Interesting

Omar Khayyam

Omar Khayyam

Omar Khayyam (also given as Umar Khayyam, l. 1048-1131 CE) was a Persian polymath, astronomer, mathematician, and philosopher but is best known in the West as a poet, the author of The Rubaiyat of Omar Khayyam. The Rubaiyat was translated and published in 1859 CE by the English poet Edward Fitzgerald (l. 1809-1883 CE) and would become one of the most popular, oft-quoted, and frequently anthologized works in the English language. Khayyam's name became so well-known among English speakers that organizations were founded in his honor which encouraged interest in other Persian poets and their work.

In the East, however, Khayyam is known primarily as a scientist, particularly as an astronomer and mathematician who contributed to the Jalali Calendar (a solar chart which corrected the Islamic Calendar) and as a philosopher whose works prefigured the existentialist and humanist movements. Until fairly recently, Khayyam was not recognized primarily as a poet in the East – certainly not of the stature of Rumi or Hafez Shiraz – and modern-day scholars have questioned whether Khayyam even wrote the poems that make up his famous Rubaiyat because, to some, the poetry represents a very different worldview from the philosophical works.

For Khayyam, the painful realities of human existence could not be explained by the Quranic insistence on a loving God & a divine plan.

This seeming contradiction, however, can be explained by Khayyam's use of poetry to express his personal feelings about life which he did not want to frame as philosophical discourse. For Khayyam, though a devout Muslim, the painful realities of human existence could not be explained by the Quranic insistence on a loving God who had created the world according to a divine plan. His beliefs brought him into conflict with devout Muslim jurists and so he tempered his public discourse and probably wrote his poems for himself.

These poems, consciously or not, draw on the pre-Islamic Persian belief system of Zorvanism in which Infinite Time is the creator and controller of all things, human life is predestined (and brief), and there is nothing one can finally do to alter one's destiny. The only rational course open to a human being, therefore, was to enjoy life as best as one could – especially through drink and good company – and to set aside worries which only served to waste the little time one had been given on earth.

Early Life & Influences

Khayyam was born in Nishapur (modern-day northeastern Iran) where he would spend most of his life. His family is thought to have been (or were descended from) tentmakers, which was a respectable and lucrative profession. His parents were certainly of the upper class as he was sent to study with the greatest teachers of the city who only accepted students from prominent families. One of these teachers was the mathematician Bahmanyar (d. 1067 CE), a former student of the great polymath and physician Avicenna (l. 980-1037 CE) and a former Zoroastrian who had converted to Islam. It is possible that Khayyam learned Zoroastrian/Zorvanist precepts from him but it has also been suggested that Khayyam's father was a former Zoroastrian, who had also converted to Islam, and if so, the young scholar would have been acquainted with the ancient faith from an early age. Khayyam's references to himself as a “student of Avicenna” are allusions to his time with Bahmanyar from whom he learned Avicenna's scientific method of observation and inquiry.

His earliest teacher appears to have been Imam Mowaffak of Nishapur, a renowned scholar and, according to Edward Fitzgerald (in his preface to the Rubaiyat), it was under Mowaffak's tutelage that he met Nizam al-Mulk (d. 1092 CE), the future vizier of Baghdad. Fitzgerald relates a passage from al-Mulk's Testament in which the vizier recounts his days in Nishapur and his two closest friends and classmates, Omar Khayyam and Hasan Ben Sabbah. One day, Ben Sabbah remarked to his friends how it was well known that those who studied under Mowaffak attained great success and how it was quite likely that at least one of them would. He then proposed that whichever of them should meet with the greatest success, that one would share it equally with the others.

The three boys agreed to this pact, and later when al-Mulk was vizier, his friends came to remind him of their agreement. Ben Sabbah demanded a lofty administrative post, which al-Mulk granted him. His ambition proved too great, however, and he tried to advance himself through court intrigue, eventually joining the Assassins and rising to a position of leadership (in which he ordered the death of al-Mulk who would be killed in 1092 CE). Khayyam, on the other hand, humbly asked if he could live peacefully under the vizier's rule and pursue his scientific studies. He was rewarded with a stipend and returned to Nishapur. Khayyam would later be criticized for refusing to take on students and acquired the reputation of an antisocial recluse. It is probable, however, that this stipend rendered teaching an unnecessary burden and enabled him to concentrate wholly on his own work.

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Mathematics, Astronomy, & Philosophy

He was instrumental in perfecting the Jalali Calendar, a solar calendar considered far more accurate than the Gregorian Calendar.

In mathematics, Khayyam wrote treatises which, according to the interpretation of some scholars, show that he understood and employed the concept of the binomial theorem and that he also was able to revise and improve upon Euclid's work with apparent ease. He also contributed to the understanding and usage of algebra and geometry, working in what he called pure arithmetic, which enabled his astronomical pursuits. Under the patronage of Nizam al-Mulk, Khayyam traveled to Isfahan in 1074 CE to a newly established observatory where he was instrumental in perfecting the Jalali Calendar, a solar calendar considered far more accurate than the Gregorian Calendar, still in use today in the region of Greater Iran.

In his philosophical works, he argued for God as a Necessary Being (very like the Unmoved Mover of Aristotle) from whom all else proceeds and, accordingly, human free will is subject to divine will. Since one has no control over when one will be born, to what station in life, in what region, or under what circumstance, one's life is necessarily begun beyond one's ability to control and proceeds from that point on with life determined by God's will. If this is so, however, then God is also responsible for the evil in the world; a serious contradiction of definition given that God, in order to be worthy of worship, must be all-good. Khayyam sidesteps this dilemma by characterizing evil as an absence of good. Evil appears when God's directives are ignored, when one pushes back against what is divinely determined, or is simply one's interpretation of a natural event.

In this view, what humans define as “evil acts” are a contradiction of God's plan, not a part of it, whereas the aftermath of such acts can still be part of the Divine Plan in so far as a person can recognize and respond correctly. Not everything, it could then be argued, is “determined” since one's response would be an act of one's own will but, at the same time, that exercise of free will is determined by one's past up to that moment.

Khayyam advances the theory (later articulated as the Hierarchy of Needs by psychologist Abraham Maslow, l. 1908-1970 CE) that one cannot pursue self-improvement or higher goals until the basic necessities of life are met. Khayyam writes:

God created the human species such that it is not possible for it to survive and reach perfection unless it is through reciprocity, assistance, and help. Until food, clothes, and a home, that are the essentials of life, are not prepared, the possibility of the attainment of perfection does not exist. (Aminrazavi & Van Brummelen, 8)

This concept is also an echo of Aristotle who, in his Nichomachean Ethics, states that the purpose of human life is happiness but, to attain this state, one must first have provided for one's physical needs (Book I, 1098b.12-32; Book III, 112b.12-30). Khayyam's concept of virtue, defined as acting in accordance with the highest precepts of the self, are also Aristotelian while his argument concerning essence – as in what it means to be a human being – is Platonic. In his use of these philosophers, as well as others and of religious concepts, Khayyam adds his own personal touch which is largely informed by Zorvanism.

Zorvanism & The Rubaiyat

Zorvanism was a sect (sometimes referred to as a heresy) of the Persian religion of Zoroastrianism which seems to have first emerged during the latter part of the Achaemenid Empire (c. 550-330 BCE) and was fully developed by the time of the Sassanian Empire (224-651 CE). Zoroastrianism held that there was one supreme, all-good and uncreated deity – Ahura Mazda (later given as Ormuzd) – from whom all else was created and that human beings had free will to choose to follow the precepts of Ahura Mazda or reject him and side with his arch-rival Angra Mainyu (also known as Ahriman), the embodiment of evil. The problem with this religious construct was that if Ahura Mazda was all-good, where had Ahriman and evil come from?

Zorvanism attempted to solve the contradiction by elevating Zorvan, a minor god of Time from Early Iranian Religion, to the position of Supreme Deity. The androgynous Zorvan, representing Infinite Time, wishes for a son and prays to himself for a good result in impregnating himself. Nothing happens, however, and he experiences a moment of doubt – in which Ahriman is conceived – but then banishes this doubt and regains faith in himself – engendering Ahura Mazda/Ormuzd. Zorvan proclaims he will give sovereignty of the world to whichever twin is born first and Ahriman, hearing this, cuts his way out of the womb and assumes mastery. Zorvan corrects this by decreeing that Ahriman will only have sovereignty for 9,000 years, after which Ahura Mazda/Ormuzd will reign. Ahura Mazda, then, is the creator of the world but the “evil” one experiences in life comes from Ahriman.

