Khayyam Saheb
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Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī (18 May 1048 – 4 December 1131) (
Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, the majority ethnic group in Iran, not to be conflated with the Iranic peoples ** Persian language, an Iranian language of the ...
: غیاث الدین ابوالفتح عمر بن ابراهیم خیام نیشابورﻯ), commonly known as Omar Khayyam (), was a Persian poet and polymath, known for his contributions to
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
,
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
,
philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
, and
Persian literature Persian literature comprises oral compositions and written texts in the Persian language and is one of the world's oldest literatures. It spans over two-and-a-half millennia. Its sources have been within Greater Iran including present-day ...
. He was born in
Nishapur Nishapur or Neyshabur (, also ) is a city in the Central District (Nishapur County), Central District of Nishapur County, Razavi Khorasan province, Razavi Khorasan province, Iran, serving as capital of both the county and the district. Ni ...
, Iran and lived during the Seljuk era, around the time of the
First Crusade The First Crusade (1096–1099) was the first of a series of religious wars, or Crusades, initiated, supported and at times directed by the Latin Church in the Middle Ages. The objective was the recovery of the Holy Land from Muslim conquest ...
. As a mathematician, he is most notable for his work on the classification and solution of
cubic equation In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d=0 in which is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...
s, where he provided a geometric formulation based on the intersection of
conic A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, thou ...
s. He also contributed to a deeper understanding of
Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...
's parallel axiom. As an astronomer, he calculated the duration of the solar year with remarkable precision and accuracy, and designed the
Jalali calendar The Jalali calendar, also referred to as ''Malikshahi'' and ''Maliki'', is a solar calendar compiled during the reign of Jalaluddin Malik-Shah I, the Sultan of the Seljuk Empire (1072–1092 CE), by the order of Grand Vizier Nizam al-Mulk, using ...
, a
solar calendar A solar calendar is a calendar whose dates indicates the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar ...
with a very precise 33-year intercalation cycle which provided the basis for the
Persian calendar The Iranian calendars or Iranian chronologies (, ) are a succession of calendars created and used for over two millennia in Iran, also known as Persia. One of the longest chronological records in human history, the Iranian calendar has been modi ...
that is still in use after nearly a millennium. There is a tradition of attributing
poetry Poetry (from the Greek language, Greek word ''poiesis'', "making") is a form of literature, literary art that uses aesthetics, aesthetic and often rhythmic qualities of language to evoke meaning (linguistics), meanings in addition to, or in ...
to Omar Khayyam, written in the form of
quatrain A quatrain is a type of stanza, or a complete poem, consisting of four Line (poetry), lines. Existing in a variety of forms, the quatrain appears in poems from the poetic traditions of various ancient civilizations including Persia, Ancient India ...
s (''
rubāʿiyāt A ''rubāʿī'' (, from Arabic ; plural: ) or ''chahārgāna(e)'' () is a poem or a verse of a poem in Persian poetry (or its derivative in English and other languages) in the form of a quatrain, consisting of four lines (four hemistichs). In ...
'' ). This poetry became widely known to the English-reading world in a translation by Edward FitzGerald (''
Rubaiyat of Omar Khayyam ''Rubáiyát of Omar Khayyám'' is the title that Edward FitzGerald (poet), Edward FitzGerald gave to his 1859 translation from Persian language, Persian to English of a selection of quatrains (') attributed to Omar Khayyam (1048–1131), dub ...
'', 1859), which enjoyed great success in the
Orientalism In art history, literature, and cultural studies, Orientalism is the imitation or depiction of aspects of the Eastern world (or "Orient") by writers, designers, and artists from the Western world. Orientalist painting, particularly of the Middle ...
of the ''
fin de siècle "''Fin de siècle''" () is a French term meaning , a phrase which typically encompasses both the meaning of the similar English idiom '' turn of the century'' and also makes reference to the closing of one era and onset of another. Without co ...
''.


