Throughout the Middle Ages a succession of Muslim scholars worked along two lines, one of which led them to generalize the concept of a number. The second can be thought of as an examination of the nature of euclidean geometry which, in modern times, culminated in the appearance of the various non-euclidean geometries. Of the latter, only the first faint foreshadowing occurred in Saljuq and Mongol Iran. Saljuq and Mongol times are to be regarded as a period of consolidation in trigonometry rather than one of innovation. In antiquity a few individuals, notably Aristotle and Seneca, had attempted explanations of rainbow formation, but with little success. That these achievements were of a lesser order than those of Archimedes, and that their consequences were incomparably less significant than the scientific breakthrough which followed the work of Newton and Leibniz is perhaps irrelevant. The scientists of Saljuq and Mongol Iran were the best of their age.

In the midst of states held together by direct military power alone, the Ismā‘īlīs, or "Assassins of Alamϋt", formed a challenging exception. In the cultural life of the time, moreover, the Ismā‘īlī state played a perceptible role, even to the point of acting as host to prominent non-Ismā‘īlī intellectuals. Shi‘is had never been satisfied with the compromises of official Muslim life, which Sunnis had accepted as more or less inevitable up to a point. The Ismā‘īlīs of the Iranian highlands and the Fertile Crescent were not destined to overthrow the Saljuqs but rather to found a society apart, which was set over against Muslim society as a whole. The rigor and self-sufficiency of the doctrine were appropriate to the new sternness required of a movement in active and universal revolt. The justification of the schism, however, was quite legitimately doctrinal.

For nearly a thousand years, Iran has generally been ruled by non-Persian dynasties, usually Turkish, but sometimes Mongol or Kurdish. The first alien rulers were the Saljuq Turks, who appeared in the Iranian world in the first half of the 5th/11th century. This domination at the highest level has had less effect on Iranian national psychology and literary consciousness than might be expected, for all of the alien ruling dynasties have come from races of low cultural development, and thus they have lacked the administrative expertise necessary for ruling a land of ancient settlement and civilization. The collapse of the native Iranian dynasties of the north-east was followed within a few decades by a major migration of Turkish peoples, the Oghuz, from the outer steppes. When the Saljuqs first appeared in Transoxiana and Khurasan in the 5th/11th century, they came as marauders and plunderers. The Saljuqs belonged to the Oghuz Turks, who appear in history as the Toquz Oghuz.