Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī[1][3] (18 May 1048 – 4 December 1131) (Persian:غیاثالدین ابوالفتح عمر بن ابراهیم خیام نیشابورﻯ), commonly known asOmar Khayyam (عمر خیّام),[a] was a Persian poet and polymath, known for his contributions tomathematics,astronomy,philosophy, andPersian literature.[4]: 94 He was born inNishapur, Iran and lived during theSeljuk era, around the time of theFirst Crusade.
As a mathematician, he is most notable for his work on the classification and solution ofcubic equations, where he provided a geometric formulation based on the intersection ofconics.[5] He also contributed to a deeper understanding ofEuclid'sparallel axiom.[6]: 284 As an astronomer, he calculated the duration of the solar year with remarkable precision and accuracy, and designed theJalali calendar, asolar calendar with a very precise 33-yearintercalation cycle[7]: 659 [b] which provided the basis for thePersian calendar that is still in use after nearly a millennium.
Omar Khayyam was born inNishapur—a metropolis inKhorasan province of theSeljuk Empire, ofPersian stock, in 1048.[8][9][10][11][12] In medieval Persian texts he is usually simply calledOmar Khayyam.[7]: 658 [c] Although open to doubt, it has often been assumed that his forebears followed the trade of tent-making, sinceKhayyam means 'tent-maker' in Arabic.[15]: 30 The historianBayhaqi, who was personally acquainted with Khayyam, provides the full details of his horoscope: "he was Gemini, the sun and Mercury being in the ascendant[...]".[16]: 471 [17]: 172–175, no. 66 This was used by modern scholars to establish his date of birth as 18 May 1048.[7]: 658
Khayyam's boyhood was spent in Nishapur,[7]: 659 a leading metropolis in theSeljuk Empire,[18]: 15 [19] which had earlier been a major center of theZoroastrian religion.[8]: 68 His full name, as it appears in Arabic sources, wasAbu’l Fath Omar ibn Ibrahim al-Khayyam.[d] 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, and Khayyam developed a firm friendship with him through the years.[8]: 20 Khayyam might have met and studied withBahmanyar, a disciple ofAvicenna.[8]: 20–21 After studying science, philosophy, mathematics and astronomy at Nishapur, about the year 1068 he traveled to the province ofBukhara, where he frequented the renowned library of theArk. In about 1070 he moved toSamarkand, where he started to compose his famousTreatise on Algebra under the patronage of Abu Tahir Abd al-Rahman ibn ʿAlaq, the governor andchief judge of the city.[20]: 4330b Khayyam was kindly received by the Karakhanid rulerShams al-Mulk Nasr, who according to Bayhaqi, would "show him the greatest honour, so much so that he would seat [Khayyam] beside him on histhrone".[15]: 34 [8]: 47
In 1073–4 peace was concluded withSultanMalik-Shah I, who had made incursions into Karakhanid dominions. Khayyam entered the service of Malik-Shah in 1074 when he was invited by theGrand VizierNizam al-Mulk to meet Malik-Shah in the city ofMarv. Khayyam was subsequently commissioned to set up an observatory inIsfahan and lead a group of scientists in carrying out precise astronomical observations aimed at the revision of the Persian calendar. The undertaking probably began with the opening of the observatory in 1074 and ended in 1079,[8]: 28–29 when Omar Khayyam and his colleagues concluded their measurements of the length of the year, reporting it as 365.24219858156 days.[5] Given that the length of the year is changing in the sixth decimal place over a person's lifetime, this is 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.