Life

Omar Khayyam was born in
Nishapur Nishapur or Neyshabur (, also ) is a city in the Central District (Nishapur County), Central District of Nishapur County, Razavi Khorasan province, Razavi Khorasan province, Iran, serving as capital of both the county and the district. Ni ...
—a metropolis in
Khorasan KhorasanDabeersiaghi, Commentary on Safarnâma-e Nâsir Khusraw, 6th Ed. Tehran, Zavvâr: 1375 (Solar Hijri Calendar) 235–236 (; , ) is a historical eastern region in the Iranian Plateau in West and Central Asia that encompasses western and no ...
province, of
Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, the majority ethnic group in Iran, not to be conflated with the Iranic peoples ** Persian language, an Iranian language of the ...
stock, in 1048. In medieval Persian texts he is usually simply called ''Omar Khayyam''. 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. The historian Bayhaqi, who was personally acquainted with Khayyam, provides the full details of his horoscope: "he was Gemini, the sun and Mercury being in the ascendant ... This was used by modern scholars to establish his date of birth as 18 May 1048. Khayyam's boyhood was spent in Nishapur, a leading metropolis in the
Seljuk Empire The Seljuk Empire, or the Great Seljuk Empire, was a High Middle Ages, high medieval, culturally Turco-Persian tradition, Turco-Persian, Sunni Islam, Sunni Muslim empire, established and ruled by the Qiniq (tribe), Qïnïq branch of Oghuz Turks. ...
,Edward 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". which had earlier been a major center of the
Zoroastrian religion Zoroastrianism ( ), also called Mazdayasnā () or Beh-dīn (), is an Iranian religion centred on the Avesta and the teachings of Zarathushtra Spitama, who is more commonly referred to by the Greek translation, Zoroaster ( ). Among the wor ...
. His full name, as it appears in Arabic sources, was ''Abu’l Fath Omar ibn Ibrahim al-Khayyam''. 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. Khayyam might have met and studied with Bahmanyar, a disciple of
Avicenna Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian ...
. After studying science, philosophy, mathematics and astronomy at Nishapur, about the year 1068 he traveled to the province of
Bukhara Bukhara ( ) is the List of cities in Uzbekistan, seventh-largest city in Uzbekistan by population, with 280,187 residents . It is the capital of Bukhara Region. People have inhabited the region around Bukhara for at least five millennia, and t ...
, where he frequented the renowned library of the Ark. In about 1070 he moved to
Samarkand Samarkand ( ; Uzbek language, Uzbek and Tajik language, Tajik: Самарқанд / Samarqand, ) is a city in southeastern Uzbekistan and among the List of oldest continuously inhabited cities, oldest continuously inhabited cities in Central As ...
, 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 Chief judge may refer to: In lower or circuit courts The highest-ranking or most senior member of a lower court or circuit court with more than one judge. * Chief judge (Australia) * Chief judge (United States) In supreme courts Some of Chief ...
of the city. 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 hayyambeside him on his
throne A throne is the seat of state of a potentate or dignitary, especially the seat occupied by a sovereign (or viceroy A viceroy () is an official who reigns over a polity in the name of and as the representative of the monarch of the territory ...
". In 1073–4 peace was concluded with
Sultan Sultan (; ', ) is a position with several historical meanings. Originally, it was an Arabic abstract noun meaning "strength", "authority", "rulership", derived from the verbal noun ', meaning "authority" or "power". Later, it came to be use ...
Malik-Shah I Malik-Shah I (, ) was the third sultan of the Seljuk Empire from 1072 to 1092, under whom the sultanate reached the zenith of its power and influence. During his youth, he spent his time participating in the campaigns of his father Alp Arslan, ...
who had made incursions into Karakhanid dominions. Khayyam entered the service of Malik-Shah in 1074 when he was invited by the
Grand Vizier Grand vizier (; ; ) was the title of the effective head of government of many sovereign states in the Islamic world. It was first held by officials in the later Abbasid Caliphate. It was then held in the Ottoman Empire, the Mughal Empire, the Soko ...
Nizam al-Mulk Abū ʿAlī Ḥasan ibn ʿAlī Ṭūsī () (1018 – 1092), better known by his honorific title of Niẓām al-Mulk (), was a Persian Sunni scholar, jurist, political philosopher and vizier of the Seljuk Empire. Rising from a low position w ...
to meet Malik-Shah in the city of Marv. Khayyam was subsequently commissioned to set up an observatory in
Isfahan Isfahan or Esfahan ( ) is a city in the Central District (Isfahan County), Central District of Isfahan County, Isfahan province, Iran. It is the capital of the province, the county, and the district. It is located south of Tehran. The city ...
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, when Omar Khayyam and his colleagues concluded their measurements of the length of the year, reporting it as 365.24219858156 days. 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 the
Ismaili Ismailism () is a branch of Shia Islam. The Isma'ili () get their name from their acceptance of Imam Isma'il ibn Jafar as the appointed spiritual successor ( imām) to Ja'far al-Sadiq, wherein they differ from the Twelver Shia, who accept ...
order of Assassins The Order of Assassins (; ) were a Nizari Isma'ilism, Nizari Isma'ili order that existed between 1090 and 1275 AD, founded by Hasan-i Sabbah, Hasan al-Sabbah. During that time, they lived in the mountains of Persia and the Levant, and held a ...
), Khayyam fell from favor at court, and as a result, he soon set out on his
pilgrimage to Mecca Hajj (; ; also spelled Hadj, Haj or Haji) is an annual Islamic pilgrimage to Mecca, Saudi Arabia, the holiest city for Muslims. Hajj is a mandatory religious duty for capable Muslims that must be carried out at least once in their lifetim ...
. A possible ulterior motive for his pilgrimage reported by
Al-Qifti Jamāl al-Dīn Abū al-Ḥasan 'Alī ibn Yūsuf ibn Ibrāhīm ibn 'Abd al-Wahid al-Shaybānī (), called al-Qifṭī (; – 1248), was an Egyptian Arab historian, biographer, encyclopedist and administrator under the Ayyubid rulers of Aleppo ...
, 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. He was then invited by the new Sultan Sanjar to Marv, possibly to work as a court
astrologer Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...
. 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. 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 A mausoleum is an external free-standing building constructed as a monument enclosing the burial chamber of a deceased person or people. A mausoleum without the person's remains is called a cenotaph. A mausoleum may be considered a type of ...
. One of his disciples
Nizami Aruzi Ahmad ibn Umar ibn Alī, known as Nizamī-i Arūzī-i Samarqandī () and also Arudi ("The Prosodist"), was a poet and prose writer who flourished between 1110 and 1161. He is particularly famous for his ''Chahar Maqala'' ("Four Discourses"), his ...
relates the story that sometime during 1112–3 Khayyam was in
Balkh Balkh is a town in the Balkh Province of Afghanistan. It is located approximately to the northwest of the provincial capital city Mazar-i-Sharif and approximately to the south of the Amu Darya and the Afghanistan–Uzbekistan border. In 2021 ...
in the company of 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". 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.


