GHIZATHUDIN ABULFATH IBN IBRAHIM AL KHAYYAMI, who is generally known under the name Omar Khayyám, spent most of his life at Naishápúr. There is a good deal of uncertainty about his dates, but he seems to have lived during the latter part of the eleventh and the beginning of the twelfth centuries. There is a tradition that he died in 1123, but we cannot place too much confidence in it. The most signficant episode in his early years was his friendship with two unusual young men, Nizam al Mulk and Hassan ibn Subbuh. According to the legend these boys agreed that if one of them should come to fame and fortune he would show kindness to the other two. The lucky one was Nizam, and he undertook to carry out the promise. He made Hassan Court Chamberlain. This was a poor move. Hassan turned out to be a troublesome courtier, and was exiled from the Court. He became the head of an exceedingly blood-thirsty and troublesome band of fanatics called Ismailians. They seem to have specialized in assassination; some etymologists tend to derive this word from Hassan, but others connect it with hashish. Omar did not ask for anything so spectacular, he merely desired to be raised so far above want that he could give his life to his favourite studies, mathematics and astronomy. This modest request was granted; he made some return by his work in reforming the calendar.
Omar's fame as a scientist has, in recent years, been completely obliterated by his brilliant reputation as a poet. A good share of the credit for this belongs to his peerless translator, Edward Fitzgerald. I have no competence to express an appreciation here, neither is there any reason for me to discuss his anti-religious philosophy. Some persons have maintained that he was grossly immoral, a libertine addicted to unnatural vice. Perhaps he was, perhaps not. The impression which I get from reading the Rubã`iyyat is that of a sophisticated and disillusioned, but not unkindly cynic, who praises the attainable delights of the senses, and treats his adversaries with caustic wit. Very likely he was an atheist, but he was willing enough to use pious phrases of a conventional pattern. Here are the opening lines of Omar (q.v., Woepcke's translation): "Au nom de Dieu, clément et miséricordieux. Louange à Dieu, seigneur des mondes, une fin heureuse à ceux qui le craignent, et point d'inimitié si ce n'est que contre les injustes. Que la bénédiction divine repose sur les prophètes, et particulièrement sur Mohammed et sur toute sa famille." He closes his essay with these words: "C'est Dieu qui facilite la solution de ces difficultés par ses bienfaits et sa générosité." He frequently wishes that God shall be merciful to this or that other scientist. Such piety is common enough in Islamic writing; very likely Omar had his tongue in his cheek while expressing himself in this fashion, but these phrases did flow from his pen.
Omar wrote a treatise, now completely lost, which seems to have contained something of great interest in the history of mathematics. He writes: "J'ai enseigné à trouver les côtés du carré-carré, du cube-cube etc. à une étendue quelconque, ce qu'on n'avait pas fait précédemment. Les démonstrations que j'ai données à cette occasion, ne sont que des démonstrations arithmétiques, fondées sur les parties arithmétiques des é1éments d'Euclide.''
Tropfke expresses the opinion: "Die letzte Bemerkung kann man offenbar nur auf Benutzung der binomschen Entwickelung auf beliebig hohe Exponenten deuten, wodurch dann Alkhajjami als Entdecker des Binomialtheorems für ganzzählige Exponenten anzusehen wäre."
 Omar Khayyám, L'Algèbre de Omar Alkhayyami, par Franz Woepcke, Paris
 J. Tropfke, Geschichte der Elementarmathematik , 3rd ed., Berlin (1930) vol. ii, p. 174.