After the death of Malik-Shah and his vizier (murdered, it is thought, by theIsmailiorder of Assassins), Khayyam fell from favor at court, and as a result, he soon set out on hispilgrimage to Mecca. A possible ulterior motive for his pilgrimage reported byAl-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 or adherence to Zoroastrianism) levelled at him by a hostile clergy.[8]: 29 [8]: 29 [21] He was then invited by the newSultan Sanjar to Marv, possibly to work as a courtastrologer.[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 theMausoleum of Omar Khayyam. One of his disciplesNizami Aruzi relates the story that sometime during 1112–3 Khayyam was inBalkh in the company ofIsfizari (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".[15]: 36 [19] 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 apricot trees had thrust their heads and dropped their flowers so that his tombstone was hidden beneath them.[15]: 37
Khayyam was famous during his life as amathematician. His surviving mathematical works include
(i)Commentary on the Difficulties Concerning the Postulates of Euclid's Elements (Risāla fī Sharḥ mā Ashkal min Muṣādarāt Kitāb Uqlīdis), completed in December 1077,[11]: 832a [23][24]: § 1 [25]: 324b
(ii)Treatise On the Division of a Quadrant of a Circle (Risālah fī Qismah Rub‘ al-Dā’irah), undated but completed prior to theTreatise on Algebra,[11]: 831b [24]: § 2 and
(iii)Treatise on Algebra (Risālah fi al-Jabr wa'l-Muqābala),[11]: 831b–832a [24]: § 3 most likely completed in 1079.[6]: 281
He furthermore wrote a treatise on thebinomial theorem and extracting thenth root of natural numbers, which has been lost.[8]: 197 [11]: 832a [24]: § 4 [25]: 325b–326b
Part of Khayyam'sCommentary on the Difficulties Concerning the Postulates of Euclid's Elements deals with theparallel axiom.[6]: 282 The treatise of Khayyam can be considered the first treatment of the axiom not based onpetitio principii, but on a more intuitive postulate. Khayyam refutes the previous attempts by other mathematicians toprove 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.[24]: § 1 [25]: 326b–327b [26]: 75 Drawing uponAristotle's views, he rejects the usage of movement in geometry and therefore dismisses the different attempt byIbn al-Haytham.[27]: 64–65 [28]: 270 [e] Unsatisfied with the failure of mathematicians to prove Euclid's statement from his other postulates, Khayyam tried to connect the axiom with the Fourth Postulate, which states that all right angles are equal to one another.[6]: 282
Khayyam was the first to consider the three distinct cases of acute, obtuse, and right angle for the summit angles of aKhayyam-Saccheri quadrilateral.[6]: 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.[28]: 270 [29]: 133 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-Euclideanhyperbolic geometry of Gauss-Bolyai-Lobachevsky, to that ofelliptic geometry, and toEuclidean geometry.[30]
"Cubic equation and intersection of conic sections" the first page of a two-chaptered manuscript kept in Tehran University.
Tusi's commentaries on Khayyam's treatment of parallels made their way to Europe.John Wallis, professor of geometry atOxford, translated Tusi's commentary into Latin. Jesuit geometerGirolamo Saccheri, whose work (euclides ab omni naevo vindicatus, 1733) is generally considered the first step in the eventual development ofnon-Euclidean geometry, was familiar with the work of Wallis. The American historian of mathematicsDavid 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."[8]: 195 [22]: 104 [31]
This treatise on Euclid contains another contribution dealing with thetheory 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 ofirrational number.[32] Displeased with Euclid's definition of equal ratios, he redefined the concept of a number by the use of a continued fraction as the means of expressing a ratio.Youschkevitch and Rosenfeld argue that "by placing irrational quantities and numbers on the same operational scale, [Khayyam] began a true revolution in the doctrine of number."[25]: 327b Likewise, it was noted byD. J. Struik that Omar was "on the road to that extension of the number concept which leads to the notion of thereal number."[6]: 284
Omar Khayyam's construction of a solution to thecubicx3 + 2x = 2x2 + 2. The intersection point produced by the circle and the hyperbola determine the desired segment.
Rashed and Vahabzadeh (2000) have argued that because of his thoroughgoing geometrical approach to algebraic equations, Khayyam can be considered the precursor ofDescartes in the invention ofanalytic geometry.[33]: 248 In theTreatise 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 theperpendicular 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.[33]: 248
Khayyam seems to have been the first to conceive a general theory of cubic equations,[5][f] and the first to geometrically solve every type of cubic equation, so far as positive roots are concerned.[34] TheTreatise on Algebra contains his work oncubic equations.[35]: 9 It is divided into three parts: (i) equations which can be solved withcompass and straight edge, (ii) equations which can be solved by means ofconic sections, and (iii) equations which involve theinverse of the unknown.[24]: § 3
Khayyam produced an exhaustive list of all possible equations involving lines, squares, and cubes.[36]: 43 He considered three binomial equations, nine trinomial equations, and seven tetranomial equations.[6]: 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.[11]: 831b [25]: 328a [37]: 49 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.[6]: 281 [38]: 157 The prerequisite lemmas for Khayyam's geometrical proof includeEuclid VI, Prop 13, andApollonius II, Prop 12.[38]: 155 The positive root of a cubic equation was determined as theabscissa of a point of intersection of two conics, for instance, the intersection of twoparabolas, or the intersection of a parabola and a circle,etc.[39]: 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".[38]: 158 This task remained open until the sixteenth century, where an algebraic solution of the cubic equation was found in its generality byCardano,Del Ferro, andTartaglia inRenaissance Italy.[6]: 282
Whoever thinksalgebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra andgeometry are different in appearance. Algebras are geometric facts which are proved by propositions five and six of Book two ofElements.