Mathematics

Khayyam was famous during his life as a
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. His surviving mathematical works include * (i) ''Commentary on the Difficulties Concerning the Postulates of Euclid's Elements'' (), completed in December 1077, * (ii) ''Treatise On the Division of a Quadrant of a Circle'' (), undated but completed prior to the ''Treatise on Algebra'', and * (iii) ''Treatise on Algebra'' (), most likely completed in 1079. He furthermore wrote a treatise on the
binomial theorem In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power expands into a polynomial with terms of the form , where the exponents and a ...
and extracting the nth root of natural numbers, which has been lost.


Theory of parallels

Part of Khayyam's ''Commentary on the Difficulties Concerning the Postulates of Euclid's Elements'' deals with the parallel axiom. The treatise of Khayyam can be considered the first treatment of the axiom not based on
petitio principii In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: ) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. Historically, begging the question refers to a fault i ...
, 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. Drawing upon
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
's views, he rejects the usage of movement in geometry and therefore dismisses the different attempt by
Ibn al-Haytham Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen; ; full name ; ) was a medieval Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, p ...
. 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. 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. 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. 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 In mathematics, hyperbolic geometry (also called Lobachevskian geometry or János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For a ...
of Gauss-Bolyai-Lobachevsky, to that of
Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...
, and to
Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ...
.
Tusi ''Tusi'', often translated as "headmen" or "chieftains", were hereditary tribal leaders recognized as imperial officials by the Yuan, Ming, and Qing dynasties of China, and the Later Lê and Nguyễn dynasties of Vietnam. They ruled certain ...
's commentaries on Khayyam's treatment of parallels made their way to Europe.
John Wallis John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...
, professor of geometry at
Oxford Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the List of oldest universities in continuou ...
, translated Tusi's commentary into Latin. Jesuit geometer Girolamo Saccheri, whose work (''euclides ab omni naevo vindicatus'', 1733) is generally considered the first step in the eventual development of
non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...
, was familiar with the work of Wallis. The American historian of mathematics
David Eugene Smith David Eugene Smith (January 21, 1860 – July 29, 1944) was an American mathematician, educator, and editor. Education and career David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cort ...
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."


Real number concept

This treatise on Euclid contains another contribution dealing with the
theory of proportions A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...
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 In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, ...
. 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, hayyambegan 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 In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
."


Geometric algebra

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 In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and als ...
. 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 In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ...
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.


