Omar Khayyam

Omar Khayyam (in Persian ʿUmar-i Khayyām) was born in 1048 in Nishapur, a great city of Khorasan in north-eastern Iran, and died there in old age, most probably in 1131. His full name, Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm, contains an honorary title (“Help of the Faith”) and his father’s name, Ibrahim. The word khayyām means “tent-maker” in Arabic, which may point to his family’s trade.

In his own lifetime he was admired as a mathematician, astronomer and philosopher. He wrote a groundbreaking book on cubic equations, a commentary on Euclid, and philosophical essays in the tradition of Avicenna, and he led the astronomers who produced a new solar calendar for the Seljuk sultan Malik-Shah.

Today, however, most people know him as a poet. Quatrains (rubāʿiyāt) about the shortness of life, wine and the mystery of existence were attributed to him in later centuries. The English poet Edward FitzGerald’s free version, The Rubáiyát of Omar Khayyám (1859), made “Omar” one of the best-known names of Persian literature. How many of these poems he really wrote is one of the great puzzles of literary history.

Khayyam lived under the Seljuks, a Turkic dynasty that took control of Iran and Iraq in the mid-eleventh century and ruled in the name of the Abbasid caliph in Baghdad. The Seljuk sultans governed through Persian administrators, and Persian became a major language of culture alongside Arabic, the language of religion and most science.

The most famous Seljuk statesman was the vizier Nizam al-Mulk, who founded colleges called Nizamiyyas to train scholars. The period was rich in learning but also dangerous. Religious and political conflicts were intense; the Ismaili movement later known in Europe as the Assassins opposed the Seljuks, and Nizam al-Mulk was murdered in 1092, probably by them. The First Crusade reached Syria and Palestine during Khayyam’s later years.

For a scholar like Khayyam, a rich patron was essential. Instruments, libraries and time for research depended on the favour of rulers and officials, and that favour could disappear suddenly when a patron died.

Khayyam grew up in Nishapur, where he studied the Quran, Arabic, religious sciences, mathematics and astronomy. The historian al-Bayhaqi, who knew him personally, recorded his horoscope, from which modern scholars have calculated his birth date as 18 May 1048. He regarded Avicenna, who had died in 1037, as his intellectual master, although he could not have studied with him directly.

Around 1068 he went to Bukhara, and around 1070 to Samarkand, where the chief judge Abu Tahir became his patron and he wrote his famous treatise on algebra. In about 1074 he was invited by Nizam al-Mulk to the court of Sultan Malik-Shah and was asked to lead astronomical work at Isfahan. For nearly two decades he enjoyed rare stability.

After Malik-Shah and Nizam al-Mulk died in 1092, support ended. According to later reports, Khayyam made the pilgrimage to Mecca, perhaps partly to answer accusations that he held unorthodox views. He later served Sultan Sanjar at Marv and eventually returned to Nishapur, where he seems to have lived quietly. His pupil Nizami Aruzi describes visiting his grave there four years after his death, under trees that dropped blossoms on it.

Khayyam’s most important mathematical work is the Treatise on the Demonstration of Problems of Algebra, written in Arabic. Building on the algebra of al-Khwarizmi and his successors, he set out to classify and solve all equations of degree up to three—those involving numbers, “roots” (the unknown), “squares” and “cubes.”

Like earlier Islamic mathematicians, he allowed only positive coefficients and positive solutions, so equations that look alike to us were separate cases for him. He listed all possible forms and found that fourteen kinds of cubic equation cannot be reduced to simpler ones. He stated that these could not be solved with straightedge and compass alone, a claim that was only proved in the nineteenth century.

For each of the fourteen types he gave a geometric solution: the unknown is represented by a line segment determined by the intersection of two conic sections—for example a parabola and a circle, or a parabola and a hyperbola. He also discussed when such an equation has no positive solution or more than one.

Khayyam knew that he had not found an arithmetical formula for the cubic. He wrote that perhaps someone after him would discover it. Such formulas were indeed found in sixteenth-century Italy by Scipione del Ferro, Niccolò Tartaglia and Gerolamo Cardano. Because he systematically connected algebra and geometry, some historians see him as a forerunner of the analytic geometry of Descartes.

