Which philosopher is known for asserting that all reality could be represented through mathematical relationships?

Pythagoras is the philosopher known for asserting that all reality could be represented through mathematical relationships. He believed that numbers and their relationships underlie the structure of the cosmos. This idea is fundamental to the Pythagorean philosophy, which posited that the world is fundamentally mathematical in nature. His belief in the significance of numbers extended to concepts of harmony, proportion, and order, influencing not only mathematics but also aspects of philosophy and even music.

The other philosophers mentioned had different focuses: Democritus is primarily known for his atomic theory of the universe, which emphasized the idea that everything is made up of small, indivisible particles called atoms. Empedocles introduced the concept of the four classical elements (earth, water, air, and fire) and focused on natural philosophy and biology, exploring the nature of being and change rather than mathematical relationships. Thales of Miletus is often considered the first philosopher in Western history and is known for his work in geometry and astronomy, but he did not specifically articulate a philosophy that framed reality in terms of mathematical relationships as prominently as Pythagoras did.