Origins
The prefix 'poly-' derives from Greek 'polýs' (πολύς), meaning 'much,' 'many,' or 'frequent.' It is one of Homer's favorite words, appearing throughout the Iliad and Odyssey in compounds describing Odysseus as 'polýtropos' (of many turns, resourceful), 'polýmetis' (of many counsels, crafty), and 'polýtlas' (much-enduring). The word traces to PIE *pelh₁- (to fill, abundance), a root of enormous productivity across the Indo-European family.
The PIE root *pelh₁- branched into three distinct but related concepts as it descended through different language families. In Greek, it became 'polýs' (many). In Latin, it produced 'plēnus' (full), 'plūs' (more), 'plēbs' (the common people, the multitude), and through various pathways gave English 'plenty,' 'plenary,' 'plural,' 'plus,' 'surplus,' 'complete,' 'complement,' 'replete,' 'supply,' and 'accomplish.' In Germanic, the same root produced *fullaz, ancestor of English 'full,' 'fill,' and 'folk' (a people, a multitude). The conceptual thread running through all these descendants is abundance and multiplicity.
The earliest English words using 'poly-' were borrowed from classical Greek through Latin. 'Polygon' (many angles) appears in English by the 1570s, from Greek 'polýgōnon' (πολύγωνον). 'Polysyllable' arrived around the same time. 'Polytheism' (belief in many gods, from 'polýs' + 'theós,' god) entered English in the early seventeenth century as European scholars developed a vocabulary for comparing world religions.
Early History
'Polyglot' (speaking many languages, from 'polýs' + 'glôtta,' tongue) was used from the seventeenth century, most famously for the great Polyglot Bibles that printed scripture in multiple languages side by side. The word has survived to name anyone who speaks several languages.
In geometry, the 'poly-' prefix is foundational. 'Polygon' (many angles), 'polyhedron' (many faces), and 'polytope' (many places, the generalization to higher dimensions) provide the systematic vocabulary for describing multi-sided figures. A pentagon has five sides, a hexagon six, but 'polygon' serves as the general term for any such figure — the 'many-sided' shape.
'Polymath' (from 'polýs' + 'máthēma,' learning) entered English in the seventeenth century to describe a person of wide-ranging knowledge. The word carries an implicit admiration: to be a polymath is to have mastered many fields, in the tradition of Aristotle, Leonardo da Vinci, or Leibniz. The related word 'mathematics' — from the same 'máthēma' — originally meant simply 'things that are learned,' only narrowing to the study of number, quantity, and space over centuries.
Development
Chemistry adopted 'poly-' extensively in the twentieth century. 'Polymer' (from 'polýs' + 'méros,' part) describes a large molecule made of many repeated subunits — literally 'many parts.' The word was applied to natural substances like cellulose and proteins before becoming central to the synthetic materials revolution: 'polyester,' 'polyethylene,' 'polypropylene,' 'polycarbonate,' 'polystyrene,' and 'polyurethane' are all named for being composed of many repeated chemical units. The plastics that define modern material culture are named, at root, for their multiplicity.
In music, 'polyphonic' (many-voiced) describes compositions with multiple independent melodic lines — the texture of a Bach fugue as opposed to a single melody with accompaniment (homophony). The word captures one of the great innovations in Western music history: the development of polyphony in medieval European church music, when composers began weaving multiple independent vocal lines into a single composition.
The twenty-first century has added 'polyamory' (from 'polýs' + Latin 'amor,' love — a hybrid Greek-Latin formation) to the lexicon, describing consensual romantic relationships involving multiple partners. This hybrid etymology — Greek 'poly-' attached to Latin 'amor' — is typical of how living English prefixes freely combine with roots from any source.