Neugebauer began his career as a mathematician, then turned to Egyptian and Babylonian mathematics, and then took up the history of mathematical astronomy. In a career which spanned sixty-five years, he largely created modern understanding of mathematical astronomy in Babylon and Egypt, through Greco-Roman antiquity, to India, the Islamic world, and Europe of the Middle Ages and the Renaissance. The noted physicist and astronomer Gerry Neugebauer at Caltech was his son.