Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī, commonly known as Omar Khayyam, was a polymath, known for his contributions to mathematics, astronomy, philosophy, and Persian poetry. He was born in Nishapur.

He received a good education in the sciences and philosophy in his native Neyshābūr before traveling to Samarkand (now in Uzbekistan), where he completed the algebra treatise, Risālah fiʾl-barāhīn ʿalā masāʾil al-jabr waʾl-muqābalah (“Treatise on Demonstration of Problems of Algebra”), on which his mathematical reputation principally rests. In this treatise he gave a systematic discussion of the solution of cubic equations by means of intersecting conic sections. Perhaps it was in the context of this work that he discovered how to extend Abu al-Wafā’s results on the extraction of cube and fourth roots to the extraction of nth roots of numbers for arbitrary whole numbers n.

Khayyam’s fame in the West rests upon the collection of robāʿīyāt, or “quatrains,” attributed to him. (A quatrain is a piece of verse complete in four lines, usually rhyming aaaa or aaba; it is close in style and spirit to the epigram.) Omar’s poems had attracted comparatively little attention until they inspired FitzGerald to write his celebrated The Rubáiyát of Omar Khayyám, containing such now-famous phrases as “A Jug of Wine, a Loaf of Bread—and Thou,” “Take the Cash, and let the Credit go,” and “The Flower that once has blown forever dies.” These quatrains have been translated into almost every major language and are largely responsible for colouring European ideas about Persian poetry. Some scholars have doubted that Omar wrote poetry. His contemporaries took no notice of his verse, and not until two centuries after his death did a few quatrains appear under his name. Even then, the verses were mostly used as quotations against particular views ostensibly held by Omar, leading some scholars to suspect that they may have been invented and attributed to Omar because of his scholarly reputation.

Each of Omar’s quatrains forms a complete poem in itself. It was FitzGerald who conceived the idea of combining a series of these robāʿīyāt into a continuous elegy that had an intellectual unity and consistency. FitzGerald’s ingenious and felicitous paraphrasing gave his translations a memorable verve and succinctness. They are, however, extremely free translations, and more recently several more faithful renderings of the quatrains have been published.