The belief that the Supreme Deity was Time, however, encouraged a fatalistic approach to life among one of the sects of Zorvanism. The fatalists believed that, since Time had created and was ultimately in control of all things, one's destiny was already written at one's birth. One was born, would live, and then would die, and there was nothing one could do between birth and death to change anything significantly in one's life. Khayyam makes use of this belief in his philosophical works but centers the whole of the Rubaiyat on the concept, best illustrated in stanza 51:

The Moving Finger writes and, having writ,

Moves on; nor all your piety nor wit

Shall lure it back to cancel half a line,

Nor all your tears wash out a word of it.

One's daily life is dictated by Time – the “moving finger” – whose writ propels one through life, whether one wants to move on or remain where one is, and there is nothing one can do to change that. Therefore, Khayyam proposes throughout the work, the best course is to eat, drink, and be as merry as one can be before one is snatched unexpectedly by death. The brevity of life, and how one should best respond, is central to the work from beginning to end. Fitzgerald's translation makes a point of forming the various poems into a narrative beginning with the opening of a tavern in the morning and moving on to one of the patrons musing on the meaning of life, injustice, evil, pleasure, and death, before closing with the moonrise at night and remembrance as the only hope for one's immortality.

Stanza 1 awakens the reader to the morning of the narrative, stanza 2 encourages one to fill one's cup “before life's liquor in its cup be dry” and stanza 3 has the patrons gathering outside the tavern door, demanding it be open for, “You know how little while we have to stay/And once departed may return no more”, while the last stanzas, 74 and 75, depict the day's end, the moon rising over the tavern's garden in the night sky, and how, on some future date unknown, the beloved of the speaker will look to the garden where they have enjoyed themselves and find him gone. The poem ends with the request that the beloved remember the speaker by turning down an empty glass at the place where they used to spend time together as envisioned in the famous stanza 11:

A book of verses underneath the bough

A jug of wine, a loaf of bread, and thou

Beside me, singing in the wilderness –

Ah, wilderness were paradise enow.

The most reasonable response to the tyranny of time is defiance in the form of sensual enjoyment, as Khayyam points out repeatedly, as, to cite just two examples, in the first lines of stanza 23, “Ah, make the most of what we yet may spend/Before we too into the dust descend” and in stanza 37:

Ah, fill the cup; what boots it to repeat

How time is slipping underneath our feet

Unborn tomorrow and dead yesterday

Why fret about them if today be sweet.

Although some scholars have claimed that Khayyam's use of wine and drunkenness is in keeping with the Sufi tradition (expressed in the works of Rumi and Hafez Shiraz), this is untenable in that Sufis of Khayyam's time rejected his work and Khayyam shows no affinity for Sufism in any of his writings. The Sufis regarded him as an overly scientific atheist based on his treatises and discourses. In his philosophical work, Khayyam addresses the nature of life and its various disappointments from an objective, scientific standpoint and emphasizes the importance of an educated, rational response to human existence. One suffers – or seems to suffer – because of one's interpretation of external events which are predetermined; this is hardly in keeping with the Sufi philosophy. In the Rubaiyat, on the other hand, he laments the brevity of life, the loss of friends, and how Time robs one of youth and pleasure; none of which fits the Sufi vision either.

Authorship & Translation

Khayyam's pessimism and embrace of a life of enlightened hedonism has encouraged some scholars to suggest the author of the Rubaiyat cannot be the same as the Omar Khayyam who wrote the philosophical discourses. The Rubaiyat, after all, rejects intellectual pursuits in favor of wine, good company, and song. Stanza 27 disparages academic pursuits completely:

Myself when young did eagerly frequent

Doctor and Saint and heard great argument

About it and about, but evermore

Came out by the same door as in I went.

This criticism, however, ignores the fact that the speaker of the poem is a fictional character, who may or may not be speaking for the author. Even if he is, the philosopher-poet, in any age or culture, is not always able to completely balance the two sides equally all the time; what the philosopher explains away, the poet rages against. Far from suggesting that the Rubaiyat cannot be written by the same author as the discourses or mathematical treatises, Khayyam's verse acts as a kind of mirror to his prose, reflecting precisely the opposite response to life.

No one contests that Khayyam wrote poetry, only that he may not have written the pieces which comprise his famous Rubaiyat. Khayyam as a poet is attested by the Persian historian and scholar Imad ad-Din al-Isfahani (l. 1125-1201 CE) and the Persian polymath Fakhr al-Din al-Razi (l. 1150-1210 CE) who quotes stanza 62 of the Rubaiyat completely. Even so, some scholars continue to keep alive the criticism that the book could be the work of another poet.

The only case in which this criticism has a valid point is with Fitzgerald's 1859 CE translation (and the editions following) of which Fitzgerald himself freely admitted having translated loosely and fashioned according to the tastes of his Victorian audience. Scholar Peter Avery notes how, in Fitzgerald's time, poets popularized a genre known as the “imitation” which sought to catch the spirit of a foreign work without bothering with precision in translation. Avery writes:

Edward Fitzgerald…did not set out to translate the quatrains of Omar Khayyam. In a letter he remarks `God Forbid' that he should be thought to be translating. He was, in fact, working in the now almost forgotten tradition of the Imitation. Since he was possessed of the genius of a poet, his imitation is one of the most successful poems in the English language…Of it, Fitzgerald used the coinage `transmogrification'. (Lewisohn, xiii)

Even so, Fitzgerald had learned Persian from his colleague and friend Edward Byles Cowell (l. 1826-1903 CE) and so he was working from Khayyam in the original language. Fitzgerald's The Rubaiyat of Omar Khayyam is, therefore, as much the work of the Victorian English poet as the medieval Persian. This “collaboration” has been recognized as one of the most successful in literary history as The Rubaiyat of Omar Khayyam would attract worldwide attention by the beginning of the 20th century CE, introduce a Western audience to Persian literature, influence countless artists in different mediums, revive interest in Khayyam scholarship in the East, and remain a bestseller for the past 100 years. Modern audiences respond to Khayyam's work as warmly as the Victorians for the same reason: the beauty of a poetic vision offering an alternative to despair in navigating a life characterized by loss and defined by the inevitability of death.


Omar Khayyam

The mathematician and poet Omar Khayyam was born in Neyshābūr (in Iran) only a few years before al-Bīrūnī’s death. He later lived in Samarkand and Eṣfahān, and his brilliant work there continued many of the main lines of development in 10th-century mathematics. Not only did he discover a general method of extracting roots of arbitrary high degree, but his Algebra contains the first complete treatment of the solution of cubic equations. Omar did this by means of conic sections, but he declared his hope that his successors would succeed where he had failed in finding an algebraic formula for the roots.

Omar was also a part of an Islamic tradition, which included Thābit and Ibn al-Haytham, of investigating Euclid’s parallel postulate. To this tradition Omar contributed the idea of a quadrilateral with two congruent sides perpendicular to the base, as shown in the figure . The parallel postulate would be proved, Omar recognized, if he could show that the remaining two angles were right angles. In this he failed, but his question about the quadrilateral became the standard way of discussing the parallel postulate.

That postulate, however, was only one of the questions on the foundations of mathematics that interested Islamic scientists. Another was the definition of ratios. Omar Khayyam, along with others before him, felt that the theory in Book V of Euclid’s Elements was logically satisfactory but intuitively unappealing, so he proved that a definition known to Aristotle was equivalent to that given in Euclid. In fact, Omar argued that ratios should be regarded as “ideal numbers,” and so he conceived of a much broader system of numbers than that used since Greek antiquity, that of the positive real numbers.


Omar Khayyam’s Contributions to Science

Algebra

At high school we learn about equations of the form ax 2 + bx + c = 0 these are called quadratic equations. Cubic equations are of the form ax 3 + bx 2 + cx + d = 0. Naturally, cubic equations are harder to solve than quadratics.

Khayyam conjectured correctly that it is not possible to solve cubic equations using the traditional Ancient Greek geometrical tools of straightedge and compass. Other methods are required.

At the age of 22, in 1070, Khayyam published one of his greatest works: Treatise on Demonstration of Problems of Algebra and Balancing. In it he showed that a cubic equation can have more than one solution. He also showed how the intersections of conic sections such as parabolas and circles can be utilized to yield geometric solutions of cubic equations. Archimedes had actually started work in this field over a thousand years earlier, when he considered the specific problem of finding the ratio of the volume of one part of a sphere to another. Khayyam considered the problem in a more general, methodical way.