Solution of cubic equations

Khayyam seems to have been the first to conceive a general theory of cubic equations, and the first to geometrically solve every type of cubic equation, so far as positive roots are concerned. The ''Treatise on Algebra'' contains his work on
cubic equation In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d=0 in which is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...
s. 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 section A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, tho ...
s, and (iii) equations which involve the
inverse Inverse or invert may refer to: Science and mathematics * Inverse (logic), a type of conditional sentence which is an immediate inference made from another conditional sentence * Additive inverse, the inverse of a number that, when added to the ...
of the unknown. Khayyam produced an exhaustive list of all possible equations involving lines, squares, and cubes. He considered three binomial equations, nine trinomial equations, and seven tetranomial equations. 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. 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. The prerequisite lemmas for Khayyam's geometrical proof include Euclid VI, Prop 13, and Apollonius II, Prop 12. The positive root of a cubic equation was determined as the
abscissa In mathematics, the abscissa (; plural ''abscissae'' or ''abscissas'') and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system: : abscissa \equiv x-axis (horizontal) coordinate : ordinate \eq ...
of a point of intersection of two conics, for instance, the intersection of two
parabola In mathematics, a parabola is a plane curve which is Reflection symmetry, mirror-symmetrical and is approximately U-shaped. It fits several superficially different Mathematics, mathematical descriptions, which can all be proved to define exactl ...
s, or the intersection of a parabola and a circle, etc. 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". This task remained open until the sixteenth century, where an algebraic solution of the cubic equation was found in its generality by Cardano, Del Ferro, and Tartaglia in
Renaissance Italy The Italian Renaissance ( ) was a period in History of Italy, Italian history between the 14th and 16th centuries. The period is known for the initial development of the broader Renaissance culture that spread across Western Europe and marked t ...
. In effect, Khayyam's work is an effort to unify algebra and geometry. This particular geometric solution of cubic equations was further investigated by M. Hachtroudi and extended to solving fourth-degree equations. Although similar methods had appeared sporadically since
Menaechmus Menaechmus (, c. 380 – c. 320 BC) was an ancient Greek mathematician, list of geometers, geometer and philosopher born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his friendship with the renowned philosopher P ...
, and further developed by the 10th-century mathematician
Abu al-Jud Abū al-Jūd Muḥammad b. Aḥmad b. al-Layth was an Iranian mathematician who lived during 10th century and was a contemporary of al-Biruni. He used conics to solve quartic and cubic equations, a century before the more famous work of Omar Khay ...
, Khayyam's work can be considered the first systematic study and the first exact method of solving cubic equations. 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."


Binomial theorem and extraction of roots

In his algebraic treatise, Khayyam alludes to a book he had written on the extraction of the nth root of natural numbers using a law he had discovered which did not depend on geometric figures. This book was most likely titled the ''Difficulties of Arithmetic'' (), 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 is a positive integer. 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 A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
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. One of Khayyam's predecessors,
al-Karaji (; c. 953 – c. 1029) was a 10th-century Persian mathematician and engineer who flourished at Baghdad. He was born in Karaj, a city near Tehran. His three principal surviving works are mathematical: ''Al-Badi' fi'l-hisab'' (''Wonderful on ...
, had already discovered the triangular arrangement of the coefficients of binomial expansions that Europeans later came to know as
Pascal's triangle In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Bla ...
; Khayyam popularized this
triangular array In mathematics and computing, a triangular array of numbers, polynomials, or the like, is a doubly indexed sequence in which each row is only as long as the row's own index. That is, the ''i''th row contains only ''i'' elements. Examples Notable ...
in Iran, so that it is now known as Omar Khayyam's triangle.