In effect, Khayyam's work is an effort to unify algebra and geometry.[41]: 241 This particular geometric solution of cubic equations was further investigated byM. Hachtroudi and extended to solving fourth-degree equations.[42] Although similar methods had appeared sporadically sinceMenaechmus, and further developed by the 10th-century mathematicianAbu al-Jud,[43]: 29 [44]: 110 Khayyam's work can be considered the first systematic study and the first exact method of solving cubic equations.[45]: 92 The mathematicianWoepcke (1851) who offered translations of Khayyam's algebra into French praised him for his "power of generalization and his rigorously systematic procedure."[46]: 10
From theIndians one has methods for obtainingsquare andcube roots, methods 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 ofThe Elements.
In his algebraic treatise, Khayyam alludes to a book he had written on the extraction of theth root of natural numbers using a law he had discovered which did not depend on geometric figures.[39] This book was most likely titled theDifficulties of Arithmetic (Mushkilāt al-Ḥisāb),[11]: 832a [24]: § 4 and is not extant.[25]: 325b 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, wheren is a positive integer.[6]: 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 themathematician 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.[48] 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 asPascal's triangle;[49]: 60 Khayyam popularized thistriangular array in Iran, so that it is now known as Omar Khayyam's triangle.[39]
Representation of the intercalation scheme of the Jalali calendar
In 1074–5, Omar Khayyam was commissioned by Sultan Malik-Shah to build anobservatory at Isfahan and reform thePersian 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.[39]: 141 Recalibrating the calendar fixed the first day of the year at the exact moment of the passing of the Sun's center acrossvernal equinox. This marks the beginning of spring orNowrūz, a day in which the Sun enters the first degree ofAries before noon.[50]: 10–11 [51] The resultant calendar was named in Malik-Shah's honor as theJalālī calendar, and was inaugurated on 15 March 1079.[52]: 269 Theobservatory itself was disused after the death of Malik-Shah in 1092.[7]: 659
The Jalālī calendar was a truesolar calendar where the duration of each month is equal to the time of the passage of the Sun across the corresponding sign of theZodiac. The calendar reform introduced a unique 33-yearintercalation cycle. As indicated by the works ofKhazini, Khayyam's group implemented an intercalation system based on quadrennial and quinquennialleap years. Therefore, the calendar consisted of 25 ordinary years that included 365 days, and 8 leap years that included 366 days.[53]: 13 The calendar remained in use acrossGreater Iran from the 11th to the 20th centuries. In 1911, the Jalali calendar became the official national calendar ofQajar Iran. In 1925, this calendar was simplified and the names of the months were modernised, resulting in themodern Iranian calendar. The Jalali calendar is more accurate than theGregorian calendar of 1582,[7]: 659 with an error of one day accumulating over 5,000 years, compared to one day every 3,330 years in the Gregorian calendar.[8]: 200 Moritz Cantor considered it the most perfect calendar ever devised.[22]: 101
One of his pupils,Nizami Aruzi, 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."[46]: 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.[8]: 30 George Saliba explains that the term‘ilm al-nujūm, used in various sources in which references to Khayyam'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 toFarabi'sEnumeration 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."[54]: 224
Khayyam has a short treatise devoted toArchimedes' 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 byEilhard Wiedemann who believed that Khayyam's solution was more accurate and sophisticated than that ofKhazini andAl-Nayrizi who also dealt with the subject elsewhere.[8]: 198
Another short treatise is concerned withmusic 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 andtetrachords.[8]: 198
Rendition of aruba'i from the Bodleian manuscript, rendered inShekasteh calligraphy.
