Pythagoras significantly impacted both mathematics and philosophy. He is best known for the Pythagorean theorem, which relates the sides of a right triangle and laid foundational principles for geometry. His emphasis on numbers as the essence of all things influenced mathematical thought and established a link between mathematics and music theory. Pythagoras also contributed to philosophical discourse, particularly regarding the concept of the soul and the idea of transmigration. His teachings would later inspire the Platonic tradition, intertwining mathematics with philosophical inquiry, thereby shaping Western intellectual heritage.