Astronomy

In 1074–5, Omar Khayyam was commissioned by Sultan Malik-Shah to build an observatory at Isfahan and reform the
Persian calendar The Iranian calendars or Iranian chronologies (, ) are a succession of calendars created and used for over two millennia in Iran, also known as Persia. One of the longest chronological records in human history, the Iranian calendar has been modi ...
. There was a panel of eight scholars working under the direction of Khayyam to make large-scale astronomical observations and revise the astronomical tables. 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 Aries may refer to: *Aries (astrology), an astrological sign *Aries (constellation), a constellation in the zodiac Arts, entertainment and media * ''Aries'' (album), by Luis Miguel, 1993 * ''Aries'' (EP), by Alice Chater, 2020 * "Aries" (song), ...
before noon. The resultant calendar was named in Malik-Shah's honor as the Jalālī calendar, and was inaugurated on 15 March 1079. The
observatory An observatory is a location used for observing terrestrial, marine, or celestial events. Astronomy, climatology/meteorology, geophysics, oceanography and volcanology are examples of disciplines for which observatories have been constructed. Th ...
itself was disused after the death of Malik-Shah in 1092. The Jalālī calendar was a true
solar calendar A solar calendar is a calendar whose dates indicates the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a 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 zodiac is a belt-shaped region of the sky that extends approximately 8° north and south celestial latitude of the ecliptic – the apparent path of the Sun across the celestial sphere over the course of the year. Within this 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 A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep ...
. Therefore, the calendar consisted of 25 ordinary years that included 365 days, and 8 leap years that included 366 days. The calendar remained in use across
Greater Iran Greater Iran or Greater Persia ( ), also called the Iranosphere or the Persosphere, is an expression that denotes a wide socio-cultural region comprising parts of West Asia, the South Caucasus, Central Asia, South Asia, and East Asia (specifica ...
from the 11th to the 20th centuries. In 1911, the Jalali calendar became the official national calendar of
Qajar Iran The Guarded Domains of Iran, alternatively the Sublime State of Iran and commonly called Qajar Iran, Qajar Persia or the Qajar Empire, was the Iranian state under the rule of the Qajar dynasty, which was of Turkic peoples, Turkic origin,Cyrus G ...
. In 1925, this calendar was simplified and the names of the months were modernised, resulting in the modern Iranian calendar. The Jalali calendar is more accurate than the
Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian cale ...
of 1582, with an error of one day accumulating over 5,000 years, compared to one day every 3,330 years in the Gregorian calendar.
Moritz Cantor Moritz Benedikt Cantor (23 August 1829 – 10 April 1920) was a German historian of mathematics. Biography Cantor was born at Mannheim. He came from a Sephardi Jewish family that had emigrated to the Netherlands from Portugal, another branch ...
considered it the most perfect calendar ever devised. One of his pupils,
Nizami Aruzi Ahmad ibn Umar ibn Alī, known as Nizamī-i Arūzī-i Samarqandī () and also Arudi ("The Prosodist"), was a poet and prose writer who flourished between 1110 and 1161. He is particularly famous for his ''Chahar Maqala'' ("Four Discourses"), his ...
, 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 cientistswho had such belief." While working for Sultan Sanjar as an astrologer he was asked to predict the weather – a job that he apparently did not do well.
George Saliba George Saliba (Arabic: جورج صليبا) is a Lebanese-American historian who is Professor of Arabic and Islamic Science at the Department of Middle Eastern, South Asian, and African Studies, Columbia University, New York, where he has been ...
explains that the term , 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 to
Farabi thumbnail, 200px, Postage stamp of the USSR, issued on the 1100th anniversary of the birth of Al-Farabi (1975) Abu Nasr Muhammad al-Farabi (; – 14 December 950–12 January 951), known in the Latin West as Alpharabius, was an early Islamic ...
's ''Enumeration of the Sciences'', that this science, , was already split into two parts, one dealing with astrology and the other with theoretical mathematical astronomy."


Other works

Khayyam has a short treatise devoted to
Archimedes' principle Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fun ...
(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 Abū’l-'Abbās al-Faḍl ibn Ḥātim al-Nairīzī (; ; , ) was a Persian mathematician and astronomer from Nayriz, now in Fars province, Iran. Life Little is known of al-Nairīzī, though his nisba refers to the town of Neyriz. He mention ...
who also dealt with the subject elsewhere. Another short treatise is concerned with
music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...
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.


