Ghiyāth al-Dīn Abu'1-Fath ‘Umar b. Ibrāhīm al-Khayyāmi (the full name of ‘Umar Khayyām as it appears in the Arabic sources) in Persian texts is usually called simply ‘Umar-i Khayyām, that is, ‘Umar the tent-maker, and it is reasonable to assume that his father or grandfather followed that trade. He was almost certainly born in Nīshāpūr, where he passed the greater part of his life and where his grave is still to be seen. Our earliest authority, the Tatimma suwān al-hikma (or Ta'frīkh hukamā’ al-Islām), by Zahīr al-Din Abu'l-Hasan Baihaqi, written some time before 549/1154–5, states quite categorically that ‘Umar was a Nīshāpūri by birth, as also were his father and his ancestors. On the other hand, a late work, the Tārīkh-i aljī of Ahmad Tatavi (988/1580) refers to another tradition according to which his family came from a village called Shamshād near Balkh, though he himself was born in the vicinity of Astarābād at the north-east corner of the Caspian. So, too, the 9th/15th-century writer Yār Ahmad Rashīdī Tabrīzī in his Tarabkhāna says that ‘Umar was born near Astarābād and passed his early life in Balkh.

The dates of his birth and death have only recently been established; thanks to the researches of the Indian scholar Govinda Tirtha and the Soviet scholars Rozenfel'd and Yushkevich, the editors of ‘Umar's scientific works, it is possible to name, with almost absolute certainty, the actual date not only of his birth but also of his death. It so happens that Baihaqī, our oldest authority, gives the full details of his horoscope, and on the basis of these data Govinda was able to calculate the exact day of ‘Umar's birth.