Plutarch, writing in the first century CE, reports that the Athenians preserved the ship in which Theseus had returned from Crete, replacing each plank as it rotted. Eventually, every plank had been replaced. Was it still the same ship? Hobbes asked the harder version: imagine the original planks had been gathered as they were discarded and reassembled into a ship. Now there are two candidates. Which one is the ship of Theseus? The puzzle is two thousand years old, has many proposed solutions, and refuses to resolve.
The Ship of Theseus is the canonical case for problems of identity over time. The intuitive criteria — material continuity, form continuity, causal/historical continuity — give different answers depending on which you weight, and most candidate criteria can be made to conflict in some scenario. Locke's psychological-continuity theory of personal identity (you are the same person if memory and personality persist) and Parfit's reductionist view (personal identity is less important than we think; only the underlying physical and psychological connections matter) extend the ship problem to persons. Modern variants are everywhere: am I the same person as the version of me ten years ago, given that nearly every cell has been replaced and most beliefs have shifted? Is the brain in a transplant the patient? Is a teleported person the original or a copy? Is a gradually digitized mind the same mind? Is Apple the same company it was in 1976 when none of its founders or original products remain? Is a theory the same theory after Kuhnian paradigm shifts? The ship is not just a thought experiment; identity-over-time is the underlying problem in personhood, organizational continuity, legal liability, intellectual-property succession, biographical narrative, and quite a bit of metaphysics.
Mind uploading, teleportation thought experiments in physics, neural prostheses, gene therapy that modifies the patient's genome, organizational successions in companies and governments — all are operating in Ship-of-Theseus territory. The 21st-century bioethics of personal identity (when does the patient become a different person? at what point does cognitive enhancement break continuity?) is a live subfield. The ancient puzzle has acquired engineering relevance.