Very few original references to Euclid survive, so little is known about his life. He was likely born c. 325 BC, although the place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes (c. 287 BC – c. 212 BC) onward, and is usually referred to as "ὁ στοιχειώτης" ("the author of Elements"). The few historical references to Euclid were written centuries after he lived, by Pappus of Alexandria c. 320 AD and Proclus c. 450 AD.
A detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be fictitious. If he came from Alexandria, he would have known the Serapeum of Alexandria, and the Library of Alexandria, and may have worked there during his time.
Euclid's arrival in Alexandria came about ten years after its founding by Alexander the Great (356 BC – 323 BC), which means he arrived c. 322 BC.
Proclus introduces Euclid only briefly in his Commentary on the Elements. According to Proclus, Euclid supposedly belonged to Plato's "persuasion" and brought together the Elements, drawing on prior work of Eudoxus of Cnidus and of several pupils of Plato (particularly Theaetetus and Philip of Opus.) Proclus believes that Euclid is not much younger than these, and that he must have lived during the time of Ptolemy I because he was mentioned by Archimedes (287–212 BC). Although the apparent citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote his works before those of Archimedes.