The basic unit of matter, now known to be divisible.
Documented
Democritus named it, physics outgrew it
Around 400 BC Democritus proposed that matter has a smallest indivisible unit: atomos, uncuttable. The word survived 2,300 years, through Dalton's chemistry, until 20th-century physics found electrons, nuclei, and then quarks inside the "uncuttable."
Assessment: Fully documented. The name is a fossil of a disproven claim, kept for historical respect.
Interesting claims
The ancients knew subatomic physics
Fringe readings claim atomism proves Greeks had lost advanced knowledge of particle physics, perhaps inherited from an older civilization.
Assessment: No evidence. Democritus reasoned philosophically, not experimentally, and got most other details wrong. Brilliant guesswork is not inherited instrumentation.
Stories
The laughing philosopher's dream
The story: Democritus, the laughing philosopher, divined the atom in pure thought, no instruments, just the argument that division must end somewhere. Aristotle hated the idea and buried it; Epicurus rescued it; Lucretius versified it; Europe forgot it for fifteen centuries. One poem survived the dark ages by being copied once.
Assessment: Documented as the history of the idea, including the near-loss: De Rerum Natura survived in a handful of manuscripts. The dream part is embroidery. The argument part is real, and it won.
Sources and further reading
Aristotle, De Generatione et Corruptione 1.2, reporting Leucippus and Democritus
Lucretius, De Rerum Natura, Books 1-2
John Dalton, A New System of Chemical Philosophy, 1808
Worth asking
When reality outgrows a name, the name usually stays. What are today's "unsplittable" claims waiting to be revised?