The earliest allusion to Omar Khayyam's poetry is from the historianImad al-Din al-Isfahani, a younger contemporary of Khayyam, who explicitly identifies him as both a poet and a scientist (Kharidat al-qasr, 1174).[8]: 49 [55]: 35 One of the earliest specimens of Omar Khayyam's Rubiyat is fromFakhr al-Din al-Razi. In his workal-Tanbih ‘ala ba‘d asrar al-maw‘dat fi’l-Qur’an (c. 1160), he quotes one of his poems (corresponding to quatrain LXII of FitzGerald's first edition).Daya in his writings (Mirṣād al-‘Ibad, c. 1230) quotes two quatrains, one of which is the same as the one already reported by Razi. An additional quatrain is quoted by the historianJuvayni (Tarikh-i Jahangushay, c. 1226–1283).[55]: 36–37 [8]: 92 In 1340Jajarmi includes thirteen quatrains of Khayyam in his work containing an anthology of the works of famous Persian poets (Mu’nis al-ahrār), two of which have hitherto been known from the older sources.[56]: 434 A comparatively late manuscript is theBodleian MS. Ouseley 140, written inShiraz in 1460, which contains 158 quatrains on 47 folia. The manuscript belonged toWilliam Ouseley (1767–1842) and was purchased by the Bodleian Library in 1844.
There are occasional quotes of verses attributed to Khayyam 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 bepseudepigraphic.[55]: 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 presents a bibliography of the manuscript tradition, concluding pessimistically that the situation has not changed significantly since Schaeder's time.[57]:307
Five of the quatrains later attributed to Omar Khayyam are found as early as 30 years after his death, quoted inSindbad-Nameh. While this establishes that these specific verses were in circulation in Omar's time or shortly later, it does not 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.[57]:305Edward 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".[7]: 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, c. 1201–1211), Qifti (Tārikh al-hukamā, 1255), andHamdallah Mustawfi (Tarikh-i guzida, 1339).[8]: 39
Boyle emphasized that there are a number of otherPersian scholars who occasionally wrote quatrains, includingAvicenna,Ghazali, andTusi. They conclude 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".[7]: 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 byEdward FitzGerald (1859). FitzGerald'sRubaiyat of Omar Khayyam contains loose translations of quatrains from the Bodleian manuscript. It enjoyed such success in thefin de siècle period that a bibliography compiled in 1929 listed more than 300 separate editions,[58] and many more have been published since.[57]:312
Khayyam considered himself intellectually to be a student ofAvicenna.[2]: 474 According to Al-Bayhaqi, he was reading the metaphysics in Avicenna'sthe Book of Healing before he died.[7]: 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, titledThe 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 withfree will anddeterminism.[2]: 475 The titles of his other works areOn 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), andAbridgement concerning natural phenomena (Mukhtasar fi’l-Tabi‘iyyāt).
We are the victims of an age when men of science are discredited, and only a few remain who are capable of engaging in scientific research. Our philosophers spend all their time in mixing true with false and are interested in nothing but outward show; such little learning as they have they extend on material ends. When they see a man sincere and unremitting in his search for the truth, one who will have nothing to do with falsehood and pretence, they mock and despise him.
A literal reading of Khayyam's quatrains leads to the interpretation of his philosophic attitude toward life as a combination ofpessimism,nihilism,Epicureanism,fatalism, andagnosticism.[8]: 6 [60] This view is taken byIranologists such asArthur Christensen,Hans Heinrich Schaeder,John Andrew Boyle,Edward Denison Ross,[61]: 365 Edward Henry Whinfield[46]: 40 andGeorge Sarton.[18]: 18 Conversely, the Khayyamic quatrains have also been described as mysticalSufi poetry.[62] In addition to his Persian quatrains, J. C. E. Bowen 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."[63]: 69 Edward FitzGerald emphasized the religious skepticism he found in Khayyam.[64] In his preface to theRubáiyát he claimed that he "was hated and dreaded by the Sufis",[65] and denied any pretense at divine allegory: "his Wine is the veritable Juice of the Grape: his Tavern, where it was to be had: hisSaki, the Flesh and Blood that poured it out for him."[66]: 62 Sadegh Hedayat is one of the most notable proponents of Khayyam's philosophy as agnostic skepticism, and according toJan Rypka (1934), he even considered Khayyam anatheist.[67] 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."[68]: 138 Omar Khayyam's poetry has been cited in the context ofNew Atheism, such as inThe Portable Atheist byChristopher Hitchens.[69]: 7
Al-Qifti (c. 1172–1248) appears to confirm this view of Khayyam's philosophy.[7]: 663 In his workThe History of Learned Men he reports that Khayyam's poems were only outwardly in the Sufi style, but were written with an anti-religious agenda.[61]: 365 He also mentions that he was at one point indicted for impiety, but went on a pilgrimage to prove he was pious.[8]: 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.[61]: 355 Khayyam on the Koran (quote 84):[70]
The Koran! well, come put me to the test, Lovely old book in hideous error drest, Believe me, I can quote the Koran too, The unbeliever knows his Koran best. And do you think that unto such as you, A maggot-minded, starved, fanatic crew, God gave the Secret, and denied it me? Well, well, what matters it! believe that too.