In his Commentary on the Difficulties in the Postulates of Euclid, completed in 1077, Khayyam examined Euclid’s fifth or “parallel” postulate, which many mathematicians felt should be provable from the other axioms. He criticised earlier attempts—including Ibn al-Haytham’s—for secretly assuming what they wanted to prove or for introducing motion into geometry, which Aristotle had rejected.

Khayyam replaced the postulate with principles he took from Aristotle about converging lines, and studied a quadrilateral with two equal sides perpendicular to a base. He considered whether its two upper angles are right, acute or obtuse, and argued that only the right-angle case is consistent. The same figure appears in the eighteenth-century work of Girolamo Saccheri and is sometimes called the Khayyam–Saccheri quadrilateral. The acute and obtuse cases are now known to correspond to non-Euclidean geometries.

The same treatise discusses ratio and proportion. Khayyam showed that Euclid’s definition of equal ratios is equivalent to another definition based on a process like continued fractions, and he argued that ratios of magnitudes—including irrational ones—can be handled as numbers. Some historians see here a step toward the modern concept of real number.

Khayyam also wrote shorter scientific works. One applies Archimedes’ principle to find the proportions of gold and silver in an alloy by weighing it in air and in water. Another deals with music theory, classifying musical intervals and scales by numerical ratios. In his algebra he mentions a lost book on extracting roots of any degree, which suggests that he knew a general rule for expanding powers of a binomial—the pattern of coefficients known in Iran as “Khayyam’s triangle” and in Europe as Pascal’s triangle, which the earlier mathematician al-Karaji had already described.

Around 1074 Sultan Malik-Shah commissioned an observatory at Isfahan, where Khayyam headed a team of about eight scholars. Their aim was to revise the astronomical tables and reform the calendar. The observatory’s results were collected in an astronomical handbook known as the Zīj-i Malikshāhī.

The new calendar, named Jalālī after one of the sultan’s titles, was inaugurated in 1079. It was a true solar calendar: the year began at Nowruz, the spring equinox, and the months followed the Sun’s passage through the signs of the zodiac. Khayyam’s team reported the length of the year as 365.24219858156 days, extremely close to modern values.

Later sources describe an intercalation system based on a 33-year cycle containing eight leap years. Such a calendar drifts by only about a day in several thousand years—more accurate than the Gregorian calendar introduced in Europe in 1582. The Jalali calendar remained in use in Iran for centuries and became the basis of the modern Iranian solar calendar adopted in 1925.

Sources call Khayyam and his colleagues experts in ʿilm al-nujūm, “the science of the stars,” a term that covered both mathematical astronomy and astrology. His pupil Nizami Aruzi remarked that he did not observe Khayyam placing much faith in astrological predictions, and the historian of science George Saliba has warned that translating the term simply as “astrology” misrepresents the astronomers’ work. Even so, later reports say that at Sanjar’s court he was expected to forecast events such as the weather.

Khayyam wrote a small number of philosophical treatises, mostly in Arabic and one in Persian. He worked within the Aristotelian-Neoplatonic tradition shaped by Avicenna. He translated and commented on one of Avicenna’s discourses on God’s unity, and according to al-Bayhaqi he was reading Avicenna’s metaphysics on the day he died.

In these works he defends the existence of God as the Necessary Existent and discusses existence, essence and universals, arguing that existence is a concept in the mind rather than something added to essences in reality. In a treatise on the necessity of contrariety in the world, he addresses the problem of evil: God creates beings that are good in themselves, while evil arises only accidentally from the contrary relations among them. He also discusses determinism, seeming to allow human agency within a framework of cosmic necessity.

In one treatise he surveys different ways of seeking knowledge—theologians, philosophers, Ismailis and Sufis—and appears to give special value to the Sufi path of purification. How this fits with the sceptical voice of the quatrains is still debated. His philosophical works were long neglected and have received serious study only in recent decades.

A rubāʿī (plural rubāʿiyāt) is a Persian poem of four lines, usually rhyming aaba, often ending with a sharp or surprising thought. The quatrains linked to Khayyam speak of the passing of time, the mystery of where we come from and go, the potter shaping clay (an image of creation), wine and friendship, and the wisdom of enjoying the present moment.

Edward FitzGerald (1809–1883) learned Persian from his friend Edward Cowell, who gave him a transcript of a manuscript in the Bodleian Library at Oxford, copied in Shiraz in 1460 and containing 158 quatrains, and later a copy of another manuscript in Calcutta. FitzGerald’s first edition of 1859 contained 75 stanzas. He called his work a “rendering” rather than a translation: some stanzas follow one Persian quatrain closely, while others combine or freely reinvent several.

