Why Pythagoras Believed Number Was Fundamental

Pythagoras was born on Samos around 570 BCE and founded a community at Croton in southern Italy. He wrote nothing that survives. Our earliest detailed account comes from Aristotle, who reports that “the so-called Pythagoreans” held that the principles of mathematics were the principles of all things.

The earliest surviving Pythagorean writings are fragments by Philolaus, from the late 5th century BCE, a generation or more after Pythagoras died.

The tetractys arranges ten points as 1 + 2 + 3 + 4 = 10. Pythagoreans reportedly swore oaths by it. The pairs it contains, 2:1, 3:2 and 4:3, are the ratios of the octave, fifth and fourth, which is part of why it mattered to them.

Most stories about Pythagoras come from biographies written 700 to 800 years after his death, by Porphyry and Iamblichus. Scholars such as Walter Burkert argue that much of the mathematics credited to him was developed later, or earlier: the “Pythagorean” theorem was used in Babylonia over a thousand years before him.

Did Pythagoras invent numerology? Not in the modern sense. The Pythagoreans gave numbers qualities (odd as limited, even as unlimited), but the letter-to-number charts sold today as “Pythagorean numerology” were popularised in the early 20th century, notably by the American writer L. Dow Balliett.