Math and Poetry

Henry Poincaré, the great French Mathematician once said:

“We have just seen, through an example, the importance of words in mathematics, but I could cite many more cases. It is scarcely credible, as Mach said, how much a well-chosen word can economize thought. I do not know whether or not I have said somewhere that mathematics is the art of giving the same name to different things. We must so understand it. It is meet that things different in substance but like in form should be run in the same mold, so to speak. When our language is well chosen it is astonishing to see how all the demonstrations made upon some known fact immediately become applicable to many new facts. Nothing has to be changed, not even the words, since the names are the same in the new cases.”
The Future of Mathematics, 1908

What makes mathematics powerful and beautiful is precisely this ability to unify ideas that initially seem unrelated. Through abstraction, mathematics strives to generalize and unify, reducing complex systems to universal principles and frameworks. Its goal is clarity, consistency, and universality — finding shared structures in seemingly disparate phenomena. For example, the same mathematical tools can describe planetary orbits, electrical circuits, and even economic systems.

In stark contrast, poetry revolves around giving different names to the same thing, using every tool the poet possesses — analogy, metaphor, and, on a larger scale, emotion. In poetry, “the wind” or even “the wind I felt this morning” can be much more than just that particularity; it can represent the flow of time, a beloved’s hair, or a whispered message. Ambiguity is key here, allowing one idea to branch out and map onto multiple ideas, feelings, and pictures. This can get extreme too: for instance, a “contronym” like “cleave” can mean both “to cut apart” and “to bind together.” Poetry celebrates the specific and unique nature of our experiences. While mathematics pursues universality, poetry embraces particularity, which emerges from the feelings, senses, and varied images we associate with particular events, people, and things.

While mathematics simplifies through abstraction, poetry complicates through individuation and speciation! Individuation is the process of branching of meaning or references. This is quite in opposition to abstraction, which happens in mathematics! You know where you start with poetry but you never know where you land! In math, you don’t know where you are but you finally know where you land! In poetry, you start from certainty and embrace the uncertainty while in mathematics you are perplexed by the uncertainty until you see everything.

As a result, poetry is inherently open to personal interpretation. An individual’s experience of a poem is its ultimate essence, whereas mathematics aims at a collective, universal understanding.

In poetry, the emotions, circumstances, and personal history of the reader give the work its potency, whereas, in mathematics, individual perspectives are largely irrelevant.

In mathematics, the observer strives to disappear; the goal is pure objectivity. Mathematical truths exist independently of whoever discovers them and whenever they do. In poetry, by contrast, the observer is central. The poet’s voice, perspective, and unique lens shape the work, making it deeply personal and subjective.

Our understanding of reality can be seen as a continuum between mathematics and poetry. Although they appear to stand on opposite ends of the spectrum, they often venture into each other’s domains. Mathematics, despite being universal and collective, still relies on personal intuition — an inherently subjective experience that guides discovery and insight. Conversely, even though poetry often focuses on the individual, it inevitably contains threads that connect us all, conveying shared ideals, morals, and emotions in ways that may surprise even the poet.

Mathematizing the world is like climbing to the summit of a mountain: regardless of where you begin, you’ll eventually reach that breathtaking peak. Poetizing the world, on the other hand, is like descending a hill: you start where everyone else starts, but you can find yourself in countless unique places.

Even though climbing the hill leads to a universal summit, your journey along the way is entirely your own — shaped by intuitions that are uniquely yours. By contrast, while descending the hill heads toward a special lowland destination, the route often intersects previously established trails — those main paths of shared ideas, values, and moral beliefs.

This interplay between mathematics and poetry — between the impersonal search for universal order and the personal celebration of human experience — grants “words” a distinctive magic and power. Both activities are fundamentally human: they embody our collective, universal side while honoring our unique, gem-like individuality.