At first the booklet did not sell, but from the 1860s it was admired by the Pre-Raphaelite poets and became hugely popular in the English-speaking world. FitzGerald revised it several times; Omar Khayyam Clubs were founded, and by 1929 more than 300 editions had appeared. Lines such as “The Moving Finger writes; and, having writ, / Moves on” became part of the English language. The poem’s success also shaped a Victorian image of the “East” as exotic and sensual.

In his lifetime Khayyam was known as a scientist, not a poet. The earliest mention of his poetry comes from al-Isfahani in 1174, more than forty years after his death, and concerns Arabic verses. Individual Persian quatrains are quoted under his name by Fakhr al-Din al-Razi (c. 1160s), Najm al-Din Daya (c. 1230), Juvayni and, in 1340, the anthologist Jajarmi, who gives thirteen. Five quatrains later attributed to him already appear, unattributed, in the Sindbad-nāma of Zahiri Samarqandi from before 1160.

Later manuscripts, by contrast, attribute hundreds of quatrains to him, and modern collections have listed well over a thousand. The poems are uneven in language and contradictory in outlook, and many “wandering quatrains” are also attributed to other poets. In 1934 Hans Heinrich Schaeder went so far as to say that Khayyam’s name should be struck from the history of Persian literature. The Iranologist François de Blois has argued that little progress has been made since.

Scholars have tried various methods to identify a core of authentic poems. Arthur Christensen accepted 121 as reasonably authentic; Mohammad-Ali Foroughi accepted 178; Ali Dashti 36; and the writer Sadegh Hedayat only 14. After the Second World War, two manuscripts claimed to be very early—published with great excitement—were shown to be forgeries, a warning about how strong the desire for an “original Khayyam” is. Most scholars agree that he probably wrote some quatrains, but that it is rarely possible to prove that a particular poem is his.

FitzGerald presented Omar as an Epicurean sceptic whose wine was “the veritable Juice of the Grape.” Many scholars, including Arthur Christensen and later the Iranian writer Sadegh Hedayat, read the quatrains as expressing doubt about religious doctrine, the afterlife and divine justice. Medieval evidence partly supports a reputation for free thought: al-Qifti claimed in the thirteenth century that the poems were only outwardly Sufi, and several famous Sufi writers, such as Najm al-Din Daya and Attar, spoke of Khayyam with hostility.

A minority of interpreters—such as J. B. Nicolas in the nineteenth century and later Idries Shah—read the wine, the tavern and the beloved as Sufi symbols of mystical ecstasy. Critics such as Mehdi Aminrazavi respond that a Sufi reading is possible only by stretching the poems to fit classical doctrine. Others, such as Seyyed Hossein Nasr, warn that basing Khayyam’s philosophy on poems of uncertain authenticity is reductive, and point to his orthodox philosophical prose.

Recent scholarship tries to read the prose and the poems together. The Stanford Encyclopedia of Philosophy entry by Aminrazavi and co-authors suggests that the tension between the rational theism of the treatises and the bewildered protest of the quatrains may reflect a conflict between abstract reasoning and lived experience of suffering, rather than proving two different authors. Whatever one decides, it is essential to separate three layers: the historical Khayyam, the medieval Persian quatrain tradition, and FitzGerald’s Victorian poem.

Khayyam’s mathematical work continued to be studied in the Islamic world. A thirteenth-century treatment of the parallel postulate in the tradition of al-Tusi, which credits Khayyam, was translated into Latin by John Wallis in Oxford and became known to Saccheri. In Europe his algebra became widely known only after Franz Woepcke published the Arabic text with a French translation in 1851.

In Iran he is a national figure. His white marble mausoleum in Nishapur, completed in 1963, stands over his headstone and is visited by many. Commissioned under Reza Shah and designed by Hooshang Seyhoun, it is a symbol of the city. The Iranian solar calendar still reflects the calendar reform associated with him.

Modern research on Khayyam is divided between historians of mathematics, who have edited and analysed his algebra and geometry, philosophers who have recently edited his treatises, and literary scholars who continue to wrestle with the quatrains. His case shows how a historical person can become a symbol: of Persian scientific brilliance, of free thought, of mystical wisdom or of Victorian melancholy, depending on who is reading.