In the language of modern mathematics, Khayyam’s solution to the equation x 3 + a 2 x = b features a parabola of equation x 2 = ay, a circle with diameter b/a 2 , and a vertical line through the intersection point. The solution is given by the distance on the x-axis between the origin and the (red) vertical line. Image by Pieter Kuiper.

Khayyam’s solutions avoided negative coefficients and negative roots because negative numbers were not acknowledged in Islamic mathematics. (Some cultures, however, had incorporated negative numbers into mathematics – for example Brahmagupta had introduced negative numbers into Indian mathematics 400 years earlier.)

Although Khayyam’s achievement was magnificent, he was personally disappointed that he needed to utilize geometry to solve cubic equations – he had hoped to discover an algorithm using only algebra.

Treatise on Demonstration of Problems of Algebra and Balancing established Khayyam as a mathematician of the first rank, and his reputation spread quickly throughout Persia.

Following Khayyam’s breakthrough there was little significant progress on cubic equations until 1535, when Niccolo Tartaglia found general solutions for all cubic equations.

Khayyam’s algebra was not the system of letters and signs we use today. His algebra was expressed in words. So, where today we write:

Khayyam wrote: What is the amount of a square so that when 6 dirhams are added to it, it becomes equal to five roots of that square?

Linking Algebra and Geometry

Algebra and Geometry were successfully linked by Pierre de Fermat and René Descartes in the 1600s, resulting in the modern x-y coordinate system.

Khayyam’s work with cubics had made him certain that algebra and geometry were linked, and he cited Euclid’s Elements to support the idea:

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved by Propositions 5 and 6 of Book 2 of Euclid’s Elements.

Length of Year

In 1073, Khayyam received an invitation to the Persian city of Isfahan, capital of the Seljuk Empire, to prepare a calendar that would work in an orderly way and be accurate forever – this was an era in which year lengths were regularly changed.

Khayyam’s invitation came from the two most powerful men in the Seljuk Empire, of which Persia was part: these were Malik Shah, Sultan of the empire, and Nizam al-Mulk, his vizier.

Khayyam recruited other talented scientists to accompany him to Isfahan in 1074. There he was paid an extraordinarily high salary and enjoyed a privileged lifestyle. Malik Shah paid Khayyam to found an observatory with an initial aim of making observations of the heavens for 30 years, during which time Saturn, the most distant planet then known, would complete an orbit.

Ptolemy’s universe – the model accepted by Omar Khayyam.

During his time in Isfahan, Khayyam measured the length of a year – to be specific the tropical year length – with remarkable accuracy and precision.

Khayyam found that 1,029,983 days made 2,820 years. This gives a tropical year length of 365.2422 days to seven significant figures. Although it has become fashionable to quote more decimal places than this, Khayyam’s input of 1,029,983 days contains seven significant figures, so it is unreasonable to quote more than this number of significant figures in the calculated year length.

Today we know that the length of a tropical year actually changes by as much as 30 minutes from year to year. The average tropical year length quoted today is 365.242189 days, which to seven significant figures is 365.2422 days – exactly the figure Khayyam arrived at almost a thousand years ago. The length of a tropical year is also increasing very slightly as time passes, although not enough between Khayyam’s era and our own to be noticeable on a scale of seven significant figures.

Malik Shah introduced Khayyam’s new calendar in the Seljuk Empire on March 15, 1079. It was used until the 20th century.

The Parallel Postulate

The 13 books of Euclid’s Elements published in about 300 BC were probably the most influential books in the entire history of mathematics. The Elements had been built on five geometric postulates – in other words five things that were assumed to be true about geometry: for example, all right angles are equal to one another.

The fifth of Euclid’s five postulates was the parallel postulate. The parallel postulate proved to be a source of puzzlement, irritation, and joy for mathematicians for millennia. The joy was usually short-lived, belonging to mathematicians who thought they had proven the postulate only to be disappointed when an error was identified in their ‘proof.’

Euclid had considered a straight line crossing two other straight lines. He looked at the situation when the interior angles (shown in the image below) add to less than 180 degrees. In these circumstances, he said that the two straight lines will eventually meet on the side of the two angles that add to less than 180 degrees.

a. When each angle is 90 degrees, the lines are parallel.
b. If one or both of the angles is less than 90 degrees, the lines will meet.

Since the time Elements was first published, mathematicians had been trying to use Euclid’s first four postulates to prove the parallel postulate. They were doomed to fail. We now know that it is impossible to prove the parallel postulate using Euclid’s other postulates.

Omar Khayyam’s attempt was interesting. In his Explanations of the Difficulties in the Postulates in Euclid’s Elements he asks his readers to consider a straight line AB:

He asks his readers to consider two equal lines that are perpendicular to AB and sees three possible arrangements, which can produce four-sided figures:

He then refutes the possibility that angles C and/or D can be anything other than right-angles and in the image above only the central option is possible. So, he believes he has proven the parallel postulate. In fact, he has not done so, all he has done is stated it in a different way.

What is interesting to historians of mathematics is that in Khayyam’s ideas – shown roughly in the images above – they can see the first glimmers of non-Euclidean geometry.

Some Personal Details and the End

Full details of Khayyam’s personal life are not known. He is believed to have married and had at least one son and one daughter.

In 1092, Malik Shah and his vizier both died – the first probably by poisoning, the second by assassination. Khayyam went into hiding during the resulting power struggle. His survival depended on lying low. He had been Malik Shah’s personal physician and become his close personal friend – which had made him enemies – and Khayyam’s poetry suggests his behavior may not have been devoutly religious – and this had also made him enemies. Khayyam actually published no poetry in his lifetime. Some of his musings would potentially have endangered his life.

After the power struggle, it took about 20 years for Khayyam to be fully rehabilitated and for him to emerge again, at 64 years of age, in the company of powerful people. However, he refused to teach. One of his poems suggests why this might be:

Omar Khayyam died at the age of 83 in his hometown of Nishapur on December 4, 1131. He was buried in a tomb whose location he had chosen in an orchard where blossom would fall twice a year.

Khayyam’s poetry was popularized in the 1800s by Edward FitzGerald’s translations in the Rubaiyat of Omar Khayyam. Khayyam became so admired in the West that in 1963 the Shah of Iran had his grave exhumed and Khayyam’s remains moved to a huge purpose-built mausoleum in Nishapur where tourists could pay homage to the great poet.

We shall end with one of Khayyam’s most famous and evocative quatrains:

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Further Reading
Edward FitzGerald (translator)
The Rubaiyat of Omar Khayyam
Howard Willford Bell, 1901

Victor J. Katz
A History of Mathematics: An Introduction
HarperCollins College Publishers, New York, 1993

Roshdi Rashed (Editor)
Encyclopedia of the History of Arabic science
Routledge, 1996

Hazhir Teimourian
Omar Khayyam: Poet, Rebel, Astronomer
The History Press, 2008

Mehdi Aminrazavi
The Wine of Wisdom: The Life, Poetry and Philosophy of Omar Khayyam
Oneworld Publications, 2013


Omar Khayyam

Umar Khayyam was born on May 18, 1048 in Nishapur, Iran. He was an outstanding mathematician and astronomer. He wrote several works including Problems of Arithmetic, a book on music and one on algebra, all before he was 25 years old.

In 1070 he moved to Samarkand in Uzbekistan which is one of the oldest cities of Central Asia. There Khayyam was supported by Abu Tahir, a prominent jurist of Samarkand This allowed him to write his most famous algebra work, Treatise on Demonstration of Problems of Algebra.

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Malik Shah the grandson of Toghril Beg, the founder of the Seljuk dynasty ruled the city of Isfahan from 1073 AD. His vizier Nizam-ul-Mulk invited Khayyam to Isfahan to set up an observatory. Other leading astronomers were also invited to work at the observatory and for 18 years Khayyam led the scientists and produced work of outstanding quality. It was a period of peace during which the political situation allowed Khayyam the opportunity to devote himself entirely to his scholarly work. During this time Khayyam led work on compiling astronomical tables and he also contributed to calendar reform in 1079. Khayyam measured the length of the year as 365.24219858156 days, we know now that the length of the year is changing in the sixth decimal place over a person's lifetime. It is also outstandingly accurate. For comparison the length of the year at the end of the 19th century was 365.242196 days, while today it is 365.242190 days.