Look not above, there is no answer there; Pray not, for no one listens to your prayer; Near is as near to God as any Far, And Here is just the same deceit as There.[70]
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.[70]
An account of him, written in the thirteenth century, shows 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. 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...."[71]: 263, vol. 1
Persian novelistSadegh Hedayat says Khayyám from "his youth to his death remained a materialist, pessimist, agnostic. Khayyam looked at all religions questions with a skeptical eye", continues Hedayat, "and hated the fanaticism, narrow-mindedness, and the spirit of vengeance of the mullas, the so-called religious scholars."[72]: 13
In the context of a piece entitledOn the Knowledge of the Principles of Existence, Khayyam endorses the Sufi path.[8]: 8 Csillik suggests the possibility that Omar Khayyam could see in Sufism an ally against orthodox religiosity.[73]: 75 Other commentators do not accept that Khayyam'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 Khayyam'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 ofbaqaa.[74] The view of Omar Khayyam as a Sufi was defended by Bjerregaard,[75]: 3 Idries Shah,[76]: 165–166 and Dougan who attributes the reputation of hedonism to the failings of FitzGerald's translation, arguing that Khayyam's poetry is to be understood as "deeply esoteric".[77] On the other hand, Iranian experts such asMohammad Ali Foroughi andMojtaba Minovi rejected the hypothesis that Omar Khayyam was a Sufi.[63]: 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 aSufi. Aminrazavi states that "Sufi interpretation of Khayyam is possible only by reading into hisRubāʿīyyāt extensively and by stretching the content to fit the classical Sufi doctrine.".[8]: 128 Furthermore, Boyle emphasizes that Khayyam was intensely disliked by a number of celebrated Sufi mystics who belonged to the same century. This includesShams Tabrizi (spiritual guide ofRumi),[8]: 58 Najm al-Din Daya who described Omar Khayyam as "an unhappy philosopher, atheist, and materialist",[63]: 71 andAttar who regarded him not as a fellow-mystic but a free-thinking scientist who awaited punishments hereafter.[7]: 663–664
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 ofAvicenna's treatiseDiscourse on Unity (al-Khutbat al-Tawhīd), where he expresses orthodox views onDivine Unity in agreement with the author.[78]: Ch. 9, 165–183 The prose works believed to be Khayyam's are written in thePeripatetic style and are explicitly theistic, dealing with subjects such asthe existence of God andtheodicy.[8]: 160 As noted by Bowen these works indicate his involvement in the problems of metaphysics rather than in the subtleties of Sufism.[63]: 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 andMuhammad. In most biographical extracts, he is referred to with religioushonorifics such asImām,The Patron of Faith (Ghīyāth al-Dīn), andThe Evidence of Truth (Hujjat al-Haqq).[8] 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.[8]: 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.[17]: 174
On the basis of all the existing textual and biographical evidence, the question remains somewhat open,[8]: 11 and as a result Khayyam has received sharply conflicting appreciations and criticisms.[61]: 350
Stamp ofAlbania in 1997, entitled "850th birth anniversary of Omar Khayyam"
The various biographical extracts referring to Omar Khayyam describe him as unequalled in scientific knowledge and achievement during his time.[g] Many called him by the epithetKing of the Wise (Arabic:ملك الحکماء,romanized: Malik al-Ḥukamā).[56]: 436 [39]: 141 Shahrazuri (d. 1300) esteems him highly as a mathematician, and claims that he may be regarded as "the successor ofAvicenna in the various branches of philosophic learning".[61]: 352 Al-Qifti (d. 1248), even though disagreeing with his views, concedes he was "unrivalled in his knowledge of natural philosophy and astronomy".[61]: 355 Despite being hailed as a poet by a number of biographers, according toJohn Andrew Boyle "it is still possible to argue that Khayyam's status as a poet of the first rank is a comparatively late development."[7]: 663
