The hidden mathematics behind why you find things beautiful

Written by Jonny Thomson on February 13, 2025. Posted in Current News

Formalism is the idea that beauty in art can be explained through its formal, mathematical structures rather than subjective experience

When Big Think spoke with the mathematician Marcus De Sautoy, he argued that the Universe is inherently mathematical, with structures like symmetry, fractals, and prime numbers shaping both nature and human creativity — from cicadas to Shakespeare.

Here we look at three suprising examples of the mathematics behind beautiful art.

Some people will hate what I say,” the mathematician Marcus du Sautoy tells me, “because it’s all about unweaving the rainbow. Some people want to retain the magic and don’t want to know why something’s working.

That’s fine. But actually, for me, you know, the rainbow becomes much more interesting when you understand what is happening to the light that makes the rainbow like that.”

Du Sautoy, the Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford, and I are speaking about “formalism” in the philosophy of art — the idea that we can explain why something is beautiful by pointing out the formal parts that make it up.

Formalism holds that we can account for aesthetic judgments in non-aesthetic terms. Maybe we find a song beautiful because of its tertian harmonies, or we like a certain photo because the angular lines converge on a point.

Formalism “unweaves the rainbow” by telling you exactly why you find something beautiful.

Not everyone is a formalist. Some aestheticians do not think you can “reduce” art to its composite parts. They think beauty is beauty entirely because it is irreducibly subjective — a pleasurable phenomenon that walks the line between emotion and mysticism.

Du Sautoy is not one of these people. He’s not only a formalist but a card-carrying, hard-lined sort of formalist. Du Sautoy believes that beauty has everything to do with mathematics.

“So, mathematics — as a subject — has a history and an evolution,” he says. “And mathematicians play a role in that. But I’m very much a Platonist at heart. I believe that there are these structures to nature that do not need a moment of creation. And so, I believe that our Universe around us is a physical piece of mathematics. And that’s why we see so many of the structures that we recognize, bubbling under the natural world. And how did mathematics emerge? It emerged out of humans trying to understand the natural world around us. So, it’s inevitable that if there is structure in nature, that they will be the first structures we discover, as mathematicians and as humans.”

The structures all around

Du Sautoy argues that the Universe is made up of structures — and mathematics is the language that we have developed to explain and represent those structures. This is true for every corner of the Universe, and it’s true in observable, day-to-day life.

It’s there in nature. Du Sautoy gives a few examples:

Chickens “always order their numbers. Smallest to the left, largest to the right.” Cicadas “hide underground for 17 years, doing absolutely nothing. How are these cicadas counting 17 years?” And symmetry, he explains, “is often a signal in the natural world, that of something we should take notice of, because symmetry very often is an indication of an animal.”

The mathematics of beauty

Du Sautoy’s formalism is an extension of his Platonism: If everything we experience is “a physical piece of mathematics,” then art will be no different. We looked at three examples from his upcoming book, Blueprints: How Mathematics Shapes Creativity.

The Golden Ratio: “Mozart, for example, used the idea of the golden ratio in The Magic Flute. Debussy and Bartók really loved the idea as well. Le Corbusier uses Fibonacci numbers as a kind of blueprint for building. Perhaps more interesting is the idea of a prime number being a blueprint. For example, a composer like Messiaen uses them to create a kind of a sense of tension in the Quartet for the End of Time.”

Pollock’s Fractals: “Jackson Pollock is famous for very abstract expressionist art — flicking paint around. And a lot of people say, ‘Well, anyone could do that.’ Turns out not everyone can, because he’s doing something quite special in his painting style, which is that he’s actually creating with his body and the paintbrush a chaotic system. And the geometry of chaos is this thing called a ‘fractal.’ So actually, what he’s making is a lot of fractal geometry, and a fractal has this wonderful property that it will never simplify. Of course, at some point and with the painting you have, it has to simplify because you will see the pixels of paint. But it’s actually one of the beautiful things about Pollock that when you’re standing in front of it, you lose your sense of scale. As you walk towards it, you’re not quite sure how close you are.”

The Number-crunching Wordsmith. “Shakespeare is obsessed with number. You think he’s a wordsmith, but actually, he was a great number cruncher, too. Number is really important to indicate something significant in his poetry. For example, what’s the most famous line in Shakespeare? You know, everything normally comes in tens; it’s iambic pentameter. But the most famous line in Shakespeare — ‘To be or not to be, that is the question’ — it’s 11 and uses the prime number to spark you out of your haze. You know, you’re sitting there listening to Hamlet and being lulled by the iambic pentameter, and then suddenly there’s this extra beat. And that’s very deliberate. He uses 11-beat and seven-beat things at significant moments.”

For du Sautoy, mathematics is the hidden scaffolding of beauty, the invisible thread that connects art, nature, and the cosmos.

If we look closely enough, we can see how far mathematics unweaves the rainbow to reveal deeper patterns beneath.

Does that diminish the beauty? Does that dispel the magic?

I think I’m with du Sautoy on this. It only makes it stronger.

See more here bigthink.com

Header image: BBC

Please Donate Below To Support Our Ongoing Work To Defend The Scientific Method

PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX. 

Trackback from your site.