Pythagoras

1. Life and Legacy

Pythagoras was born on the island of Samos and traveled extensively to Egypt, Babylonia, and surrounding regions. Gathering wisdom from diverse cultures, he established the Pythagorean School—an interdisciplinary center where mathematics, music, ethics, and spiritual beliefs were deeply intertwined.

2. The Pythagorean Theorem

One of his most enduring contributions is the geometric principle:

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
a² + b² = c²

This theorem forms the basis of Euclidean geometry and remains fundamental in architecture, physics, engineering, and astronomy.

3. Music and Mathematics

Pythagoras explored the relationship between numbers and musical harmony. He discovered that string lengths produce notes based on whole-number ratios:

• Halving the string creates a note one octave higher (ratio 1:2)
• Ratios like 2:3 and 3:4 correspond to musical intervals such as fifths and fourths

His work laid the foundation for acoustics and proved that music is governed by mathematical laws.

4. Philosophical and Mystical Beliefs

The Pythagorean worldview centered on the idea that:

• Numbers are the essence of the universe
• Odd and even numbers represent opposing cosmic forces
• The soul is immortal and undergoes reincarnation
• Harmony reflects moral and cosmic order

Pythagoreans treated mathematics not just as a tool, but as a path to ethical and spiritual enlightenment.

5. Influence on Western Thought

Pythagoras' teachings influenced Plato, Euclidean geometry, and mathematical philosophy for centuries. His numerical vision of cosmic balance continues to inspire both scientific reasoning and metaphysical inquiry.

• Geometry: His theorem remains central in math education
• Music Theory: Scientific study of sound originates from his ratios
• Philosophy: His notions of universal order shaped Platonic and Neoplatonic traditions

6. Conclusion

Pythagoras unified mathematics, nature, and spiritual philosophy into a coherent system of thought. His legacy bridges disciplines and eras, reminding us that abstract truths—like numbers and harmony—can illuminate both the physical world and the inner life of the soul.