Outside the world of mathematics, Khayyam is best known as a result of Edward Fitzgerald's popular translation in 1859 of nearly 600 short four line poems the Rubaiyat. Khayyam's fame as a poet has caused some to forget his scientific achievements which were much more substantial. Versions of the forms and verses used in the Rubaiyat existed in Persian literature before Khayyam, and only about 120 of the verses can be attributed to him with certainty.


Contents

Omar Khayyam was born in 1048 in Nishapur, a leading metropolis in Khorasan during medieval times that reached its zenith of prosperity in the eleventh century under the Seljuq dynasty. [11] : 15 [12] [13] Nishapur was also a major center of the Zoroastrian religion, and it is likely that Khayyam's father was a Zoroastrian who had converted to Islam. [14] : 68 His full name, as it appears in the Arabic sources, was Abu’l Fath Omar ibn Ibrahim al-Khayyam. [15] In medieval Persian texts he is usually simply called Omar Khayyam. [16] Although open to doubt, it has often been assumed that his forebears followed the trade of tent-making, since Khayyam means tent-maker in Arabic. [17] : 30 The historian Bayhaqi, who was personally acquainted with Omar, provides the full details of his horoscope: "he was Gemini, the sun and Mercury being in the ascendant[. ]". [18] : 471 This was used by modern scholars to establish his date of birth as 18 May 1048. [10] : 658

His boyhood was spent in Nishapur. [10] : 659 His gifts were recognized by his early tutors who sent him to study under Imam Muwaffaq Nishaburi, the greatest teacher of the Khorasan region who tutored the children of the highest nobility. Omar made a great friendship with him through the years. [14] : 20 Khayyam was also taught by the Zoroastrian convert mathematician, Abu Hassan Bahmanyar bin Marzban. [19] After studying science, philosophy, mathematics and astronomy at Nishapur, about the year 1068 he traveled to the province of 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, the governor and chief judge of the city. [20] Omar Khayyam was kindly received by the Karakhanid ruler Shams al-Mulk Nasr, who according to Bayhaqi, would "show him the greatest honour, so much so that he would seat [Omar] beside him on his throne". [17] : 34 [14] : 47

In 1073–4 peace was concluded with Sultan Malik-Shah I who had made incursions into Karakhanid dominions. Khayyam entered the service of Malik-Shah in 1074–5 when he was invited by the Grand Vizier Nizam al-Mulk to meet Malik-Shah in the city of Marv. Khayyam was subsequently commissioned to set up an observatory in Isfahan and lead a group of scientists in carrying out precise astronomical observations aimed at the revision of the Persian calendar. The undertaking began probably in 1076 and ended in 1079 [14] : 28 when Omar Khayyam and his colleagues concluded their measurements of the length of the year, reporting it to 14 significant figures with astounding accuracy.

After the death of Malik-Shah and his vizier (murdered, it is thought, by the Ismaili order of Assassins), Omar fell from favor at court, and as a result, he soon set out on his pilgrimage to Mecca. A possible ulterior motive for his pilgrimage reported by Al-Qifti, was a public demonstration of his faith with a view to allaying suspicions of skepticism and confuting the allegations of unorthodoxy (including possible sympathy to Zoroastrianism) leveled at him by a hostile clergy. [21] [14] : 29 He was then invited by the new Sultan Sanjar to Marv, possibly to work as a court astrologer. [1] He was later allowed to return to Nishapur owing to his declining health. Upon his return, he seems to have lived the life of a recluse. [22] : 99

Omar Khayyam died at the age of 83 in his hometown of Nishapur on 4 December 1131, and he is buried in what is now the Mausoleum of Omar Khayyam. One of his disciples Nizami Aruzi relates the story that sometime during 1112–3 Khayyam was in Balkh in the company of Al-Isfizari (one of the scientists who had collaborated with him on the Jalali calendar) when he made a prophecy that "my tomb shall be in a spot where the north wind may scatter roses over it". [17] : 36 [12] Four years after his death, Aruzi located his tomb in a cemetery in a then large and well-known quarter of Nishapur on the road to Marv. As it had been foreseen by Khayyam, Aruzi found the tomb situated at the foot of a garden-wall over which pear trees and peach trees had thrust their heads and dropped their flowers so that his tombstone was hidden beneath them. [17]

Khayyam was famous during his life as a mathematician. His surviving mathematical works include: A commentary on the difficulties concerning the postulates of Euclid's Elements (Risāla fī šarḥ mā aškala min muṣādarāt kitāb Uqlīdis, completed in December 1077 [6] ), On the division of a quadrant of a circle (Risālah fī qismah rub‘ al-dā’irah, undated but completed prior to the treatise on algebra [6] ), and On proofs for problems concerning Algebra (Maqāla fi l-jabr wa l-muqābala, most likely completed in 1079 [8] : 281 ). He furthermore wrote a treatise on the binomial theorem and extracting the n th root of natural numbers, which has been lost. [14] : 197

Theory of parallels Edit

A part of Khayyam's commentary on Euclid's Elements deals with the parallel axiom. [8] : 282 The treatise of Khayyam can be considered the first treatment of the axiom not based on petitio principii, but on a more intuitive postulate. Khayyam refutes the previous attempts by other mathematicians to prove the proposition, mainly on grounds that each of them had postulated something that was by no means easier to admit than the Fifth Postulate itself. [6] Drawing upon Aristotle's views, he rejects the usage of movement in geometry and therefore dismisses the different attempt by Al-Haytham. [23] [24] Unsatisfied with the failure of mathematicians to prove Euclid's statement from his other postulates, Omar tried to connect the axiom with the Fourth Postulate, which states that all right angles are equal to one another. [8] : 282

Khayyam was the first to consider the three distinct cases of acute, obtuse, and right angle for the summit angles of a Khayyam-Saccheri quadrilateral. [8] : 283 After proving a number of theorems about them, he showed that Postulate V follows from the right angle hypothesis, and refuted the obtuse and acute cases as self-contradictory. [6] His elaborate attempt to prove the parallel postulate was significant for the further development of geometry, as it clearly shows the possibility of non-Euclidean geometries. The hypotheses of acute, obtuse, and right angles are now known to lead respectively to the non-Euclidean hyperbolic geometry of Gauss-Bolyai-Lobachevsky, to that of Riemannian geometry, and to Euclidean geometry. [25]

Tusi's commentaries on Khayyam's treatment of parallels made its way to Europe. John Wallis, professor of geometry at Oxford, translated Tusi's commentary into Latin. Jesuit geometer Girolamo Saccheri, whose work (euclides ab omni naevo vindicatus, 1733) is generally considered as the first step in the eventual development of non-Euclidean geometry, was familiar with the work of Wallis. The American historian of mathematics David Eugene Smith mentions that Saccheri "used the same lemma as the one of Tusi, even lettering the figure in precisely the same way and using the lemma for the same purpose". He further says that "Tusi distinctly states that it is due to Omar Khayyam, and from the text, it seems clear that the latter was his inspirer." [22] : 104 [26] [14] : 195

The real number concept Edit

This treatise on Euclid contains another contribution dealing with the theory of proportions and with the compounding of ratios. Khayyam discusses the relationship between the concept of ratio and the concept of number and explicitly raises various theoretical difficulties. In particular, he contributes to the theoretical study of the concept of irrational number. [6] Displeased with Euclid's definition of equal ratios, he redefined the concept of a number by the use of a continuous fraction as the means of expressing a ratio. Rosenfeld and Youschkevitch (1973) argue that "by placing irrational quantities and numbers on the same operational scale, [Khayyam] began a true revolution in the doctrine of number." Likewise, it was noted by D. J. Struik that Omar was "on the road to that extension of the number concept which leads to the notion of the real number." [8] : 284

Geometric algebra Edit

Rashed and Vahabzadeh (2000) have argued that because of his thoroughgoing geometrical approach to algebraic equations, Khayyam can be considered the precursor of Descartes in the invention of analytic geometry. [27] : 248 In The Treatise on the Division of a Quadrant of a Circle Khayyam applied algebra to geometry. In this work, he devoted himself mainly to investigating whether it is possible to divide a circular quadrant into two parts such that the line segments projected from the dividing point to the perpendicular diameters of the circle form a specific ratio. His solution, in turn, employed several curve constructions that led to equations containing cubic and quadratic terms. [27] : 248

The solution of cubic equations Edit

Khayyam seems to have been the first to conceive a general theory of cubic equations [28] and the first to geometrically solve every type of cubic equation, so far as positive roots are concerned. [29] The treatise on algebra contains his work on cubic equations. [30] It is divided into three parts: (i) equations which can be solved with compass and straight edge, (ii) equations which can be solved by means of conic sections, and (iii) equations which involve the inverse of the unknown. [31]

