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Ömer Hayyam



  Ömer Hayyam, 12th century poet and philosopher

Ömer Hayyam, 12th century poet and philosopherGhiyās od-Dīn Abul-Fatah Omār ibn Ibrāhīm Khayyām Nishābūrī  (Ömer Hayyam, Turkish), (Persian: غیاث الدین ابو الفتح عمر بن ابراهیم خیام نیشابوری) or Omar Khayyam (Nishapur, current Persia (then a Seljuk capital in Khorasan (present Northeast Iran), May 18, 1048 – December 4, 1131) was a poet, mathematician, philosopher and astronomer who lived in Persia. His name is also given as Omar al-Khayyami[1].

He is best known for his poetry, and outside Iran, for the quatrains (rubaiyaas) in Rubaiyat of Omar Khayyam, popularized through Edward Fitzgerald's re-created translation. His substantial mathematical contributions include his Treatise on Demonstration of Problems of Algebra, which gives a geometric method for solving cubic equations by intersecting a hyperbola with a circle[2]. He also contributed to calendar reform and may have proposed a heliocentric theory well before Copernicus.

Early life

Khayyam was born in Nishapur, then a Seljuk capital in Khorasan (present Northeast Iran), rivalling Cairo or Baghdad. He is thought to have been born into a family of tent makers (literally, al-khayyami means "tent maker"); later in life he would make this into a play on words:

Khayyam, who stitched the tents of science,
Has fallen in grief's furnace and been suddenly burned,
The shears of Fate have cut the tent ropes of his life,
And the broker of Hope has sold him for nothing! [2]

He spent part of his childhood in the town of Balkh (present northern Afghanistan), studying under the well-known scholar Sheik Muhammad Mansuri. Subsequently, he studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorassan region.

According to a well-known legend called Three Schoolmates, two other exceptional students studied under the Imam Mowaffaq at about the same time: Nizam-ul-Mulk (b. 1018), who went on to become the Vizier to the Seljukid Empire, and Hassan-i-Sabah (b.1034), who became the leader of the Hashshashin (Nizar Ismaili) sect. It was said that these students became friends, and after Nizam-ul-Mulk became Vizier, Hassan-i-Sabah and Omar Khayyám each went to him, and asked to share in his good fortune. Hassan-i-Sabah demanded and was granted a place in the government, but he was ambitious, and was eventually removed from power after he participated in an unsuccessful effort to overthrow his benefactor, the Vizier. Omar Khayyám was more modest and asked merely for a place to live, study science, and pray. He was granted a yearly pension of 1,200 mithkals of gold from the treasury of Nishapur. He lived on this pension for the rest of his life.


Omar Khayyam was famous during his times as a mathematician. He wrote the influential Treatise on Demonstration of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Arabic Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders:

From the Indians one has methods for obtaining square and cube roots, methods which are based on knowledge of individual cases, namely the knowledge of the squares of the nine digits 12, 22, 32 (etc.) and their respective products, i.e. 2 × 3 etc. We have written a treatise on the proof of the validity of those methods and that they satisfy the conditions. In addition we have increased their types, namely in the form of the determination of the fourth, fifth, sixth roots up to any desired degree. No one preceded us in this and those proofs are purely arithmetic, founded on the arithmetic of The Elements. - Omar Khayyam: Treatise on Demonstration of Problems of Algebra[3]
His method for solving cubic equations by intersecting a conic section with a circle (see some examples with a parabola worked out on a calculator[4]). Although his approach at achieving this had earlier been attempted by Menaechmus, Mahavira Acharya and others, Khayyám provided a generalization extending it to all cubics. In addition he discovered the binomial expansion. His method for solving quadratic equations is also similar to what is used today.

