The Math Teacher Who Started a Cult
Around 530 BCE, in the Greek city of Croton (southern Italy), a philosopher named Pythagoras founded something that was part school, part religion, and part secret society. His followers—the Pythagoreans—lived together communally, followed strict rules about what they could eat and wear, and devoted their lives to studying mathematics.
But they didn't study math the way you do in school. They believed numbers were the fundamental nature of reality itself. Not that numbers described reality—that numbers were reality.
This might sound crazy. Or it might sound profound. Or maybe both. Let's investigate.
The Historical Context
Pythagoras born on the island of Samos
Traveled to Egypt and Babylon, studying their mathematics and mysticism
Founded his school/brotherhood in Croton, Italy
Pythagoras died, but his followers continued for hundreds of years, influencing Plato and later philosophers
What Did They Actually Believe?
Core Mathematical Beliefs:
"All is Number" — Their central doctrine. They believed everything in the universe could be understood through numbers and their relationships. Music, astronomy, ethics, the soul—all reducible to mathematical principles.
The Tetractys — Their sacred symbol: a triangle of ten dots arranged in four rows (1, 2, 3, 4). They believed this represented the fundamental structure of the cosmos. They literally swore oaths by it.
The Music of the Spheres — They believed planets made harmonious musical sounds as they moved, based on mathematical ratios. We can't hear it, they said, because we've heard it since birth so we're used to it.
Transmigration of Souls — They believed in reincarnation. Pythagoras claimed to remember his past lives. (This connects to your dad's Platonic interests—Plato learned this from the Pythagoreans!)
Mathematical Harmony = Moral Goodness — They believed virtuous living required living according to mathematical principles. A balanced life = mathematical balance.
Weird Lifestyle Rules:
No beans! — They refused to eat beans. Nobody knows exactly why. Some theories: beans cause flatulence (disrupts philosophical contemplation), beans resemble fetal humans, or beans were associated with voting (putting beans in jars) and they avoided politics.
Silence period: — New members had to remain silent for five years, only listening to teachings. Only after this could they speak in discussions.
Communal property: — Everything was shared. "Friends hold in common what they have" was their motto.
Secret knowledge: — Mathematical discoveries were kept secret within the brotherhood. Revealing secrets to outsiders was grounds for expulsion or worse.
The Crisis That Shook Their World
The Pythagoreans believed all numbers could be expressed as ratios of whole numbers (what we call rational numbers). This fit their worldview perfectly—reality is orderly, mathematical, rational.
Then one of them (probably Hippasus) proved something devastating: The square root of 2 cannot be expressed as a ratio of whole numbers. It's irrational.
This was a theological crisis. If irrational numbers exist, then numbers aren't as perfect and orderly as they thought. Reality has chaos in it. Legend says they drowned Hippasus at sea for revealing this secret (though historians doubt this actually happened).
But they couldn't hide the truth. Irrational numbers are real, and the Pythagorean worldview had to evolve.
Your Investigation
Part 1: The Tetractys Exploration (20 minutes)
Draw the Tetractys (triangle of 10 dots: one dot on top, then two, then three, then four).
The Pythagoreans saw deep meaning in this:
- 1 = unity, the beginning
- 2 = duality, the first division
- 3 = harmony (combining 1 and 2)
- 4 = the material world (four elements, four seasons, four directions)
- 10 = perfection (1+2+3+4)
Task: Create your own "sacred symbol" based on a mathematical pattern. What does it represent? Write a paragraph explaining its meaning.
Part 2: Musical Mathematics (30 minutes)
The Pythagoreans discovered that musical harmony is mathematical. When you pluck a string and then pluck a string half as long, you get the same note an octave higher (2:1 ratio). Other beautiful ratios create other harmonious intervals.
Experiment (if you have an instrument):
- Find notes that sound good together
- Research the mathematical ratios between them
- Do the "better sounding" combinations have simpler mathematical ratios?
Writing: Does the fact that music is mathematical mean the Pythagoreans were onto something? Or is this just a coincidence?
Part 3: Philosophical Essay (60 minutes)
Write a 2-3 page essay addressing:
Main Question: Were the Pythagoreans crazy or insightful?
Consider these angles:
- What They Got Right: The universe IS deeply mathematical. Physics equations describe reality with incredible precision. DNA is information encoded mathematically. Crystals form in mathematical patterns. Music IS mathematical ratios. Were they crazy, or were they seeing something true?
- What They Got Wrong: The bean thing was probably nonsense. Drowning people over irrational numbers (if true) was definitely wrong. Keeping mathematical knowledge secret hindered human progress. What does this tell us about the danger of taking good ideas too far?
- Modern Connections: Today, many physicists believe the universe is fundamentally mathematical. Eugene Wigner talked about the "unreasonable effectiveness of mathematics." Max Tegmark argues that physical reality IS a mathematical structure. Are modern physicists just sophisticated Pythagoreans?
- The Personal Question: Do YOU think reality is fundamentally mathematical? Or are numbers just useful tools we invented to describe reality? Defend your position.
Modern Pythagoreans?
Consider These Modern Ideas:
Digital Physics: Some scientists think the universe is literally a computational simulation—everything is information and computation. That's very Pythagorean (all is number!).
String Theory: Proposes the universe is made of tiny vibrating strings—musical strings, essentially. The "music of the spheres" in modern form?
The Golden Ratio in Nature: Phi (1.618...) appears throughout nature without anyone planning it. Pythagorean mysticism or legitimate observation of mathematical reality?
The Big Picture
What This Means for Your Math Class
The Pythagoreans took mathematics seriously—maybe too seriously, but they took it seriously. They didn't see math as a boring subject to get through. They saw it as the secret language of the cosmos, the key to understanding everything.
Were they wrong? In some ways, yes. Reality isn't only mathematical. Consciousness, beauty, meaning—these seem to be more than just numbers. Drowning people over mathematical disputes is definitely wrong.
But were they completely wrong? Modern physics increasingly suggests the universe is mathematical at its deepest level. Quantum mechanics is pure math. Relativity is geometry. The Standard Model is group theory. The more we dig into reality, the more we find math.
When you're working through equations in math class, you're not just solving for x. You're learning the language that describes reality. Whether numbers are the fundamental nature of existence or just our best tool for understanding it, they're clearly essential to how the universe works.
The Pythagoreans' big insight was this: Mathematics isn't just calculation—it's contemplation of truth itself. When you understand the Pythagorean theorem or solve a quadratic equation, you're touching something real and eternal. You're connecting with patterns that existed before humans and will exist after we're gone.
You don't need to join a cult or give up beans. But you can approach mathematics with the sense that you're learning something profound—not just memorizing formulas, but uncovering the structure of reality. That's not crazy. That's wisdom.