Origins
The English word 'three' descends from Old English 'þrēo' (feminine and neuter; the masculine form was 'þrīe'), from Proto-Germanic *þrijiz, ultimately from the Proto-Indo-European root *tréyes. Like the numerals 'one' and 'two,' it is among the most securely reconstructed words in comparative linguistics, with cognates in virtually every branch of the Indo-European family.
The cognate set is impressively regular. Latin 'trēs,' Greek 'treîs,' Sanskrit 'tráyas,' Old Irish 'trí,' Lithuanian 'trỹs,' Old Church Slavonic 'trĭje,' Armenian 'erekʿ' (with regular Armenian sound changes), and Albanian 'tre' all descend from PIE *tréyes. The word is so stable that it was among the first cognate sets identified by Sir William Jones and the early comparative linguists who established the Indo-European hypothesis in the late 18th century.
The initial consonant of 'three' provides a classic demonstration of Grimm's Law, the systematic sound shift that distinguishes Germanic from other Indo-European branches. PIE *t regularly became Proto-Germanic *þ (the voiceless dental fricative spelled 'th' in English). This is the same shift that relates Latin 'tenuis' to English 'thin,' Latin 'tū' to English 'thou,' and Latin 'tonāre' to English 'thunder.' The shift was first systematically described by Jacob Grimm in 1822 and remains one of the foundational discoveries of historical linguistics.
Germanic Development
Like 'two,' Old English 'three' was inflected for gender and case — a complexity entirely lost in Modern English. The masculine nominative was 'þrīe,' the feminine and neuter nominative 'þrēo,' the genitive 'þrēora' for all genders, and the dative 'þrim.' This system was inherited from Proto-Germanic and parallels the inflection patterns of low numerals in Latin, Greek, and Sanskrit.
The number three has generated a rich family of derivatives in English. 'Third' comes from Old English 'þridda' (with metathesis — the reversal of 'r' and the vowel — from earlier *þridja). 'Thrice' is formed with an adverbial suffix like 'once' and 'twice.' 'Thirteen' is from Old English 'þrēotīene' (three + ten), and 'thirty' from 'þrītig' (three tens). Through Latin, English acquired 'triple,' 'trinity,' 'trio,' 'trivial' (from Latin 'triviālis,' belonging to the crossroads or 'trivium' where three roads meet), and 'tribe' (from Latin 'tribus,' possibly referring to the original three divisions of Rome). Through Greek came 'triad,' 'trigonometry,' and the prefix 'tri-' in countless technical terms.
The cultural significance of three is vast and cross-cultural. The number appears with striking frequency in mythology, religion, and narrative: the Christian Trinity, the Hindu Trimūrti, the three Fates of Greek mythology, the three Norns of Norse mythology, the narrative rule of three in storytelling. Some anthropologists have suggested that the special status of three reflects a cognitive threshold — the largest quantity that humans can perceive instantly without counting (a phenomenon called 'subitizing'). Whether this cognitive fact drove the cultural prominence of three, or whether the relationship is coincidental, remains debated.
Old English Period
Phonologically, the development from Old English 'þrēo' to Modern English 'three' is mostly regular. The long 'ēo' diphthong monophthongized to a long 'ē' in Middle English, which then underwent the Great Vowel Shift to become /iː/. The initial /θr/ cluster has been maintained in standard English, though many dialects simplify it: in some varieties of English, 'three' is pronounced with an initial /f/ ('free'), a merger of /θ/ and /f/ that is widespread in London English and other urban dialects.
The form *tréyes itself appears to be an old plural — the PIE numeral 'three' was grammatically plural, reflecting the fact that three of something is inherently more than one. This contrasts with 'one' (singular) and 'two' (which in many IE languages triggered the dual number, a grammatical category between singular and plural). The disappearance of the dual in most modern IE languages has obscured this once-important three-way distinction in number grammar.