In the Treatise he also wrote on the triangular array of binomial coefficients known as Pascal's triangle. In 1077, Omar wrote Sharh ma ashkala min musadarat kitab Uqlidis (Explanations of the Difficulties in the Postulates of Euclid). An important part of the book is concerned with Euclid's famous parallel postulate, which had also attracted the interest of Thabit ibn Qurra. Al-Haytham had previously attempted a demonstration of the postulate; Omar's attempt was a distinct advance, and his criticisms made their way to Europe, and may have contributed to the eventual development of non-Euclidean geometry.

Omar Khayyám also had other notable work in geometry, specifically on the theory of proportions.


Like most mathematicians of the period, Omar Khayyám was also famous as an astronomer. In 1073, the Seljuk dynasty Sultan Sultan Jalal al-Din Malekshah Saljuqi (Malik-Shah I, 1072-92), invited Khayyám to build an observatory, along with various other distinguished scientists. Eventually, Khayyám and his colleagues measured the length of the solar year as 365.24219858156 days (correct to six decimal places). This calendric measurement has only an 1 hour error every 5,500 years, whereas the Gregorian Calendar, adopted in Europe four centuries later, has a 1 day error in every 3,330 years, but is easier to calculate.

Calendar Reform

Omar Khayyam was part of a panel that introduced several reforms to the Persian calendar, largely based on ideas from the Hindu calendar. On March 15, 1079, Sultan Malik Shah I accepted this corrected calendar as the official Persian calendar[5].

This calendar was known as Jalali calendar after the Sultan, and was in force across Greater Iran from the 11th to the 20th centuries. It is the basis of the Iranian calendar which is followed today in Iran and Afghanistan. While the Jalali calendar is more accurate than the Gregorian, it is based on actual solar transit, (similar to Hindu calendars), and requires an Ephemeris for calculating dates. The lengths of the months can vary between 29 and 32 days depending on the moment when the sun crossed into a new zodiacal area (an attribute common to most Hindu calendars). This meant however, that seasonal errors were lower than in the Gregorian calendar.

The modern day Iranian calendar standardizes the month lengths based on a reform from 1925, thus minimizing the effect of solar transits. Seasonal errors are somewhat higher than in the Jalali version, but leap years are calculated as before.

Omar Khayyám also built a star map (now lost), which was famous in the Persian and Islamic world.

Heliocentric Theory

It is said that Omar Khayyam also estimated and proved to an audience that included the then-prestigious and most respected scholar Imam Ghazali, that the universe is not moving around earth as was believed by all at that time. By constructing a revolving platform and simple arrangement of the star charts lit by candles around the circular walls of the room, he demonstrated that earth revolves on its axis, bringing into view different constellations throughout the night and day (completing a one-day cycle). He also elaborated that stars are stationary objects in space which if moving around earth would have been burnt to cinders due to their large mass. Some of these ideas may have been transmitted into the Christian science post Renaissance.


Main article: Rubaiyat of Omar Khayyam
Omar Khayyám's poetic work has eclipsed his fame as a mathematician and scientist.

He is believed to have written about a thousand four-line verses or quatrains (rubaai's). In the English-speaking world, he was introduced through the The Rubáiyát of Omar Khayyám which are rather free-wheeling English translations by Edward Fitzgerald (1809-1883).

Other translations of parts of the rubáiyát (rubáiyát meaning "quatrains") exist, but Fitzgerald's are the most well known. Translations also exist in languages other than English.

Omar Khayyam's personal beliefs are not very clearly known, but much is discernible from his poetic oeuvre. However, he was clearly quite liberal in his views; e.g. in one of his rubaiya, he apparently says: "Enjoy wine and women and don't be afraid, God has compassion".


(These poems were translated by Edward FitzGerald and are potentially more revealing of the thoughts of Edward than Omar.)

And, as the Cock crew, those who stood before
The Tavern shouted - "Open then the Door!
You know how little time we have to stay,
And once departed, may return no more."

Alike for those who for TO-DAY prepare,
And that after a TO-MORROW stare,
A Muezzin from the Tower of Darkness cries
"Fools! your reward is neither Here nor There!"

Why, all the Saints and Sages who discuss'd
Of the Two Worlds so learnedly, are thrust
Like foolish Prophets forth; their Words to Scorn
Are scatter'd, and their mouths are stopt with Dust.

