Hesiod begins the Theogony with an encounter, and it is one of the most disquieting passages in Greek literature. The Muses came to him while he was pasturing lambs under Helicon, and the first thing they said was an insult: shepherds living in the fields, mere bellies, disgraces. Then the claim that matters — we know how to say many false things that resemble the truth, and we know, when we wish, how to speak the truth. Then they gave him a staff of laurel and breathed a divine voice into him.
A poem opens by having its own sources of inspiration announce that they lie convincingly when they feel like it. Nothing in the ancient world is a sharper warning about the reliability of poetry, and it comes from the poets' own patron goddesses.
Three, then nine, and the portfolio comes later
The count is not fixed. Pausanias reports that the oldest tradition at Helicon named three — Melete (practice), Mneme (memory) and Aoide (song) — and that the nine were introduced later by Pieros of Macedon, who gave them the names now standard. Delphi also had a triad, named after the three strings of the lyre. Other sources give four, seven or eight.
Hesiod's nine, with their names, is the version that won: Calliope (beautiful voice), Clio, Euterpe, Thalia, Melpomene, Terpsichore, Erato, Polyhymnia, Urania. Note that he gives names and no job descriptions. The tidy allocation everyone learns — Clio history, Urania astronomy, Melpomene tragedy with her mask, Terpsichore dance — is late, largely Roman and Byzantine, and appears in art before it is fixed in text. Any list presenting the nine specialisms as classical Greek is presenting a Roman schoolroom convention.
Their mother is Mnemosyne, Memory, and their father Zeus, after nine consecutive nights. In an oral culture that is not a decorative genealogy: poetry is memory, the poet's craft is the storage and retrieval of a tradition without writing, and the daughters of Memory are the mechanism by which anything from the past reaches the present.
What invoking them actually claims
Homer's openings — "Sing, goddess, of the anger" and "Tell me, Muse, of the man" — are requests for information, not decoration. The clearest case is in Iliad 2, before the Catalogue of Ships, where the poet says he could not tell the multitude of the Greeks even with ten tongues and ten mouths, unless the Muses remind him, because they are present and know everything while mortals hear only rumour. The Muse is the difference between hearsay and eyewitness, and the invocation is the poet's claim to be reporting rather than inventing.
That is why the practice survived so long. Virgil, Ovid, Dante, Milton, Pope and Byron all invoke, and Milton's invocation in Paradise Lost is a careful negotiation — he calls on a Heavenly Muse instead, "Urania" by meaning if not by name, explicitly not the pagan one.
Helicon and Pieria
Their two homes are Mount Helicon in Boeotia, with the springs Hippocrene — struck open by the hoof of Pegasus — and Aganippe, and Pieria in Macedonia at the foot of Olympus, which is why they are called Pierides. The Valley of the Muses at Thespiae held a real sanctuary with a festival, the Mouseia, involving musical and dramatic competitions, and a substantial collection of statuary. Pausanias saw it and describes the images, several by named sculptors.
The word museum comes directly from mouseion, a place of the Muses. The great one at Alexandria, founded under the early Ptolemies, was a research institution with a salaried body of scholars, dining hall, walkways and the Library attached — closer to an endowed university faculty than to a gallery. The modern museum, full of objects and short of scholars, has kept the name and inverted the function.
The contests they win
They compete and they do not lose gracefully. The Pierides, nine daughters of King Pieros, challenged them and were turned into magpies, chattering endlessly — Ovid tells it in Metamorphoses 5, and the contest itself takes up most of the book, with each side singing a long song. Thamyris, a Thracian bard, boasted he could beat them and was blinded and had his gift of song and lyre-playing taken away; the Iliad mentions it in passing as a known story. The Sirens are said in one tradition to have lost to them and been stripped of their wing feathers, which the Muses wore as crowns.
That pattern is not incidental. The Muses guarantee that poetry is a gift from outside, and every one of these stories punishes someone for claiming it as a personal talent.
Individually
A few of them have stories of their own. Calliope, chief of the nine, is the mother of Orpheus by Apollo or by the Thracian king Oeagrus — which makes the greatest singer in Greek myth literally the son of epic poetry. Urania and Clio are given various children in the genealogies. Melpomene is named in some sources as the mother of the Sirens by the river Achelous, a striking pairing of the good song and the deadly one. Otherwise they act as a group, and Greek art usually shows them as a group.
Amuse, music, mosaic
Their linguistic descendants are unusually numerous. Music is mousike, "the art of the Muses", which in Greek meant the whole complex of poetry, song, dance and instruction, not sound alone. Museum is theirs. Mosaic probably reaches English through a medieval Latin word connected to grottoes of the Muses. And "a muse" in the modern sense — a specific person who inspires an individual artist, usually a woman, usually silent — is a nineteenth-century Romantic construction that has almost nothing to do with the goddesses, who were plural, professional, occasionally abusive, and worshipped at a sanctuary with a competition schedule.
Cult, astronomy, and Plato’s suspicion
Were they worshipped or just invoked?
Genuinely worshipped, with sanctuaries, festivals, priesthoods and dedications. The Valley of the Muses at Thespiae is the principal site, with the quadrennial Mouseia; Athenian philosophical schools kept a mouseion in their grounds, and Plato's Academy and Aristotle's Lyceum both had one, which is why philosophers are described as making offerings to them. Schools in general placed themselves under their protection.
Which Muse gets astronomy, and why?
Urania, whose name means "heavenly", and the assignment reflects a Greek view that astronomy and harmonics were branches of the same mathematical study — the music of the spheres is not a metaphor in Pythagorean and Platonic thought. She is shown with a globe and a pointer. Her portfolio is the clearest sign that the nine cover organised knowledge generally, not just the arts as a modern reader would define them.
Does anyone besides Hesiod claim to have met them?
Archilochus was said to have encountered them as a boy while leading a cow to market, receiving a lyre in exchange, according to an inscription set up on Paros centuries later. Later poets imitated the Hesiodic initiation scene deliberately — Callimachus and Ennius both stage versions of it, Ennius dreaming that Homer's soul passed into him. The convention became a way of claiming a poetic lineage, which is roughly what a modern epigraph does.
Why does Plato distrust them?
Because if poetic knowledge comes from outside the poet, the poet cannot explain or defend it. In the Ion, Socrates presses a professional reciter of Homer until he admits he has no expertise, and describes inspiration as a chain of magnetised iron rings hanging from the Muse — impressive, and entirely passive. The Republic's hostility to poetry follows from that. It is essentially the anxiety Hesiod's own Muses raise when they mention how well they lie.