Medieval Islam became the principal heir to ancient Greek science, and Islamic civilisation remained the world leader in virtually every field of science between 800-1300 AD. The sheer level of scientific activity underlines this point, as the number of Islamic scientists during the four centuries after the Prophet matched the number of Greek scientists during the four centuries following Thales. Islamic scientists established the first truly international scientific community stretching from Iberia to Central Asia. Yet, medieval Islamic science is sometimes dismissed as a conduit passively transmitting ancient Greek science to the European Middle Ages. A moment's thought, however, shows how unreasonable it is to evaluate the history of Islamic science only or even largely as a link to European science, or even to subsume Islamic science into the ‘Western tradition’. Medieval Islam and its science must be judged on their own terms, and those terms are as much Eastern as Western.