Oh, come with old Khayyam, and leave the Wise
To talk; one thing is certain, that Life flies;
One thing is certain, and the Rest is Lies;
The Flower that once has blown for ever dies.

Myself when young did eagerly frequent
Doctor and Saint, and heard great Argument
About it and about: but evermore
Came out of the same Door as I went.

With them the Seed of Wisdom did I sow,
And with my own hand labour'd it to grow:
And this was all the Harvest that I reap'd -
"I came like Water, and like Wind I go."

Into this Universe, and why not knowing,
Nor whence, like Water willy-nilly flowing:
And out of it, as Wind along the Waste,
I know not whither, willy-nilly blowing.

The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.

And that inverted Bowl we call The Sky,
Whereunder crawling coop't we live and die,
Lift not thy hands to It for help - for It
Rolls impotently on as Thou or I.

Views on Islam

Despite a strong Islamic training, it is clear that Omar Khayyam himself was undevout and had no sympathy with popular religion,[6] but was not a convinced atheist. It is almost certain that he objected to the notion that every particular event and phenomenon was the result of divine intervention. Nor did he believe in any Judgment Day or rewards and punishments after life. Instead, he supported the view that laws of nature explained all phenomena of observed life. One hostile orthodox account of him shows him as "versed in all the wisdom of the Greeks" and as insistent that studying science on Greek lines is necessary.[6] He came into conflict with religious officials several times, and had to explain his views on Islam on multiple occasions; there is even one story about a treacherous pupil who tried to bring him into public odium. The contemporary Ibn al Kifti wrote that Omar Khayyam "performed pilgrimages not from piety but from fear" of his contemporaries who divined his unbelief.[6]

Khayyam's viewpoint regarding Islam in general and its various aspects such as eschatology, Islamic taboos and divine revelation can be clearly discerned through an unbiased examination of his writings, particularly the quatrains, which as a rule reflect his intrinsic conclusions. Although a great number of quatrains erroneously attributed to Khayyam manifest a more colorful irreligiousness and hedonism, nevertheless, the number of his original quatrains that advocate laws of nature and deny the idea of resurrection and eternal life readily outweigh others that express the slightest devotion or praise to God or Islamic beliefs. The following two quatrains are representative of numerous others that serve to reject many tenets of Islamic dogma:

خيام اگر ز باده مستى خوش باش
با ماه رخى اگر نشستى خوش باش
چون عاقبت كار جهان نيستى است
انگار كه نيستى، چو هستى خوش باش

which translates in Fitzgerald's work as:

And if the Wine you drink, the Lip you press,
End in the Nothing all Things end in — Yes —
Then fancy while Thou art, Thou art but what
Thou shalt be — Nothing — Thou shalt not be less.

A more literal translation could read:

If with wine you are drunk be happy,
If seated with a moon-faced (beauty?), be happy,
Since the end purpose of the universe is nothing-ness;
Hence then you shall be naught, then while you are, be happy!

آنانكه ز پيش رفته‌اند اى ساقى
درخاك غرور خفته‌اند اى ساقى
رو باده خور و حقيقت از من بشنو
باد است هرآنچه گفته‌اند اى ساقى

which Fitzgerald has boldy interpreted as:

Why, all the Saints and Sages who discuss’d
Of the Two Worlds so learnedly — are thrust
Like foolish Prophets forth; their Words to Scorn
Are scatter’d, and their Mouths are stopt with Dust.

A literal translation, in an ironic echo of "all is vanity", could read:

Those who have gone forth, thou cup-bearer,
Have fallen upon the dust of pride, thou cup-bearer,
Drink wine and hear from me the truth:
(Hot) air is all that they have said, thou cup-bearer.

