "Creativity" that I teach relatively regularly at an American university. It's an interdisciplinary course predicated on the assumption that creativity is not the territory exclusively inhabited and owned by the privileged few but that creativity is to be found in the entire range of lived human practices. Students in this course explore, among other things, not only the apparent similarities and dissimilarities between mathematics and poetry as such, but also the poetic in mathematics and the mathematical in poetry.

We use the text instructively titled Strange Attractors: Poems of Love and Mathematics, edited by Sarah Glaz and JoAnne Growney, among other works. That international anthology not only features mathematically inspired poems by such figures as John Donne, Elizabeth Barret Browning, Emily Dickinson, Rafael Alberti, Langston Hughes, Pablo Neruda, Duniya Mikhail, but also some great selections from Dante's Divina Commedia (Paradiso: Canto XXXIII).

We had numerous discussions surrounding those works, making all sorts of points vis-à-vis the relationship between mathematics and poetry while one consensus had already emerged: that all the poets I've cited above have what my students themselves came to call a "strong mathematical imagination." I then shared with them the words of the great nineteenth-century mathematician Karl Weierstrass: "It is true that a mathematician, who is not somewhat of a poet, will never be a perfect mathematician."

Weierstrass suggests that both poets and mathematicians pay utmost attention to language itself, avoiding what's unnecessary or even inelegant, and that both cannot operate without using their imagination, striving for the highest excellence at the levels of both language and imagination. The nineteenth-century English mathematician Augustus de Morgan even puts it bluntly: "The moving power of mathematical invention is not reasoning but imagination." 

Remaining attentive to the power of both imagination and language, students in my "Creativity" class further explored certain connections among poetry, music, and mathematics, while even choreographing some lines from Dante's Divine Comedy—lines that deploy geometrical images and metaphors with superb effects! Our conversation surrounding the metaphor of "squaring the circle" led to a fascinating discussion concerning numbers themselves—numbers that are rational, irrational, algebraic, even transcendental. And I was then continuously thinking of Pablo Neruda's poem called "Ode to Numbers" side by side with Alain Badiou's book Number and Numbers as well as the American poet Carl Sandburg's poem "Number Man," while we also talked about the effects of what are called "logarithmic spirals"—ones famously described by the French mathematician and philosopher René Descartes and ones abundantly available in nature itself.

And, finally, the class as a whole, I thought, experienced the sheer beauty of mathematics itself, as we watched and discussed a few videos about the infinite geometry of doodling itself, making the point that to doodle is to produce an infinite number of beautiful spatial patterns—patterns that can even sing, dance, act. Is geometry itself then music spatialized? The answer in the class was in the affirmative. And speaking of patterns, I recall the English mathematician G.H. Hardy: "A mathematician, like a painter or poet, is a maker of patterns."

Now one might still wonder what is actually so poetic about mathematics. The writer JoAnne Growney (whom I mentioned earlier) brings up certain examples of fine poetry within mathematics in the form of rhetorical questions: "Is Euclid's proof of the infinitude of primes poetic? What about the Pythagorean Theorem or the equation that asserts that the sum of all negative powers of 2 is equal to 1?" She offers her own choice that I find agreeable. It's the "Pigeonhole Principle," which, as she succinctly puts it, "is a statement that, like a mantra, and like a good poem, takes on new meaning again and again: if the number of pigeons residing in your pigeon house is more than the number of pigeonholes, then at least one pigeonhole must have more than one pigeon."

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Let me now categorically and quickly make a few more points concerning the relationship between mathematics and poetry, while also keeping in mind the question of music as well as the world in which we produce our poetic, mathematical, and musical works.

To begin with, basic things like rhythm, rhyme, order, pattern, symmetry, symbols—ones that variously obtain in poetic production—immediately involve the mathematical itself. Moreover, while both poetry and mathematics deliver their "truths"—as Emily Dickinson once put it: "Tell all the truth but tell it slant"—it is also true that both mathematics and poetry also continue to suggest and provoke all possible combinations and configurations of symbolic and tropic phenomena, which, however, remain anchored in the material world in the final instance.

And, of course, music and mathematics—as many musicologists have shown—speak to one another in various ways. But their exchanges do not merely reside in how they symbolically represent our world, but also lie in the ways in which both 'make' and mobilize abstractions that—however heightened and 'pure'—cannot simply free-float out of the horizon of human history.

Further, as far as mathematics in particular is concerned, it cannot but function rhetorically ('rhetoric' being the art and science of persuasion). Think, then, of the ways in which mathematics, like poetry, uses analogies, homologies, contiguities, substitutions, equivalences, and so on—or, say, simile, metaphor, metonymy, synecdoche, and so on—while also mathematics, like music in particular, uses refrains and repetitions—also to be found in poetry—while even improvising so many different kinds of syllogisms in their attempts to persuade.

But all mathematical and poetic tropologics—if you will—finally remain anchored in the material world insofar as the act of making connections and combinations—an act that is of course common to both mathematics and poetry—cannot operate in vacuo, but certainly needs a base. And that very base is constituted by the body and nature.

Azfar Hussain teaches in the Integrative, Religious, and Intercultural Studies Department within the Brooks College of Interdisciplinary Studies, Grand Valley State University in Michigan, and is Vice-President of the Global Center for Advanced Studies, New York, USA.