The discovery that the Earth is round is most commonly ascribed to the ancient Greek philosopher Pythagoras, while the credit for proving it is usually given to Aristotle. It appears that most ancient Greek philosophers that followed him believed in a round Earth. Since the records from that time are not perfect, it is quite possible that someone before him was aware of the Earth's round shape.
Aristotle demonstrated the Earth was round by drawing on a variety of evidence: the curvature of the horizon, the way constellations appear in the sky and the way a ship disappears over the horizon, for example. Contrary to popular belief, Christopher Columbus did not discover that the Earth was round, and no debate over the Earth's shape occurred in preparation for his voyage; rather, the circumference of the Earth was what was at issue.