Omar Khayyam

Lore & Background

Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshāpūrī was born in Nishapur in 1048. His full name in Arabic sources was Abu’l Fath Omar ibn Ibrahim al-Khayyam. He studied religious sciences, Arabic grammar, and literature under Mawlana Qadi Muhammad, then mathematics, astronomy, and cosmological doctrines under Khawjah Abu’l-Hasan al-Anbari.

His gifts were recognized by his early tutors, who sent him to study under Imam Muwaffaq Nishaburi. After studying at Nishapur, about 1068 he traveled to Bukhara, then around 1070 to Samarkand, where he composed his Treatise on Algebra under the patronage of Abu Tahir Abd al-Rahman ibn ʿAlaq. In 1073–4 peace was concluded with Sultan Malik-Shah I, and Khayyam entered his service in 1074 when he was invited by the Grand Vizier Nizam al-Mulk to meet Malik-Shah in the city of Marv. He was commissioned to set up an observatory in Isfahan and lead scientists in revising the Persian calendar, concluding in 1079.

After the deaths of Malik-Shah and his vizier, Khayyam fell from favor and set out on his pilgrimage to Mecca. He was later invited by Sultan Sanjar to Marv, possibly as a court astrologer, then allowed to return to Nishapur due to declining health. He died at age 83 in Nishapur on 4 December 1131 and is buried in what is now the Mausoleum of Omar Khayyam.

Reader's Guide

As a mathematician, Khayyam provided the first general solution for all third-degree polynomials using the intersection of two conic sections, performing geometric calculations by selecting a unit length while adhering to the rule of homogeneity. In On the Division of a Quarter of a Circle, he attempted approximate numerical solutions for cubic equations using trigonometric tables.

He contributed to understanding Euclid's parallel axiom and described the Khayyam–Saccheri quadrilateral in his 11th century book Risāla fī šarḥ mā aškala min muṣādarāt kitāb Uqlīdis. As an astronomer, he calculated the solar year with remarkable precision and designed the Jalali calendar, a solar calendar with a 33-year intercalation cycle that provided the basis for the Persian calendar still in use. There is a tradition of attributing poetry to him in the form of quatrains (rubāʿiyāt), widely known in English through Edward FitzGerald's 1859 translation Rubaiyat of Omar Khayyam.

Did You Know?

• Khayyam's date of birth was established as 18 May 1048 using his horoscope provided by the historian Bayhaqi.
• The length of the year he reported in 1079 was 365.24219858156 days, outstandingly accurate for its time.
• His tomb in Nishapur is at the foot of a garden-wall, where pear and apricot trees drop flowers over it, as he had prophesied.