This paper was given as a public lecture to open the 2005 Conference of Greek Studies. It presents a case for locating the origins of science with the ancient Greeks. Although this was once a common view, it has come under fire in the latter part of the twentieth century. The main case is presented briefly, along with some new considerations in favour of the Greeks as the originators of science. There is then a discussion of some of the strategies that might be employed to counter some of the objections that have been raised, either relating to some of the weaknesses of Greek science or to some of the methodological issues involved in approaching ancient Greek science