Omar Khayyam

Ghiyath al-Din Abu’l-Fath Umar ibn Ibrahim Khayyam Nishapuri was born in 1048 in Nishapur, one of the chief cities of Khorasan (now north-eastern Iran), which had been under Seljuk rule since 1038. The year of his birth is known from a horoscope recorded by the historian al-Bayhaqi, who knew him personally. The name “Khayyam” means “tent-maker” in Arabic, and his father Ibrahim or earlier forebears may have practised that trade.

Khayyam studied in Nishapur and, according to the National Encyclopedia of Uzbekistan, later in Balkh, Bukhara and Samarkand. In philosophy he called Avicenna (Ibn Sina) his teacher, although he could never have met him: Avicenna died eleven years before Khayyam was born. While still young he wrote “The Difficulties of Arithmetic”, a now lost treatise on extracting roots of any degree, and an essay on dividing a quadrant of a circle, in which he reduced a geometric problem to a cubic equation and solved it by intersecting a hyperbola with a circle.

Around 1070 Khayyam settled in Samarkand. There he enjoyed the patronage of the city’s chief judge, Abu Tahir, and, as al-Bayhaqi relates, the Karakhanid ruler Shams al-Mulk Nasr treated him with marked honour. In Samarkand he completed his “Treatise on Demonstration of Problems of Algebra”. He sorted all equations of the first, second and third degree into 25 types, singled out the 14 types of cubic equation that cannot be reduced to simpler ones, and gave each a geometric solution as the intersection of two conic sections. He did not find a general numerical solution and expressed the hope that those who came after him would; Italian algebraists achieved it in the 16th century.

In 1074 Sultan Malik-Shah and his vizier Nizam al-Mulk invited Khayyam to the Seljuk capital, Isfahan. He directed a team of eight astronomers who made observations at a new observatory and prepared a reform of the calendar. The result was a solar calendar called Jalali after one of the sultan’s titles, Jalal al-Dawla, introduced on 15 March 1079. Its year begins with Nowruz at the vernal equinox, and eight years in every 33 are leap years, a scheme more accurate than the Gregorian calendar adopted in Europe five centuries later. The observatory also produced the astronomical tables “Zij-i Malikshahi”, of which only part of the star catalogue survives.

In December 1077 Khayyam completed his “Commentary on the Difficulties Concerning the Postulates of Euclid’s Elements”. In its first part he replaced Euclid’s fifth, parallel, postulate with principles he regarded as more self-evident and studied the quadrilateral now known as the Khayyam–Saccheri quadrilateral; in the second and third parts he reworked the theory of ratios and proposed treating the ratio of any two magnitudes, commensurable or not, as a number. He also wrote philosophical treatises in Arabic and Persian on being, obligation and necessity, and translated Avicenna’s sermon on divine unity into Persian with his own explanations. His method for finding the proportions of gold and silver in an alloy survives in “The Balance of Wisdom” by his student al-Khazini.

In 1092 Nizam al-Mulk was assassinated, and a month later Malik-Shah died. The sultan’s widow withdrew support from the observatory and its work came to an end. Khayyam lost his standing at court; opponents accused him of free-thinking, and according to the historian al-Qifti he made the pilgrimage to Mecca. Later he lived at the court of Malik-Shah’s son, Sultan Sanjar, in Merv, and in 1112–1113 he was in Balkh, where his student Nizami Aruzi of Samarkand was in his company.

Khayyam spent his last years in Nishapur. Al-Bayhaqi relates that shortly before his death he was reading the metaphysics of Avicenna’s “Book of Healing”. The Encyclopaedia Iranica and the Encyclopaedia Britannica date his death to 1131, while some scholars place it in the 1120s. Four years later Nizami Aruzi visited his grave and found it, as Khayyam had once foretold, covered with blossoms from the trees of the neighbouring garden. In 1963 a new mausoleum designed by the architect Hooshang Seyhoun was built over the grave in Nishapur.

In his lifetime Khayyam was known above all as a scientist. Quatrains under his name appear in sources written after his death, and the number of poems attributed to him grew many times over the centuries; which of them are genuinely his is still debated. The Rubaiyat won worldwide fame through Edward FitzGerald’s free English rendering of 1859. In Uzbek literature Abdurauf Fitrat devoted a study to him, “The Persian Poet Omar Khayyam” (1929), and the Uzbek translations of the quatrains are associated above all with the orientalist Shoislom Shomuhamedov. A crater on the far side of the Moon and the asteroid 3095 Omarkhayyam bear his name.