In Popular Culture

Historical Fiction
Omar Khayyam appears as major character in the novel Samarkand by Amin Maalouf.
Omar's life is dramatized in the 1957 film Omar Khayyam starring Cornel Wilde, Debra Paget, Raymond Massey, Michael Rennie, and John Derek.
Most recently, his life was dramatized by the Iranian-American director Kayvan Mashayekh in The Keeper: The Legend of Omar Khayyam released in independent theaters June 2005.
A lunar crater Omar Khayyam was named after him in 1970.
An asteroid 3095 Omarkhayyam was named after him in 1980.
Khayyam's soul has a pivotal role in a well-versed 1997 novel in Persian, titled "خيام و آن دروغ دلاويز" (English "Khayyam and That Delightful Fabrication") and authored by Hooshang Mo'eenzadeh (هوشنگ معين‌زاده). The story's protagonist, "Haj Rajab (حاج رجب)", meets -among many other personalities- Khayyam's soul in the afterworld who recites his materialistic poems in public and mocks divine power eventhough he is presumably residing in God's paradise, leading Haj Rajab to strongly question fundamentals of his pious past earthly life.

Cultural References
Salman Rushdie's novel Shame makes reference to Omar Khayyam with a character by the same name.
Khayyám is quoted in Martin Luther King Jr.'s speech, Why I oppose the war in Vietnam. "It is time for all people of conscience to call upon America to come back home. Come home America. Omar Khayyám is right 'The moving finger writes and having writ, moves on.'"
Omar Khayyám appears as a comedic sidekick in the film Son of Sinbad. He is portrayed by Vincent Price and parts of his poems are distributed throughout his dialogue.
He is also a topic of discussion between two characters in Jack London's novel The Sea-Wolf.
In a series of "Rocky and Bullwinkle" cartoons, the story line revolves around the "Ruby Yacht of Omar Khayyam" - a jewelled toy boat.
One of the two founders of Discordianism, Omar Khayyam Ravenhurst, named himself after Omar Khayyam.
The 1953 musical Kismet features a character based on Omar Khayyám.
A sparkling wine made in India, sometimes referred to as Indian Champagne is called Omar Khayyam.

1. "Omar Khayyam". Encyclopædia Britannica. (2007). Retrieved on 2007-06-09. Gives his name as Ghiyath al-Din Abu al-Fath 'Umar ibn Ibrahim al-Nisaburi al-Khayyami (the last two differ from the version here), and lists mathematician before poet in his identity.
2. Omar Khayyam. The MacTutor History of Mathematics archive.
3. Muslim extraction of roots. Mactutor History of Mathematics.
4. June Jones. Omar Khayyam and a Geometric Solution of the Cubic.
5. "Omar Khayyam". The Columbia Encyclopedia, Sixth Edition.. (2001-05). Retrieved on 2007-06-10. Here Omar Khayyam is described as "poet and mathematician", i.e. poet appearing first.
6. Robertson (1914). "Freethought under Islam", A Short History of Freethough, Ancient and Modern Volume I (Elibron Classics). Watts & Co., London, 263. ISBN 0543851907. “A hostile orthodox account of him, written in the thirteenth century, represents him as "versed in all the wisdom of the Greeks," and as wont to insist on the necessity of studying science on Greek lines. Of his prose works, two, which were stand authority, dealt respectively with precious stones and climatology.
Beyond question the poet-astronomer was undevout; and his astronomy doubtless helped to make him so. One contemporary writes: "I did not observe that he had any great belief in astrological predictions; nor have I seen or heard of any of the great (scientists) who had such belief." In point of fact he was not, any more than Abu';-Ala, a convinced atheist, but he had no sympathy with popular religion. "He gave his adherence to no religious sect. Agnosticism, not faith, is the keynote of his works." Among the sects he saw everywhere strife and hatred in which he could have no part.”

Other References
-E.G. Browne. Literary History of Persia. (Four volumes, 2,256 pages, and 25 years in the writing). 1998. ISBN 0-700-70406-X
-Jan Rypka, History of Iranian Literature. Reidel Publishing Company. 1968 OCLC 460598. ISBN 90-277-0143-1

Source: Wikipedia




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