Thomas Hyde was the first European to call attention to Khayyam and to translate one of his quatrains into Latin (Historia religionis veterum Persarum eorumque magorum, 1700).[79]: 525 Western interest in Persia grew with theOrientalism movement in the 19th century.Joseph von Hammer-Purgstall (1774–1856) translated some of Khayyam's poems into German in 1818, andGore Ouseley (1770–1844) into English in 1846, but Khayyam remained relatively unknown in the West until after the publication ofEdward FitzGerald'sRubaiyat of Omar Khayyam in 1859. FitzGerald's work at first was unsuccessful but was popularised byWhitley Stokes from 1861 onward, and the work came to be greatly admired by thePre-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".[80]: 202 Khayyam's poems have been translated into many languages; many of the more recent ones are more literal than that of FitzGerald.[81]
FitzGerald's translation was a factor in rekindling interest in Khayyam as a poet even in his native Iran.[82]: 55–72 Sadegh Hedayat in hisSongs of Khayyam (Taranehha-ye Khayyam, 1934) reintroduced Khayyam's poetic legacy to modern Iran. Under thePahlavi dynasty, a newmonument of white marble, designed by the architectHoushang Seyhoun, was erected over his tomb. A statue byAbolhassan Sadighi was erected inLaleh 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 apavilion to theUnited Nations Office in Vienna, inaugurated atVienna International Center.[83] In 2016, three statues of Khayyam were unveiled: one at theUniversity of Oklahoma, one in Nishapur and one in Florence, Italy.[84] Over 150composers have used theRubaiyat as their source of inspiration. The earliest such composer wasLiza Lehmann.[85]
FitzGerald rendered Khayyam'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 calledOmar, the Tentmaker: A Romance of Old Persia in 1898.Omar the Tentmaker ofNaishapur is a historical novel by John Smith Clarke, published in 1910. "Omar the Tentmaker" is also the title of a 1914 play byRichard Walton Tully in an oriental setting, adapted as asilent film in 1922. US GeneralOmar Bradley was given the nickname "Omar the Tent-Maker" in World War II.[86]: 13
The diverse talents and intellectual pursuits of Khayyam captivated manyOttoman andTurkish writers throughout history.[87] Scholars often viewed Khayyam as a means to enhance their own poetic prowess and intellectual depth, drawing inspiration and recognition from his writings.[88] For many Muslim reformers, Khayam's verses provided a counterpoint to the conservative norms prevalent in Islamic societies, allowing room for independent thought and a libertine lifestyle.[88] Figures likeAbdullah Cevdet,Rıza Tevfik, andYahya Kemal utilized Khayyam's themes to justify their progressive ideologies or to celebrate liberal aspects of their lives, portraying him as a cultural, political, and intellectual role model who demonstrated Islam's compatibility with modern conventions.[88] Similarly, Turkish leftist poets and intellectuals, includingNâzım Hikmet,Sabahattin Eyüboğlu, A. Kadir, and Gökçe, appropriated Khayyam to champion their socialist worldview, imbuing his voice with a humanistic tone in the vernacular.[88] Khayyam's resurgence in spokenTurkish since the 1980s has transformed him into a poet of the people, with numerous books and translations revitalizing his historical significance.[88] Conversely, scholars like Dāniş, Tevfik, andGölpınarlı advocated for source criticism and the identification of authentic quatrains to discern the genuine Khayyam amidst historical perceptions of his sociocultural image.[88]
A line of English translation of ''The Moving Finger'' quatrain.Persian Rubiyats of Omar Khayyam on one the faculty buildings ofLeiden University
The quatrain by Omar Khayyam known as "The Moving Finger", in the form of its translation by the English poetEdward Fitzgerald is one of the most popular quatrains in theAnglosphere.[89] It reads:
“We may cry out desperately for time to pause in her passage, but time is adamant to every plea and rushes on. Over the bleached bones and jumbled residues of numerous civilizations are written the pathetic words, ‘Too late.’ There is an invisible book of life that faithfully records our vigilance or our neglect. Omar Khayyam is right: ‘The moving finger writes, and having writ moves on.’”
