Pythagoras: The Mathematician Who Brought Order to the Universe

"Number rules the universe." — Pythagoras

Introduction

Pythagoras is one of the most iconic figures in the history of mathematics. Best known for the Pythagorean Theorem, his influence goes far beyond right-angled triangles. He was a philosopher, a mathematician, a mystic, and the founder of a unique school of thought that blended mathematics, spirituality, and ethics. But who was Pythagoras really, and why does his name echo through the centuries?

Let’s dive into his life, contributions, and the fascinating legacy he left behind.

Early Life

·        Born: c. 570 BCE on the island of Samos, Greece

·        Died: c. 495 BCE in Metapontum, Magna Graecia (modern-day southern Italy)

Pythagoras was born into a well-off family. His father, Menarches, was a merchant. From an early age, Pythagoras was exposed to travel, ideas, and cultures. He reportedly studied with Thales, one of the earliest Greek philosophers, and possibly travelled to Egypt and Babylon, absorbing a wide range of mathematical and religious knowledge.

The Pythagorean Brotherhood

Around 530 BCE, Pythagoras settled in Croton, in southern Italy, where he founded a philosophical and religious school known as the Pythagorean Brotherhood. This wasn’t just a school—it was a secretive, almost cult-like community that followed strict rules of conduct and believed in the mystical power of numbers.

Tenets of the Brotherhood:

·        Belief in the transmigration of souls (reincarnation)

·        Emphasis on purity, vegetarianism, and discipline

·        Reverence for numbers and their relationship to the cosmos 

Mathematical Contributions

1. Pythagorean Theorem

Undoubtedly his most famous contribution:

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Mathematically: a² + b² = c²

While this theorem was known to Babylonians centuries earlier, Pythagoras (or his followers) provided the first formal proof.

2. Numbers and Harmony

Pythagoras discovered that musical intervals could be expressed using simple ratios of whole numbers. For example:

·        Octave = 2:1

·        Fifth = 3:2

·        Fourth = 4:3

This led to the concept of harmony in music and the idea that the universe itself resonates with mathematical harmony—a notion that laid the foundation for what later became known as the Music of the Spheres.

3. Figurate Numbers

Pythagoreans studied figurate numbers—numbers that can form regular geometric shapes (like triangular, square, and pentagonal numbers). This was an early blend of arithmetic and geometry.

4. Irrational Numbers

The discovery that not all numbers could be expressed as ratios of integers (like √2) was both revolutionary and unsettling for the Pythagoreans. Legend says the member who revealed this secret was thrown overboard at sea!

Mathematical Foundation:

·        The Pythagorean Theorem is foundational in Euclidean geometry, used in architecture, engineering, physics, computer graphics, and more.

·        Statistically, right triangle relationships appear in regression analysis, distance metrics, and machine learning algorithms (e.g., Euclidean distance in k-means clustering).

Influence:

·        Numerous theorems and corollaries are derived from or related to the Pythagorean Theorem.

·        A 2023 academic study estimated that the theorem appears, in some form, in over 370,000 peer-reviewed publications.

Interesting Facts and Stories

1. The Symbol of the Tetractys

Pythagoreans worshipped the Tetractys, a triangular figure made of ten dots (1+2+3+4). It symbolized harmony and the perfection of numbers.

2. Founder of a Religious Movement

 Beyond his mathematical contributions, Pythagoras founded a religious movement known as Pythagoreanism. This group combined religious rituals with philosophical teachings, emphasizing the transmigration of souls and a strict lifestyle involving dietary restrictions and ethical conduct.

3. The Reincarnated Warrior

Pythagoras claimed he could remember past lives. He once said he had been a soldier named Euphorbus in the Trojan War and recognized his own shield in a museum.

4. Mathematical Vegetarianism

He was a strict vegetarian and associated certain foods with moral or spiritual impurity. Beans, in particular, were taboo!

5. Death is a mystery

The death of Pythagoras, is shrouded in mystery and legend. There are no definitive historical records about how he died, and much of what we "know" is based on later sources, often centuries after his time, mingling history with myth.

Here are the main theories and legends surrounding his death:

1. The Croton Uprising Theory

According to some accounts, Pythagoras was living in Croton (a city in southern Italy) when political upheaval occurred.

• What happened: The Pythagorean school, which was also a kind of political society, had become powerful and elitist. It attracted enemies.
• The attack: Around 495 BCE, during an uprising, the Pythagoreans' meeting house (or school) was burned down by political opponents.
• Pythagoras’ fate: Some say he died in the fire. Others claim he escaped, but died shortly after due to stress or grief.

2. The Fava Bean Legend

This is perhaps the most bizarre and legendary account.

• Background: Pythagoras reportedly believed fava beans contained the souls of the dead and refused to eat or even touch them.
• The story: When fleeing enemies, he came upon a field of fava beans. Rather than cross it (and violate his taboo), he chose to stop and was caught and killed—either by being stabbed, captured, or letting himself die.
• Interpretation: This tale emphasizes his strict adherence to his philosophical or religious principles, even to death.

3. Natural Causes

Some ancient sources (like Diogenes Laërtius) suggest he died of natural causes—likely old age—while living in Metapontum, another city in southern Italy.

• This version is the least dramatic but considered more historically plausible by some scholars.

Historical Context

Because Pythagoras left no writings, and his teachings were passed down orally and often anonymously by his followers, it’s difficult to separate fact from legend.

Even early biographers like Porphyry and Iamblichus, who wrote about him centuries later, often mixed myth, mysticism, and philosophy.

Summary of Theories

Theory	Details	Source Type
Killed during uprising	Died when enemies attacked Pythagorean school	Some historical support
Refused to cross bean field	Killed due to his bean taboo	Myth/legend
Died of natural causes	Passed away in Metapontum, possibly of old age	Traditional account

Conclusion

Pythagoras’ life blurs the lines between myth and reality, but his impact is indisputable. He didn’t just explore numbers—he worshipped them, seeing mathematics as the bridge between the mundane and the divine.

To this day, his ideas echo in classrooms, laboratories, and concert halls around the world. Whether or not he truly authored all the theorems in his name, his vision of a mathematically ordered universe still shapes how we understand reality.

References (for further reading)

·        Katz, V. J. (2004). A History of Mathematics: An Introduction

·        Kline, M. (1990). Mathematical Thought from Ancient to Modern Times

·        Livio, M. (2009). The Equation That Couldn't Be Solved

·        Stanford Encyclopedia of Philosophy: Pythagoras