Archelaus was a Greek philosopher who lived during the 5th century BCE. His origins are uncertain, as some ancient sources call him an Athenian and others a Milesian. According to tradition, he was a pupil of the philosopher Anaxagoras and is famously reported to have been a teacher of Socrates. This connection positions him as a historical link between earlier speculative thinkers and the new ethical focus that Socrates would bring to Athenian philosophy.

He is considered the last of the Presocratic "natural philosophers" who primarily investigated the physical world. Archelaus wrote in verse, using the Ionic dialect, but none of his works survive today. His philosophical ideas adapted those of his teacher. He retained the concept of a cosmic organizing principle, often called Mind, but some accounts suggest he interpreted this in a more materialist way, associating it with air.

His significance lies in this transitional role. He not only dealt with traditional questions about the cosmos but also, according to later reports, began to apply philosophical reasoning to human society. He is credited with early theories about the origins of law, justice, and social institutions. While the claim that he taught Socrates is accepted by ancient sources, some modern scholars view this lineage as symbolic of a philosophical transition rather than a strictly historical fact. Nonetheless, Archelaus represents an important figure in the shift from explaining nature to examining human life.