Khayyam produced an exhaustive list of all possible equations involving lines, squares, and cubes. [32] : 43 He considered three binomial equations, nine trinomial equations, and seven tetranomial equations. [8] : 281 For the first and second degree polynomials, he provided numerical solutions by geometric construction. He concluded that there are fourteen different types of cubics that cannot be reduced to an equation of a lesser degree. [6] For these he could not accomplish the construction of his unknown segment with compass and straight edge. He proceeded to present geometric solutions to all types of cubic equations using the properties of conic sections. [33] : 157 [8] : 281 The prerequisite lemmas for Khayyam's geometrical proof include Euclid VI, Prop 13, and Apollonius II, Prop 12. [33] : 155 The positive root of a cubic equation was determined as the abscissa of a point of intersection of two conics, for instance, the intersection of two parabolas, or the intersection of a parabola and a circle, etc. [34] : 141 However, he acknowledged that the arithmetic problem of these cubics was still unsolved, adding that "possibly someone else will come to know it after us". [33] : 158 This task remained open until the sixteenth century, where algebraic solution of the cubic equation was found in its generality by Cardano, Del Ferro, and Tartaglia in Renaissance Italy. [8] : 282 [6]

In effect, Khayyam's work is an effort to unify algebra and geometry. [36] : 241 This particular geometric solution of cubic equations has been further investigated by M. Hachtroudi and extended to solving fourth-degree equations. [37] Although similar methods had appeared sporadically since Menaechmus, and further developed by the 10th-century mathematician Abu al-Jud, [38] [39] Khayyam's work can be considered the first systematic study and the first exact method of solving cubic equations. [40] The mathematician Woepcke (1851) who offered translations of Khayyam's algebra into French praised him for his "power of generalization and his rigorously systematic procedure." [41] : 10

Binomial theorem and extraction of roots Edit

Omar Khayyam, Treatise on Demonstration of Problems of Algebra [42]

In his algebraic treatise, Khayyam alludes to a book he had written on the extraction of the n th root of the numbers using a law he had discovered which did not depend on geometric figures. [34] This book was most likely titled The difficulties of arithmetic (Moškelāt al-hesāb), [6] and is not extant. Based on the context, some historians of mathematics such as D. J. Struik, believe that Omar must have known the formula for the expansion of the binomial ( a + b ) n > , where n is a positive integer. [8] : 282 The case of power 2 is explicitly stated in Euclid's elements and the case of at most power 3 had been established by Indian mathematicians. Khayyam was the mathematician who noticed the importance of a general binomial theorem. The argument supporting the claim that Khayyam had a general binomial theorem is based on his ability to extract roots. [43] One of Khayyam's predecessors, Al-Karaji, had already discovered the triangular arrangement of the coefficients of binomial expansions that Europeans later came to know as Pascal's triangle [44] Khayyam popularized this triangular array in Iran, so that it is now known as Omar Khayyam's triangle. [34]

In 1074–5, Omar Khayyam was commissioned by Sultan Malik-Shah to build an observatory at Isfahan and reform the Persian calendar. There was a panel of eight scholars working under the direction of Khayyam to make large-scale astronomical observations and revise the astronomical tables. [34] : 141 Recalibrating the calendar fixed the first day of the year at the exact moment of the passing of the Sun's center across vernal equinox. This marks the beginning of spring or Nowrūz, a day in which the Sun enters the first degree of Aries before noon. [45] [46] The resultant calendar was named in Malik-Shah's honor as the Jalālī calendar, and was inaugurated on 15 March 1079. [47] The observatory itself was disused after the death of Malik-Shah in 1092. [10] : 659

The Jalālī calendar was a true solar calendar where the duration of each month is equal to the time of the passage of the Sun across the corresponding sign of the Zodiac. The calendar reform introduced a unique 33-year intercalation cycle. As indicated by the works of Khazini, Khayyam's group implemented an intercalation system based on quadrennial and quinquennial leap years. Therefore, the calendar consisted of 25 ordinary years that included 365 days, and 8 leap years that included 366 days. [48] The calendar remained in use across Greater Iran from the 11th to the 20th centuries. In 1911 the Jalali calendar became the official national calendar of Qajar Iran. In 1925 this calendar was simplified and the names of the months were modernized, resulting in the modern Iranian calendar. The Jalali calendar is more accurate than the Gregorian calendar of 1582, [10] : 659 with an error of one day accumulating over 5,000 years, compared to one day every 3,330 years in the Gregorian calendar. [14] : 200 Moritz Cantor considered it the most perfect calendar ever devised. [22] : 101

One of his pupils Nizami Aruzi of Samarcand relates that Khayyam apparently did not have a belief in astrology and divination: "I did not observe that he (scil. Omar Khayyam) had any great belief in astrological predictions, nor have I seen or heard of any of the great [scientists] who had such belief." [41] : 11 While working for Sultan Sanjar as an astrologer he was asked to predict the weather – a job that he apparently did not do well. [14] : 30 George Saliba (2002) explains that the term ‘ilm al-nujūm, used in various sources in which references to Omar's life and work could be found, has sometimes been incorrectly translated to mean astrology. He adds: "from at least the middle of the tenth century, according to Farabi's enumeration of the sciences, that this science, ‘ilm al-nujūm, was already split into two parts, one dealing with astrology and the other with theoretical mathematical astronomy." [49] : 224

A popular claim to the effect that Khayyam believed in heliocentrism is based on Edward FitzGerald's popular but anachronistic rendering of Khayyam's poetry, in which the first lines are mistranslated with a heliocentric image of the Sun flinging "the Stone that puts the Stars to Flight". In fact the most popular version of FitzGerald's translation of the first lines of Khayyam's Rubaiyat is "Awake! For Morning in the bowl of night has flung the stone that puts the stars to flight." [50] [51]

He has a short treatise devoted to Archimedes' principle (in full title, On the Deception of Knowing the Two Quantities of Gold and Silver in a Compound Made of the Two). For a compound of gold adulterated with silver, he describes a method to measure more exactly the weight per capacity of each element. It involves weighing the compound both in air and in water, since weights are easier to measure exactly than volumes. By repeating the same with both gold and silver one finds exactly how much heavier than water gold, silver and the compound were. This treatise was extensively examined by Eilhard Wiedemann who believed that Khayyam's solution was more accurate and sophisticated than that of Khazini and Al-Nayrizi who also dealt with the subject elsewhere. [14] : 198

Another short treatise is concerned with music theory in which he discusses the connection between music and arithmetic. Khayyam's contribution was in providing a systematic classification of musical scales, and discussing the mathematical relationship among notes, minor, major and tetrachords. [14] : 198

The earliest allusion to Omar Khayyam's poetry is from the historian Imad ad-Din al-Isfahani, a younger contemporary of Khayyam, who explicitly identifies him as both a poet and a scientist (Kharidat al-qasr, 1174). [14] : 49 [52] : 35 One of the earliest specimens of Omar Khayyam's Rubiyat is from Fakhr al-Din Razi. In his work Al-tanbih ‘ala ba‘d asrar al-maw‘dat fi’l-Qur’an (ca. 1160), he quotes one of his poems (corresponding to quatrain LXII of FitzGerald's first edition). Daya in his writings (Mirsad al-‘Ibad, ca. 1230) quotes two quatrains, one of which is the same as the one already reported by Razi. An additional quatrain is quoted by the historian Juvayni (Tarikh-i Jahangushay, ca. 1226–1283). [52] : 36–37 [14] : 92 In 1340 Jajarmi includes thirteen quatrains of Khayyam in his work containing an anthology of the works of famous Persian poets (Munis al-ahrār), two of which have hitherto been known from the older sources. [53] A comparatively late manuscript is the Bodleian MS. Ouseley 140, written in Shiraz in 1460, which contains 158 quatrains on 47 folia. The manuscript belonged to William Ouseley (1767–1842) and was purchased by the Bodleian Library in 1844.

