Pythagoras of Samos

Pythagoras is the oldest named figure in Western physics, and much of what's attributed to him is probably the work of his followers, the Pythagoreans, a secretive mathematical-religious brotherhood. What survives is a cluster of ideas: numbers govern the world, the universe is ordered by proportion, and the order can be heard.

The story goes that Pythagoras walked past a blacksmith's shop and noticed that hammers of different weights rang in consonant intervals when their weights were in simple integer ratios. Whether true or not (the physics of hammer weights doesn't quite work out), the core observation — that two vibrating strings sound consonant when their lengths are in ratios like 2:1, 3:2, 4:3 — does. He strung a single string over a movable bridge (the monochord) and built up an entire musical theory from integer proportions.

He never asked what vibration was, let alone what a wave was. He never wrote down an equation in the modern sense. But he noticed that something countable — some hidden discrete structure — sat underneath something continuous and audible. That observation, two and a half millennia before Fourier formalised it, is the seed of this entire topic.