According to Pythagoras, what rules the universe?

The assertion that numbers and laws of geometry rule the universe reflects Pythagoras's belief in the fundamental importance of numerical relationships and mathematical principles in understanding the cosmos. Pythagorean philosophy posited that numbers are not merely counting tools but essential elements that shape reality itself. This perspective indicates that the universe operates according to certain laws that can be expressed mathematically, and that shapes, patterns, and relationships in nature can be understood through geometry.

This viewpoint laid the groundwork for later developments in mathematics and science, highlighting how numerical and geometric principles can explain natural phenomena. Pythagoras and his followers viewed harmony in music, for instance, as a demonstration of numerical ratios, suggesting an intrinsic mathematical order to the universe. Hence, the belief that numbers and geometric laws govern existence aligns closely with Pythagorean thought and is central to understanding their contribution to philosophy, mathematics, and science.