In 1934Harold Lamb published a historical novelOmar Khayyam. The French-Lebanese writerAmin Maalouf based the first half of his historical fiction novelSamarkand on Khayyam's life and the creation of his Rubaiyat. The sculptorEduardo Chillida produced four massive iron pieces titledMesa de Omar Khayyam (Omar Khayyam's Table) in the 1980s.[94][95]
Google has released twoGoogle 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.[97]
^With an error of one day accumulating over 5,000 years, it was more precise than theGregorian calendar of 1582, which has an error of one day every 3,330 years.[8]: 200
^Katz (1998), p. 270. Excerpt:In some sense, his treatment was better than Ibn al-Haytham's because he explicitly formulated a new postulate to replace Euclid's rather than have the latter hidden in a new definition.
^O'Connor & Robertson (July 1999):However, Khayyam himself seems to have been the first to conceive a general theory of cubic equations.
^Arberry, A.J. (2008).Aspects of Islamic Civilization: As Depicted in the Original Texts. Routledge. p. 16.ISBN978-0-415-42600-8.Omar composed his shafts of wit and shapes of beauty in his native Persian, which by the tenth century had recovered from the stunning blow dealt it by Arabic.
^Peter Avery and John Heath-Stubbs,The Ruba'iyat of Omar Khayyam, (Penguin Group, 1981), 14; "These dates, 1048–1031, tell us that Khayyam lived when the Seljuq Turkish Sultans were extending and consolidating their power over Persia and when the effects of this power were particularly felt in Nishapur, Khayyam's birthplace."
^abEdward FitzGerald,Rubaiyat of Omar Khayyam, Ed. Christopher Decker, (University of Virginia Press, 1997), xv; "The Seljuq Turks had invaded the province of Khorasan in the 1030s, and the city of Nishapur surrendered to them voluntarily in 1038. Thus Omar Khayyam grew to maturity during the first of the several alien dynasties that would rule Iran until the twentieth century".
^Rosenfeld, Boris A.;Youschkevitch, A.P. (1996). "Geometry". InRoshdi Rashed; in collaboration with Régis Morelon (eds.).Encyclopedia of the History of Arabic Science. Vol. II. London & New York: Routledge. pp. 115–159.ISBN0-415-02063-8.
^Smith, D.E. (1935). "Euclid, Omar Khayyâm, and Saccheri".Scripta Mathematica.III (1):5–10.OCLC14156259.
^Vahabzadeh, Bijan (2005). Jafar Aghayani-Chawoshi (ed.). "Omar Khayyam and the Concept of Irrational Numbers".Farhang: Quarterly Journal of Humanities and Cultural Studies. Issue Topic: Commemoration of Khayyam (3).XVIII (53–54):125–134.
^Oaks, Jeffrey A. (2011)."Khayyām's Scientific Revision of Algebra"(PDF).Suhayl: International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation.X:47–75.
^Knoebel, Art; Laubenbacher, Reinhard; Lodder, Jerry (2007).Mathematical Masterpieces: Further Chronicles by the Explorers. Springer.ISBN978-0-387-33060-0.
^abcBlois, François de (2004).Persian Literature - A Bio-Bibliographical Survey. Volume 5: Poetry of the Pre-Mongol Period. London & New York: Routledge.ISBN9780947593476.
^Ambrose George Potter,A Bibliography of the Rubaiyat of Omar Khayyam (1929).
^"Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature" Abdullah DouganWho is the Potter? Gnostic Press 1991ISBN0-473-01064-X
^Simidchieva, M. (2011). FitzGerald's Rubáiyát and Agnosticism. In A. Poole, C. Van Ruymbeke, & W. Martin (Eds.), FitzGerald's Rubáiyát of Omar Khayyám: Popularity and Neglect. Anthem Press.
Boyle, J. A., ed. (1968).The Cambridge History of Iran. Volume V: The Saljug and Mongol Periods. New York: Cambridge University Press.ISBN978-0-521-06936-6.
Contemporary Persian and Classical Persian are the same language, but writers since 1900 are classified as contemporary. At one time, Persian was a common cultural language of much of the non-Arabic Islamic world. Today it is the official language ofIran,Tajikistan and one of the two official languages ofAfghanistan.
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