There are occasional quotes of verses attributed to Omar in texts attributed to authors of the 13th and 14th centuries, but these are of doubtful authenticity, so that skeptical scholars point out that the entire tradition may be pseudepigraphic. [52] : 11

Hans Heinrich Schaeder in 1934 commented that the name of Omar Khayyam "is to be struck out from the history of Persian literature" due to the lack of any material that could confidently be attributed to him. De Blois (2004) presents a bibliography of the manuscript tradition, concluding pessimistically that the situation has not changed significantly since Schaeder's time. [54] Five of the quatrains later attributed to Omar are found as early as 30 years after his death, quoted in Sindbad-Nameh. While this establishes that these specific verses were in circulation in Omar's time or shortly later, it doesn't imply that the verses must be his. De Blois concludes that at the least the process of attributing poetry to Omar Khayyam appears to have begun already in the 13th century. [55] Edward Granville Browne (1906) notes the difficulty of disentangling authentic from spurious quatrains: "while it is certain that Khayyam wrote many quatrains, it is hardly possible, save in a few exceptional cases, to assert positively that he wrote any of those ascribed to him". [10] : 663

In addition to the Persian quatrains, there are twenty-five Arabic poems attributed to Khayyam which are attested by historians such as al-Isfahani, Shahrazuri (Nuzhat al-Arwah, ca. 1201–1211), Qifti (Tārikh al-hukamā, 1255), and Hamdallah Mustawfi (Tarikh-i guzida, 1339). [14] : 39

Boyle and Frye (1975) emphasize that there are a number of other Persian scholars who occasionally wrote quatrains, including Avicenna, Ghazzali, and Tusi. He concludes that it is also possible that for Khayyam poetry was an amusement of his leisure hours: "these brief poems seem often to have been the work of scholars and scientists who composed them, perhaps, in moments of relaxation to edify or amuse the inner circle of their disciples". [10] : 662

The poetry attributed to Omar Khayyam has contributed greatly to his popular fame in the modern period as a direct result of the extreme popularity of the translation of such verses into English by Edward FitzGerald (1859). FitzGerald's Rubaiyat of Omar Khayyam contains loose translations of quatrains from the Bodleian manuscript. It enjoyed such success in the fin de siècle period that a bibliography compiled in 1929 listed more than 300 separate editions, [56] and many more have been published since. [57]

Khayyam considered himself intellectually to be a student of Avicenna. [58] According to Al-Bayhaqi, he was reading the metaphysics in Avicenna's the Book of Healing before he died. [10] : 661 There are six philosophical papers believed to have been written by Khayyam. One of them, On existence (Fi’l-wujūd), was written originally in Persian and deals with the subject of existence and its relationship to universals. Another paper, titled The necessity of contradiction in the world, determinism and subsistence (Darurat al-tadād fi’l-‘ālam wa’l-jabr wa’l-baqā’), is written in Arabic and deals with free will and determinism. [58] : 475 The titles of his other works are On being and necessity (Risālah fī’l-kawn wa’l-taklīf), The Treatise on Transcendence in Existence (Al-Risālah al-ulā fi’l-wujūd), On the knowledge of the universal principles of existence (Risālah dar ‘ilm kulliyāt-i wujūd), and Abridgement concerning natural phenomena (Mukhtasar fi’l-Tabi‘iyyāt).

Religious views Edit

A literal reading of Khayyam's quatrains leads to the interpretation of his philosophic attitude toward life as a combination of pessimism, nihilism, Epicureanism, fatalism, and agnosticism. [14] : 6 [59] This view is taken by Iranologists such as Arthur Christensen, H. Schaeder, Richard N. Frye, E. D. Ross, [60] : 365 E.H. Whinfield [41] : 40 and George Sarton. [11] : 18 Conversely, the Khayyamic quatrains have also been described as mystical Sufi poetry. [61] In addition to his Persian quatrains, J. C. E. Bowen (1973) mentions that Khayyam's Arabic poems also "express a pessimistic viewpoint which is entirely consonant with the outlook of the deeply thoughtful rationalist philosopher that Khayyam is known historically to have been." [62] : 69 Edward FitzGerald emphasized the religious skepticism he found in Khayyam. [63] In his preface to the Rubáiyát he claimed that he "was hated and dreaded by the Sufis", [64] and denied any pretense at divine allegory: "his Wine is the veritable Juice of the Grape: his Tavern, where it was to be had: his Saki, the Flesh and Blood that poured it out for him." [65] : 62 Sadegh Hedayat is one of the most notable proponents of Khayyam's philosophy as agnostic skepticism, and according to Jan Rypka (1934), he even considered Khayyam an atheist. [66] Hedayat (1923) states that "while Khayyam believes in the transmutation and transformation of the human body, he does not believe in a separate soul if we are lucky, our bodily particles would be used in the making of a jug of wine." [67] In a later study (1934–35) he further contends that Khayyam's use of Sufic terminology such as "wine" is literal and that he turned to the pleasures of the moment as an antidote to his existential sorrow: "Khayyam took refuge in wine to ward off bitterness and to blunt the cutting edge of his thoughts." [68] In this tradition, Omar Khayyam's poetry has been cited in the context of New Atheism, e.g. in The Portable Atheist by Christopher Hitchens. [69]

Al-Qifti (ca. 1172–1248) appears to confirm this view of Omar's philosophy. [10] : 663 In his work The History of Learned Men he reports that Omar's poems were only outwardly in the Sufi style, but were written with an anti-religious agenda. [60] : 365 He also mentions that he was at one point indicted for impiety, but went on a pilgrimage to prove he was pious. [14] : 29 The report has it that upon returning to his native city he concealed his deepest convictions and practised a strictly religious life, going morning and evening to the place of worship. [60] : 355

In the context of a piece entitled On the Knowledge Of the Principals of Existence, Khayyam endorses the Sufi path. [14] : 8 Csillik (1960) suggests the possibility that Omar Khayyam could see in Sufism an ally against orthodox religiosity. [70] : 75 Other commentators do not accept that Omar's poetry has an anti-religious agenda and interpret his references to wine and drunkenness in the conventional metaphorical sense common in Sufism. The French translator J. B. Nicolas held that Omar's constant exhortations to drink wine should not be taken literally, but should be regarded rather in the light of Sufi thought where rapturous intoxication by "wine" is to be understood as a metaphor for the enlightened state or divine rapture of baqaa. [71] The view of Omar Khayyam as a Sufi was defended by Bjerregaard (1915), [72] Idries Shah (1999), [73] and Dougan (1991) who attributes the reputation of hedonism to the failings of FitzGerald's translation, arguing that Omar's poetry is to be understood as "deeply esoteric". [74] On the other hand, Iranian experts such as Mohammad Ali Foroughi and Mojtaba Minovi rejected the hypothesis that Omar Khayyam was a Sufi. [62] : 72 Foroughi stated that Khayyam's ideas may have been consistent with that of Sufis at times but there is no evidence that he was formally a Sufi. Aminrazavi (2007) states that "Sufi interpretation of Khayyam is possible only by reading into his Rubāʿīyyāt extensively and by stretching the content to fit the classical Sufi doctrine." [14] : 128 Furthermore, Frye (1975) emphasizes that Khayyam was intensely disliked by a number of celebrated Sufi mystics who belonged to the same century. This includes Shams Tabrizi (spiritual guide of Rumi), [14] : 58 Najm al-Din Daya who described Omar Khayyam as "an unhappy philosopher, atheist, and materialist", [62] : 71 and Attar who regarded him not as a fellow-mystic but a free-thinking scientist who awaited punishments hereafter. [10] : 663

Seyyed Hossein Nasr argues that it is "reductive" to use a literal interpretation of his verses (many of which are of uncertain authenticity to begin with) to establish Omar Khayyam's philosophy. Instead, he adduces Khayyam's interpretive translation of Avicenna's treatise Discourse on Unity (Al-Khutbat al-Tawhīd), where he expresses orthodox views on Divine Unity in agreement with the author. [75] The prose works believed to be Omar's are written in the Peripatetic style and are explicitly theistic, dealing with subjects such as the existence of God and theodicy. [14] : 160 As noted by Bowen these works indicate his involvement in the problems of metaphysics rather than in the subtleties of Sufism. [62] : 71 As evidence of Khayyam's faith and/or conformity to Islamic customs, Aminrazavi mentions that in his treatises he offers salutations and prayers, praising God and Muhammad. In most biographical extracts, he is referred to with religious honorifics such as Imām, The Patron of Faith (Ghīyāth al-Dīn), and The Evidence of Truth (Hujjat al-Haqq). [14] He also notes that biographers who praise his religiosity generally avoid making reference to his poetry, while the ones who mention his poetry often do not praise his religious character. [14] : 48 For instance Al-Bayhaqi's account which antedates by some years other biographical notices, speaks of Omar as a very pious man who professed orthodox views down to his last hour. [76] : 174

