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How did medieval scholars connect Pythagoras with the quadrivium?

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Marble bust of Pythagoras, the ancient Greek mathematician and philosopher, showing a bearded man with a head covering and calm expression. — Pythagoreanism Greek philosopher and mathematician Pythagoras, portrait bust.

Medieval scholars connected Pythagoras to the quadrivium—the four liberal arts of arithmetic, geometry, astronomy, and music theory—by regarding him as the "father" of these specialized disciplines.1

This connection was primarily facilitated through the writings of Boethius, a 6th-century philosopher whose Latin redactions of Greek scientific works served as a vital bridge for Western knowledge. Specifically, Boethius’s Arithmetic, which was based on the work of Nicomachus of Gerasa, provided medieval scholars with their primary access to Pythagorean number theory.2

By integrating these mathematical and harmonic concepts into the monastic and cathedral school curricula, medieval educators solidified the association between Pythagorean thought and the structural foundations of the quadrivium.21