The tradition descending from Pythagoras of Samos (c. 570–495 BCE) and his school at
Croton, whose signature doctrine is that number and numerical ratio are the
principle of all things — the source of the "harmony of the spheres," the tetraktys,
and the marriage of arithmetic to cosmology that underlies the whole
"sacred-mathematics" thread of this corpus. It comes with a heavy source-critical
caveat: almost nothing survives from Pythagoras himself, and much "Pythagorean"
lore is later (especially Neoplatonic) reconstruction.
Croton, whose signature doctrine is that number and numerical ratio are the
principle of all things — the source of the "harmony of the spheres," the tetraktys,
and the marriage of arithmetic to cosmology that underlies the whole
"sacred-mathematics" thread of this corpus. It comes with a heavy source-critical
caveat: almost nothing survives from Pythagoras himself, and much "Pythagorean"
lore is later (especially Neoplatonic) reconstruction.
What can be reasonably attributed to the early school: a religious brotherhood with
dietary/ritual rules and belief in transmigration; the discovery that consonant
musical intervals correspond to simple whole-number ratios; and the cultivation of
mathematics (arithmētikē, harmonics, geometry, astronomy — later the quadrivium) as
a path to understanding cosmic order. Later Neopythagoreanism (1st c. BCE–3rd c. CE)
and Neoplatonism elaborated a full number-mysticism and produced the biographies
(Porphyry, Iamblichus) that are our fullest — but least reliable — sources.
Era (prose)
Archaic–Classical Greece (6th c. BCE); Neopythagorean revival 1st c. BCE–3rd c. CE
Region (prose)
Magna Graecia (Croton, S. Italy); Ionia (Samos)
Key persons
Evidence
Label
"The elements of numbers are the elements of all things"
Body
Aristotle reports that "the so-called Pythagoreans, having been brought up in the
study of mathematics, thought its principles were the principles of all things …
and supposed the elements of numbers to be the elements of all things."
Citation
Aristotle, *Metaphysics* I.5, 985b23–986a3 (Ross trans.) —
https://www.perseus.tufts.edu/hopper/text?doc=Aristot.+Met.+1.985b
Source tier
Label
Whole-number ratios of the musical concords (real) vs the smithy legend (myth)
Body
The octave (2:1), fifth (3:2) and fourth (4:3) correspond to simple whole-number
length ratios — a genuine Pythagorean insight; but the popular origin story of
Pythagoras deducing this from hammer-weights at a smithy is legendary and physically
false (pitch does not scale that way with hammer mass).
Citation
ratios via Philolaus (DK B6) and Nicomachus, *Manual of Harmonics*; the
smithy anecdote in Nicomachus and Iamblichus.
Curation status
Label
SOURCE CRITICISM (the load-bearing caveat)
Body
Much of what is popularly "Pythagorean" (elaborate gematria, the golden-ratio
mysticism, the full harmony-of-the-spheres cosmology) is later construction, largely
Neoplatonic.
Citation
Walter Burkert, *Lore and Science in Ancient Pythagoreanism* (Harvard
Univ. Press, 1972); Carl A. Huffman, *Philolaus of Croton* (Cambridge, 1993) and
*Archytas of Tarentum* (2005).
Source tier
Curation status
Import key
9779030624a2fb2cfa08711247409f7c34463fa4
Import hash
eb99769d6beb2de6ac5cc4b6f041b5448236f728