Archytas of Tarentum
Pythagorean statesman, mathematician, and the friend who saved Plato's life.
Overview
A leading Pythagorean, brilliant mathematician, general, and seven-times ruler of Tarentum, Archytas united philosophy with public life. He advanced mathematics (famously solving the doubling of the cube and working on proportion and acoustics), founded mathematical mechanics, and argued that the universe is unbounded. A close friend of Plato, he intervened to rescue him from the tyrant Dionysius II of Syracuse.
What they supported — and why
Mathematics is the key to knowledge
SupportedThe mathematical sciences — arithmetic, geometry, astronomy, music — yield true understanding and even guide morals and politics.
WhyCalculation and proportion reveal the order in things and can reconcile social conflict, so they are the surest form of knowledge.
The universe is unbounded
SupportedStanding at the supposed edge of the cosmos, could you not stretch out your hand or staff? — so there can be no fixed boundary.
WhyAny proposed edge invites the question of what lies beyond it, so the universe cannot be finitely bounded.
Harmony and moderation in politics
SupportedRight proportion, as in music, underlies justice and social concord.
WhyThe same mathematical harmony that orders sound can order a balanced, just community.
Causes championed
- Mathematics in the service of life
- Harmony in politics
- The unity of theory and practice
Issues wrestled with
- How does mathematics ground knowledge?
- Is the universe bounded?
- How is a just society ordered?
Hurdles faced
- Balancing philosophy with the demands of rule and war
Works & books
1 catalogued. Status shows how much survives to today.
Mathematical and philosophical works
Fragments onlyTreatises on mathematics, music, and mechanics; survive in fragments and reports via Ptolemy and Diogenes Laërtius.
Read the texts free
Their works online — Open Library catalogues 5 works & editions, 1 of them free to read in full.
The influence network
See Archytas of Tarentum in the map →Influenced by
Influenced
In their words
“If I were at the outermost edge of the heaven, could I stretch my hand or staff outward, or not?”
— the unbounded-universe argument, via Eudemus
Legacy
The model of the philosopher-statesman-scientist, his mathematics shaped Plato and, through the quadrivium, all of medieval education.
Further reading
Cross-checked against these authoritative references.