On the basis of all the existing textual and biographical evidence, the question remains somewhat open, [14] : 11 and as a result Khayyam has received sharply conflicting appreciations and criticisms. [60] : 350

The various biographical extracts referring to Omar Khayyam describe him as unequalled in scientific knowledge and achievement during his time. [77] Many called him by the epithet King of the Wise (Arabic: ملك الحکماء ‎). [53] : 436 [34] : 141 Shahrazuri (d. 1300) esteems him highly as a mathematician, and claims that he may be regarded as "the successor of Avicenna in the various branches of philosophic learning." [60] : 352 Al-Qifti (d. 1248) even though disagreeing with his views concedes he was "unrivalled in his knowledge of natural philosophy and astronomy." [60] : 355 Despite being hailed as a poet by a number of biographers, according to Richard Nelson Frye "it is still possible to argue that Khayyam's status as a poet of the first rank is a comparatively late development." [10] : 663

Thomas Hyde was the first European to call attention to Omar and to translate one of his quatrains into Latin (Historia religionis veterum Persarum eorumque magorum, 1700). [78] : 525 Western interest in Persia grew with the Orientalism movement in the 19th century. Joseph von Hammer-Purgstall (1774–1856) translated some of Khayyam's poems into German in 1818, and Gore Ouseley (1770–1844) into English in 1846, but Khayyam remained relatively unknown in the West until after the publication of Edward FitzGerald's Rubaiyat of Omar Khayyam in 1859. FitzGerald's work at first was unsuccessful but was popularised by Whitley Stokes from 1861 onward, and the work came to be greatly admired by the Pre-Raphaelites. In 1872 FitzGerald had a third edition printed which increased interest in the work in America. By the 1880s, the book was extremely well known throughout the English-speaking world, to the extent of the formation of numerous "Omar Khayyam Clubs" and a "fin de siècle cult of the Rubaiyat". [79] Khayyam's poems have been translated into many languages many of the more recent ones are more literal than that of FitzGerald. [80]

FitzGerald's translation was a factor in rekindling interest in Khayyam as a poet even in his native Iran. [81] Sadegh Hedayat in his Songs of Khayyam (Taranehha-ye Khayyam, 1934) reintroduced Omar's poetic legacy to modern Iran. Under the Pahlavi dynasty, a new monument of white marble, designed by the architect Houshang Seyhoun, was erected over his tomb. A statue by Abolhassan Sadighi was erected in Laleh Park, Tehran in the 1960s, and a bust by the same sculptor was placed near Khayyam's mausoleum in Nishapur. In 2009, the state of Iran donated a pavilion to the United Nations Office in Vienna, inaugurated at Vienna International Center. [82] In 2016, three statues of Khayyam were unveiled: one at the University of Oklahoma, one in Nishapur and one in Florence, Italy. [83] Over 150 composers have used the Rubaiyat as their source of inspiration. The earliest such composer was Liza Lehmann. [6] The French-Lebanese writer Amin Maalouf based the first half of his historical fiction novel Samarkand on Khayyam's life and the creation of his Rubaiyat.

FitzGerald rendered Omar's name as "Tentmaker", and the anglicized name of "Omar the Tentmaker" resonated in English-speaking popular culture for a while. Thus, Nathan Haskell Dole published a novel called Omar, the Tentmaker: A Romance of Old Persia in 1898. Omar the Tentmaker of Naishapur is a historical novel by John Smith Clarke, published in 1910. "Omar the Tentmaker" is also the title of a 1914 play by Richard Walton Tully in an oriental setting, adapted as a silent film in 1922. US General Omar Bradley was given the nickname "Omar the Tent-Maker" in World War II. [84]

The lunar crater Omar Khayyam was named in his honour in 1970, as was the minor planet 3095 Omarkhayyam discovered by Soviet astronomer Lyudmila Zhuravlyova in 1980. [85]

Google has released two Google Doodles commemorating him. The first was on his 964th birthday on 18 May 2012. The second was on his 971st birthday on 18 May 2019. [86]

"A Ruby kindles in the vine", illustration for FitzGerald's Rubaiyat of Omar Khayyam by Adelaide Hanscom Leeson (c. 1905).


Omar Khayyam’s non-fiction writings

Umar Khayyam writes himself: “This [Tasawwuf or Sufism] is the best of all ways, because none of the perfections of God are kept away from it, and there are no obstacles or veils put before it. Therefore, whatever [ignorance] comes to man is due to the impurity of his nature if the veil be lifted and the screen and obstacle removed, the truth of things as they are will become manifest. And the Master [the Prophet Muhammad] upon whom be peace – indicated this when he said: ‘Truly, during the days of your existence, inspirations come from God. Do you not want to follow them?’ Tell unto reasoners that, for the lovers of God [Gnostics], intuition is guide, not discursive thought ”.

Historian Ibn al-Qifti writes that Omar Khayyam was once skeptical about faith, but later, became a practicing Muslim, went to hajj, and after coming back visited the mosque day and night. Shams Tabriz (Sufi guide of Rumi) and a few other Sufis didn’t like Omar. This is not abnormal, as Ibn Sina was also called a disbeliever in his lifetime and he always replied back in return. Even the great hadith scholar Ibn Hibban was accused of atheism, and had to leave town. Omar Khayyam went to hajj in order to prove that he was indeed a believer.

The most important book for Omar Khayyam’s biography is by Abu’l Hasan al-Bayhaqi. He describes the death of Omar Khayyam as such:

“Ḥakim was studying the Ilāhiyyāt of Shifā and once he came to the section on unity and multiplicity, stopped in order to pray and utter his last words. His companions gathered and he [Khayyām] announced his last will and testament and performed his noon prayer. He neither ate nor drank again until he performed his night prayer. He bowed and placed his forehead on the ground and said: ‘O God, I know Thee in as much as my ability allows, forgive me for I know Thy way is the way towards Thee’, and then died .”

Shahrazuri describes Omar’s last day similarly. There he further writes that Omar Khayyam was making sujood (prostration) and asking Allah to forgive his sins at the time of his being skeptic. He died at that state, while making sujood.


Omar Khayyam History | Umar Khayyam

Abu Alfatah Omar Bin Ibrahim Khayyam was a great poet of Persian language and an expert mathematician. He was born in 1039 in the Manisha Pur during the regime of Tughral. His father’s name was Ibrahim and he was called Khayyam because of his occupation. That’s why he was also called Omar Khayyam. He was not only famous in the eastern region but also in the west. His poetry was translated almost in every religious language of the world. His poetry is very famous and got much appreciation. The poetry, which is very famous in recent times was only a way to pass his leisure time. He was considered as a great scientist of the era of Saljoqi.

Education and work:

After getting his education, Omar Khayyam went to Turkistan, got training from Qazi Abu Zahir and then he was sent to the palace of Shamsul Malik Khaqan in Bukhara. After sometime, he was send to Malik Shah Saljoqi and there he got the duty to construct the royal building.
After one year, Omar Khayyam Saljoqis took the charge of his congenital city Manisha Pur and made a great contribution to the progress of the city. He could not get the company of Ibn E Sina but he got guidance related to mathematics from pupils of Ibn E Sina. Because of that, he used to call himself pupil of Ibn E Sina. After completing his education in Manisha Pur, he wrote a book named “Maka’abaat” and gave solutions to the many problems of mathematics. But his book did not get the due attention and he decided to go to Samar Qand. In Samar Qand an wealthy man Abu Tahir, who was one of the adductor of the king of Turkmenistan Shamsul Malik, attached Omar Khayyam to his work and it was he because of whom Khayyam wrote the book “Jabro Mukabla”. He started that book in 1067 and completed in 1974. It was the 4th book of algebra in Muslim era. Although he was interested in mathematics but he was a great physician as well. That is why he was introduced in the court of the king as a physician.

The son of the king was suffering from a disease called smallpox. Omar Khayyam provided medical assistance and kings’ son recovered soon. Because of that, he was appointed as a physician in the court.
Umar always used to complain that his work in the field of mathematics did not get the due recognition. People admired him as a physician because of their personal benefits. Soon he got the job in observatory center and got huge funds for observatory purposes. Here he got the chance to bring the changes according to his own. He died in 1131 in Manisha Pur.


History Documented In Films

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74 Famous Quotes By Omar Khayyam, The Man Who Donned Multiple Hats

Tomorrow! - Why, tomorrow I may be Myself with yesterday's sev'n thousand years.


Into this universe, and why not knowing Nor whence, like water willy-nilly flowing And out of it, as wind along the wate, I know not whither, willy-nilly blowing.


