How a Triangle Changed Everything

Pythagoras and the strange, beautiful moment when numbers, music and belief became one.

The Big Idea

The world appears disordered: noise without rhythm, movement without meaning.

Pythagoras had a better idea. He saw pattern and proportion behind the confusion.

Everything, he said, is number — harmony disguised as movement, maths masquerading as music.

He believed that everything could be explained through numbers, that behind every note, shape and star there was a pattern waiting to be discovered, or perhaps simply heard.

The Man and the Moment

Pythagoras was born around 570 BCE on the island of Samos, a bright speck in the Aegean Sea just off the coast of Ionia. I’ve been there — it’s very nice, great tavernas and beaches — but Pythagoras was probably too busy to sunbathe.

The world he grew up in was buzzing with new ideas. Thales had already suggested that nature had rules. Pythagoras went further. He wanted not just to understand those rules but to live by them.

He travelled widely to Egypt, Babylon, possibly India gathering geometry, mysticism and gossip in equal measure. When he finally settled in Croton, southern Italy, he founded what might be described as the world’s first self-improvement cult.

The Pythagoreans lived together, studied music and mathematics, and followed a strict set of rules that included vegetarianism, secrecy and, bizarrely, a ban on eating beans. No one is quite sure why. Some said beans resembled human embryos; others thought they caused wind, which was apparently undignified for philosophers. Whatever the reason, refusing to eat beans became a spiritual principle and an enduring reminder that intelligence and eccentricity are often roommates.

To outsiders, Pythagoras must have seemed both brilliant and slightly terrifying. He was said to have a golden thigh (don’t ask), to remember his previous lives, and to command animals by speaking to them in verse. Shades of a Hellenic Doctor Doolittle.

His followers treated him less like a teacher and more like a minor deity. When he entered a room, they stood in silence. When he spoke, they called it revelation. He had, in short, invented the influencer economy two and a half thousand years early. A cult leader and real stable genius if ever there was one.

Why It Mattered

Behind the myth was a staggering insight. Pythagoras noticed that the same ratios that made strings on a lyre produce harmonious notes also appeared in geometry and the motion of the planets.

Order, he realised, was not just visible but audible. The world was a system of proportion.

That might sound quaint now, but it was the beginning of mathematical physics, the idea that the universe can be described in numbers and relationships rather than stories and superstitions. To say “everything is number” was to suggest that beauty, harmony and truth are not accidents but reflections of a hidden order.

In that sense, he wasn’t just doing maths; he was writing the first verse of a song that scientists are still humming. When we say “laws of nature,” we’re still using his vocabulary.

He also gave us the Pythagorean theorem, the famous a² + b² = c² — though he probably didn’t invent it. The Babylonians knew it earlier. What Pythagoras did was turn it into philosophy.

The triangle, for him, wasn’t just geometry; it was a symbol of balance and connection, a sacred shape in the architecture of existence.

It’s easy to laugh at his mystical side — reincarnation, silence, the bean ban but his big idea endures. He believed the universe had meaning built into it, that harmony was not just aesthetic but fundamental. You can hear that faith in every scientist still convinced that the next formula might just explain everything.

The Legacy

The Pythagorean brotherhood didn’t end well. Their secrecy and strangeness made them a target for suspicion. According to legend, a mob in Croton burned their meeting house while they were inside. Some escaped; Pythagoras possibly didn’t. The details are vague, as they often are when a philosopher becomes a myth.

But his ideas survived, smuggled out by his followers. Plato was deeply influenced by him, and through Plato, so was almost everyone else. The idea that mathematical beauty reveals truth became a cornerstone of Western thought.

Kepler’s laws of planetary motion, Newton’s equations, Einstein’s relativity, all Pythagorean at heart.

And the music didn’t stop there. The “music of the spheres” lived on in art, architecture and the way we talk about the universe. When physicists describe the vibrations of strings and fields, they’re speaking a language first hummed in Pythagoras’s lyre room.

He also helped fuse spirituality and science, for better and worse. His search for numerical purity became the ancestor of both modern physics and modern perfectionism.

We still chase symmetry, pattern and order in a world that rarely sits still.

There’s something both noble and dangerous in that. Numbers can describe almost everything, but they can’t tell you what it feels like. Pythagoras opened the door to logic, but he also left us haunted by the gap between calculation and compassion.

In Our Time

If Pythagoras were alive today, he’d probably run a wellness retreat that offered geometry workshops at sunrise and lectures on cosmic harmony after lunch. The bean ban would be gluten-free, and the admission fee would be substantial.

He’d have a podcast called The Shape of Everything and a loyal following of people convinced that Fibonacci sequences can fix their chakras.

Yet he’d also feel oddly at home in our data-driven world. We still worship numbers. We count our steps, track our moods, rate our sleep, measure our “engagement.” We treat the quantified self as salvation.

Pythagoras would nod approvingly. Finally, humanity taking numbers seriously, then quietly ask whether all this measurement was making anyone wiser.

He’d be fascinated by modern physics, where his old idea of harmony has returned as vibration, resonance and string theory. He’d love AI too, the notion that numbers can think. For him, it would be proof that his faith in mathematics wasn’t misplaced.

But perhaps he’d also be wary. He saw numbers as sacred, not mechanical. To him, they were living symbols, not tools for profit or control. He might look at our algorithms and say, “You’ve turned the music into noise.”

Still, he’d admire the ambition. In a sense, AI is the latest version of the Pythagorean dream, the belief that the pattern can replicate itself, that reason can create more reason.

It’s just that, unlike him, we rarely pause to ask whether the harmony we’re building still sounds beautiful.

We could all use a little of his awe: that blend of logic and wonder, intellect and reverence.

Pythagoras reminds us that behind every equation lies a question too large for maths to solve — the question of why there’s harmony at all.

Key Teachings and Ideas

The Pythagorean Theorem (6th century BCE) — His name lives on in every maths classroom. The square on the hypotenuse and all that. Proof that triangles can change the world.

The Harmony of the Spheres — Pythagoras claimed that the planets produced cosmic music as they moved. The first theory of celestial jazz.

The Rule of the Tetractys — A mystical symbol made of ten dots arranged in a triangle, representing harmony in the universe. Also doubles nicely as a pub quiz question.

The Essence

“Everything is number.” — Pythagoras (allegedly, between meals without beans)

Numbers reveal the rhythm of the world, but they can’t play the melody for us.

Pythagoras heard that music and tried to teach it. The rest of us are still learning the tune.