Omar Khayyam

Lore & Background

Omar Khayyam was born in Nishapur—a metropolis in Khorasan province of the Seljuk Empire, of Persian stock, in 1048. His full name was Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshāpūrī. The historian Bayhaqi, personally acquainted with Khayyam, provided his horoscope, which modern scholars used to establish his date of birth as 18 May 1048. Khayyam's boyhood was spent in Nishapur. Having memorized much of the Quran at a young age, he studied religious sciences, Arabic grammar, and literature under Mawlana Qadi Muhammad, then transferred to Khawjah Abu’l-Hasan al-Anbari to pursue mathematics, astronomy, and cosmological doctrines, including Ptolemy's Almagest. His gifts were recognized by his early tutors, who sent him to study under Imam Muwaffaq Nishaburi. About 1068 he traveled to Bukhara, where he frequented the renowned library of the Ark. In about 1070 he moved to Samarkand, where he started to compose his famous Treatise on Algebra under the patronage of Abu Tahir Abd al-Rahman ibn ʿAlaq. In 1074 he entered the service of Sultan Malik-Shah I, commissioned to set up an observatory in Isfahan and lead a group of scientists in precise astronomical observations aimed at revising the Persian calendar. The undertaking ended in 1079, when Khayyam and his colleagues reported the length of the year as 365.24219858156 days. After Malik-Shah's death, Khayyam fell from favor and set out on his pilgrimage to Mecca. He was later invited by Sultan Sanjar to Marv, possibly to work as a court astrologer, and eventually returned to Nishapur, where he died at age 83 on 4 December 1131. He is buried in what is now the Mausoleum of Omar Khayyam.

Reader's Guide

Omar Khayyam's significance as a mathematician includes being the first to provide a general solution for all third-degree polynomials by using the intersection of two conic sections, a method often later attributed to Descartes, but Khayyam performed these geometric calculations by selecting a unit length while strictly adhering to the rule of homogeneity. In his work On the Division of a Quarter of a Circle, he attempted to derive approximate numerical solutions for cubic equations using trigonometric tables. He contributed to a deeper understanding of Euclid's parallel axiom, and the Saccheri quadrilateral is sometimes called a Khayyam–Saccheri quadrilateral to credit him for describing it in his 11th century book Risāla fī šarḥ mā aškala min muṣādarāt kitāb Uqlīdis. As an astronomer, he calculated the duration of the solar year with remarkable precision and accuracy, and designed the Jalali calendar, a solar calendar with a very precise 33-year intercalation cycle which provided the basis for the Persian calendar still in use after nearly a millennium. His surviving mathematical works include Commentary on the Difficulties Concerning the Postulates of Euclid's Elements (completed December 1077), Treatise On the Division of a Quadrant of a Circle, and Treatise on Algebra (most likely completed 1079). He also wrote a treatise on the binomial theorem and extracting the nth root of natural numbers, which has been lost. The poetry attributed to him, written in the form of quatrains (rubāʿiyāt), became widely known to the English-reading world in Edward FitzGerald's 1859 translation, Rubaiyat of Omar Khayyam, which enjoyed great success in the Orientalism of the fin de siècle.

Did You Know?

• Khayyam's date of birth was established by modern scholars using his horoscope, which the historian Bayhaqi recorded as 'Gemini, the sun and Mercury being in the ascendant'.
• He calculated the solar year as 365.24219858156 days; for comparison, the length of the year at the end of the 19th century was 365.242196 days.
• The Saccheri quadrilateral is sometimes called a Khayyam–Saccheri quadrilateral because Khayyam described it in his 11th century book on Euclid's postulates.
• Khayyam's tomb was located by his disciple Nizami Aruzi four years after his death, hidden beneath flowers from pear and apricot trees, as Khayyam had prophesied.
• His Treatise on Algebra was written under the patronage of Abu Tahir Abd al-Rahman ibn ʿAlaq, the governor and chief judge of Samarkand.