The moving finger writes and having writ, moves on.


Myself when young did eagerly frequent doctor and saint, and heard great argument about it and about: but evermore came out by the same door as in I went.


To-day is thine to spend, but not to-morrow Counting on morrows breedeth bankrupt sorrow: O squander not this breath that Heaven hath lent thee Make not too sure another breath to borrow.


The Grape that can with Logic absolute The Two-and-Seventy jarring Sects confute: The sovereign Alchemist that in a trice Life's leaden metal into Gold transmute.


Algebras are geometric facts which are proved.


You know, my friends, with what a brave carouse I made a Second Marriage in my house favored old barren reason from my bed, and took the daughter of the vine to spouse.


The entire world shall be populous with that action which saves one soul from despair.


Here's to the man Who owns the land That bears the grapes That makes the wine That tastes as good As this does.


Come, fill the Cup, and in the Fire of Spring The Winter Garment of Repentance fling: The Bird of Time has but a little way To fly-and Lo! the Bird is on the Wing.


Dust into Dust, and under Dust to lie, Sans Wine, sans Song, sans Singer, and-sans End!


The Revelations of Devout and Learn'd Who rose before us, and as Prophets burn'd, Are all but Stories, which, awoke from Sleep They told their comrades, and to Sleep return'd.


Indeed the Idols I have loved so long, have done my credit in this World much wrong have drowned my Glory in a shallow Cup, and sold my Reputation for a Song.


The Flower that once has blown forever dies.


Wake! For the Sun, who scatter'd into flight The Stars before him from the Field of Night, Drives Night along with them from Heav'n, and strikes The Sultan's Turret with a Shaft of Light


He who has one enemy shall meet him everywhere.


And this I know whether the one True Light Kindle to Love, or Wrath consume me quite, One flash of it within the Tavern caught Better than in the temple lost outright.


Think, in this batter'd Caravanserai Whose portals are alternate Night and Day, How Sultan after Sultan with his Pomp Abode his destin'd Hour and went his way.


Heaven but the vision of fulfilled desire, and Hell the shadow from a soul on fire.


Ah Love! could you and I with him conspire To grasp this sorry Scheme of Things entire Would we not shatter it to bits-and then Re-mould it nearer to the Heart's Desire?


To friends and eke to foes true kindness show No kindly heart unkindly deeds will do Harshness will alienate a bosom friend. And kindness reconcile a deadly foe.


The unbeliever knows his Koran best.


Fools, your reward is neither here nor there.


I can’t reveal the mystery to either saint or sinner I can’t state at length what I’ve said curtly I achieve an altered state that I can’t explain I have a secret that I cannot share.


I hide my distress, just likethe blessed birds hide themselveswhen they are preparing to die. Wine! Wine, roses, music and yourindifference to my sadness, my loved-one!


Awake, my Little ones, and fill the Cup Before Life's Liquor in its Cup be dry.


For in and out, above, about, below, 'Tis nothing but a Magic Shadow-show, Played in a Box whose Candle is the Sun, Round which we Phantom Figures come and go.


But helpless Pieces of the Game He plays Upon this Checker-board of Nights and Days Hither and thither moves, and checks, and slays, And one by one back in the Closet lays.


I hide my grief, just like the blessed birds hide themselves when they are preparing to die, my love.


This body is a tent which for a space Does the pure soul with kingly presence grace When he departs, comes the tent-pitcher, Death, Strikes it, and moves to a new halting-place.


Drink! for you know not when you came, nor why Drink! for you know not why you go, nor where.


We are in truth but pieces on this chess board of life, which in the end we leave, only to drop one by one into the grave of nothingness.


Living Life Tomorrow's fate, though thou be wise, Thou canst not tell nor yet surmise Pass, therefore, not today in vain, For it will never come again.


The secret must be kept from all non-people. The mystery must be hidden from all idiots.


Oh! My beloved! fill the cup, that clears to-day of past regrets and future fears.


Justice is the soul of the universe.


The thoughtful soul to solitude retires.


Dead yesterdays and unborn tomorrows, why fret about it, if today be sweet.


Why ponder thus the future to foresee, and jade thy brain to vain perplexity? Cast off thy care, leave Allah’s plans to him – He formed them all without consulting thee.


Hearts are like tapers, which at beauteous eyes Kindle a flame of love that never dies And beauty is a flame, where hearts, like moths, Offer themselves a burning sacrifice.


So I be written in the Book of Love. I do not care about that Book Above. Erase my name, or write it as you will. So I be written in the Book of Love.


Yes, the first morning of creation wrote what the last dawn of reckoning shall read.


You know how little while we have to stay, And, once departed, may return no more.


A hair divides what is false and true.


If I don't enjoy myself now, when shall I?


When I want to understand what is happening today or try to decide what will happen tomorrow, I look back.


Think not I dread to see my spirit fly, Through the dark gates of fell mortality Death has no terrors when the life is true 'Tis living ill that makes us fear to die.


There was a door to which I found no key: There was the veil through which I might not see.


In monasteries, seminaries, retreats and synagogues, they fear hell and seek paradise. Those who know the mysteries of God never let that seed be planted in their souls.


My friend, let's not think of tomorrow, but let's enjoy this fleeting moment of life.


A loaf of bread, a jug of wine, and thou.


Give me a flagon of red wine, a book of verses, a loaf of bread, and a little idleness. If with such store I might sit by thy dear side in some lonely place, I should deem myself happier than a king in his kingdom.


The rose that once has bloomed forever dies.


I came like Water, and like Wind I go.


The value of three things is justly appreciated by all classes of men: youth, by the old health, by the diseased and wealth, by the needy.


I have not asked for life. But I try to accept whatever life brings without surprise. And I shall depart again without having questioned anyone about my strange stay here on earth.


To wisely live your life, you don't need to know much Just rememeber two main rules for the beginning: You better starve, than eat whatever And better be alone, than with whoever.


I sent my Soul through the Invisible, Some letter of that After-life to spell: And by and by my Soul return'd to me, And answer'd: 'I Myself am Heav'n and Hell


To be free of belief and unbelief is my religion.


Drink wine. This is life eternal. This is all that youth will give you. It is the season for wine, roses and drunken friends. Be happy for this moment. This moment is your life.


The moving finger writes, and having written moves on. Nor all thy piety nor all thy wit, can cancel half a line of it.


Be happy for this moment. This moment is your life.


It’s too bad if a heart lacks fire, and is deprived of the light of a heart ablaze. The day on which you are without passionate love is the most wasted day of your life.


Don't cry upon you losses Don't mesure today with tommorows Don't trust to passed and coming day Believe in now - and be happy today.


As far as you can avoid it, do not give grief to anyone. Never inflict your rage on another. If you hope for eternal rest, feel the pain yourself but don’t hurt others.


Men talk of heaven, - there is no heaven but here Men talk of hell, - there is no hell but here Men of hereafters talk and future lives, - O love, there is no other life - but here.


How sad, a heart that does not know how to love, that does not know what it is to be drunk with love. If you are not in love, how can you enjoy the blinding light of the sun, the soft light of the moon?


We are thinking about bad only those who are worse than we are, and those who are better than us . I'm just not up to us . One does not follow it than smell roses. Another of the bitter herbs will produce honey. Give bread to one - will remember forever. Another life donation - do not understand .


Old Khayyám, say you, is a debaucheeIf only you were half so good as he!He sins no sins but gentle drunkenness,Great-hearted mirth, and kind adultery.But yours the cold heart, and the murderous tongue,The wintry soul that hates to hear a song,The close-shut fist, the mean and measuring eye,And all the little poisoned ways of wrong.


Realise this: one day your soul will depart from your body and you will be drawn behind the curtain that floats between us and the unknown. While you wait for that moment, be happy, because you don't know where you came from and you don't know where you will be going.


How much more of the mosque, of prayer and fasting? Better go drunk and begging round the taverns. Khayyam, drink wine, for soon this clay of yours Will make a cup, bowl, one day a jar. When once you hear the roses are in bloom, Then is the time, my love, to pour the wine Houris and palaces and Heaven and Hell- These are but fairy-tales, forget them all.


When you are so full of sorrow that you can't walk, can't cry anymore, think about the green foliage that sparkles after the rain. When the daylight exhausts you, when you hope a final night will cover the world, think about the awakening of a young child.


You've seen the world, and all you've seen is nothing and everything, as well, that you have said and heard is nothing. You've sprinted everywhere between here and the horizon it is nothing. And all the possessions you've treasured up at home are nothing.


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