Omar Khayyam

Omar Khayyam, born in 1048 in Nishapur (in present-day Iran), was a Persian scholar and poet active during the Seljuk era, roughly contemporary with the First Crusade. He made significant contributions across mathematics, astronomy, philosophy, and Persian literature.

In mathematics, Khayyam was the first to find a general method for solving all third-degree polynomials, using the intersection of two conic sections. Unlike later mathematicians, he performed these geometric calculations by selecting a unit length and strictly following the rule of homogeneity. He also attempted to derive approximate numerical solutions for cubic equations using trigonometric tables, and he advanced understanding of Euclid's parallel axiom. The Saccheri quadrilateral is sometimes called the Khayyam–Saccheri quadrilateral because Khayyam described it in his 11th-century book *Explanations of the Difficulties in the Postulates of Euclid*.

As an astronomer, Khayyam calculated the solar year with extraordinary precision and designed the Jalali calendar, a solar calendar with a highly accurate 33-year intercalation cycle. This calendar became the basis for the Persian calendar, still in use nearly a thousand years later.

Khayyam is also traditionally associated with poetry composed in quatrains (*rubāʿiyāt*). These verses became widely known in the English-speaking world through Edward FitzGerald's 1859 translation, *Rubaiyat of Omar Khayyam*, which achieved great success during the fin de siècle period of Orientalism.

Born Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshāpūrī, he was of Persian stock. His name "Khayyam" means "tent-maker" in Arabic, though it is uncertain if his family actually followed that trade. The historian Bayhaqi, who knew Khayyam personally, recorded his horoscope, allowing modern scholars to fix his birth date as 18 May 1048.

Khayyam spent his boyhood in Nishapur, a major Seljuk metropolis and former center of Zoroastrianism. He memorized much of the Quran at a young age, studying religious sciences, Arabic grammar, and literature under Mawlana Qadi Muhammad. He later studied mathematics, astronomy, and cosmology—including Ptolemy's *Almagest*—under Khawjah Abu’l-Hasan al-Anbari. His early tutors recognized his gifts and sent him to study under Imam Muwaffaq Nishaburi, the region's greatest teacher, with whom Khayyam formed a lasting friendship. He may also have studied with Bahmanyar, a disciple of Avicenna. Around 1068, after completing his studies in Nishapur, he traveled to Bukhara, where he frequented the famous library of the Ark. By about 1070, he had moved to Samarkand and began writing his *Treatise on Algebra* under the patronage of the governor and chief judge Abu Tahir Abd al-Rahman ibn ʿAlaq. The Karakhanid ruler Shams al-Mulk Nasr received him kindly, often seating him beside him on his throne.

In 1073–74, peace was made with Sultan Malik-Shah I, who had invaded Karakhanid lands. In 1074, Khayyam entered Malik-Shah's service when Grand Vizier Nizam al-Mulk invited him to meet the sultan in Marv. Khayyam was then commissioned to establish an observatory in Isfahan and lead a team of scientists in precise astronomical observations to revise the Persian calendar. The work likely began with the observatory's opening in 1074 and concluded in 1079, when Khayyam and his colleagues measured the year's length as 365.24219858156 days—remarkably accurate, even by modern standards.

After the deaths of Malik-Shah and his vizier (the latter reportedly murdered by the Ismaili Assassins), Khayyam fell out of favor at court and soon set out on a pilgrimage to Mecca. According to Al-Qifti, this may have been a public demonstration of faith to counter suspicions of skepticism or unorthodoxy, including possible sympathy for Zoroastrianism. He was later invited by Sultan Sanjar to Marv, possibly as a court astrologer, but eventually returned to Nishapur due to declining health, living as a recluse.

Khayyam died at age 83 in Nishapur on 4 December 1131 and is buried in what is now the Mausoleum of Omar Khayyam. His disciple Nizami Aruzi relates that around 1112–13, while in Balkh with the scientist Isfizari, Khayyam prophesied that his tomb would lie where the north wind could scatter roses over it.