Poetry

The earliest allusion to Omar Khayyam's poetry is from the historian Imad al-Din al-Isfahani, a younger contemporary of Khayyam, who explicitly identifies him as both a poet and a scientist (, 1174).Ali Dashti (translated by L. P. Elwell-Sutton), ''In Search of Omar Khayyam'', Routledge Library Editions: Iran (2012) One of the earliest specimens of Omar Khayyam's Rubiyat is from
Fakhr al-Din al-Razi Fakhr al-Dīn al-Rāzī () or Fakhruddin Razi () (1149 or 1150 – 1209), often known by the sobriquet Sultan of the Theologians, was an influential Iranian and Muslim polymath, scientist and one of the pioneers of inductive logic. He wrote var ...
. In his work (), he quotes one of his poems (corresponding to quatrain LXII of FitzGerald's first edition). Daya in his writings (, 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 historian
Juvayni Juvayni (), also spelled in English as Juwayni, Juvaini, or Joveini, is a Persian last name, meaning from the city of Juvayn in Khorasan, Iran Iran, officially the Islamic Republic of Iran (IRI) and also known as Persia, is a country in ...
(, c. 1226–1283). In 1340
Jajarmi Muhammad ibn Badr (), commonly known as Jajarmi, was a 14th-century Persian poet and anthologist from Isfahan, Iran Iran, officially the Islamic Republic of Iran (IRI) and also known as Persia, is a country in West Asia. It borders Iraq ...
includes thirteen quatrains of Khayyam in his work containing an anthology of the works of famous Persian poets (), two of which have hitherto been known from the older sources. A comparatively late manuscript is the
Bodleian The Bodleian Library () is the main research library of the University of Oxford. Founded in 1602 by Sir Thomas Bodley, it is one of the oldest libraries in Europe. With over 13 million printed items, it is the second-largest library in ...
MS. Ouseley 140, written in
Shiraz Shiraz (; ) is the List of largest cities of Iran, fifth-most-populous city of Iran and the capital of Fars province, which has been historically known as Pars (Sasanian province), Pars () and Persis. As of the 2016 national census, the popu ...
in 1460, which contains 158 quatrains on 47 folia. The manuscript belonged to
William Ouseley Sir William Ouseley HFRSE FSAScot (1767 – September 1842), was a British oriental studies, orientalist. Early life Ouseley was born in Monmouthshire (historic), Monmouthshire, the eldest son of Captain Ralph Ouseley (1739), Ralph Ouseley an ...
(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 be
pseudepigraphic A pseudepigraph (also :wikt:anglicized, anglicized as "pseudepigraphon") is a false attribution, falsely attributed work, a text whose claimed author is not the true author, or a work whose real author attributed it to a figure of the past. Th ...
.
Hans Heinrich Schaeder Heinz Heinrich Schaeder (31 January 1896 – 13 March 1957) was a German Orientalist and Iranologist. Life Heinz Heinrich Schaeder was born in Göttingen, Germany on 31 January 1896. He was the son of theologist Erich Schaeder, brother of hi ...
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.:307
/sup> Five of the quatrains later attributed to Omar Khayyam are found as early as 30 years after his death, quoted in ''
Sindbad-Nameh The ''Seven Wise Masters'' (also called the ''Seven Sages'' or ''Seven Wise Men'') is a cycle of stories of Sanskrit, Persian or Hebrew origins. Frame Narrative The Sultan sends his son, the young Prince, to be educated away from the court in t ...
''. 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.:305
/sup>
Edward Granville Browne Edward Granville Browne FBA (7 February 1862 – 5 January 1926) was a British Iranologist. He published numerous articles and books, mainly in the areas of history and literature. Life Browne was born in Stouts Hill, Uley, Gloucestershire, ...
(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". 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 (, c. 1201–1211), Qifti (, 1255), and
Hamdallah Mustawfi Hamdallah Mustawfi Qazvini (; 1281 – after 1339/40) was a Persian official, historian, geographer and poet. He lived during the last era of the Mongol Ilkhanate, and the interregnum that followed. A native of Qazvin, Mustawfi belonged to fami ...
(, 1339). Boyle emphasized that there are a number of other Persian scholars who occasionally wrote quatrains, including
Avicenna Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian ...
, Ghazali, and
Tusi ''Tusi'', often translated as "headmen" or "chieftains", were hereditary tribal leaders recognized as imperial officials by the Yuan, Ming, and Qing dynasties of China, and the Later Lê and Nguyễn dynasties of Vietnam. They ruled certain ...
. 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". 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 ''Rubáiyát of Omar Khayyám'' is the title that Edward FitzGerald (poet), Edward FitzGerald gave to his 1859 translation from Persian language, Persian to English of a selection of quatrains (') attributed to Omar Khayyam (1048–1131), dub ...
'' contains loose translations of quatrains from the Bodleian manuscript. It enjoyed such success in the
fin de siècle "''Fin de siècle''" () is a French term meaning , a phrase which typically encompasses both the meaning of the similar English idiom '' turn of the century'' and also makes reference to the closing of one era and onset of another. Without co ...
period that a bibliography compiled in 1929 listed more than 300 separate editions, and many more have been published since. :312
/sup>


Philosophy

Khayyam considered himself intellectually to be a student of
Avicenna Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian ...
. According to Al-Bayhaqi, he was reading the metaphysics in Avicenna's ''
the Book of Healing ''The Book of Healing'' (; ; also known as ) is a scientific and philosophical encyclopedia written by Abu Ali ibn Sīna (also known as Avicenna). He most likely began to compose the book in 1014, completed it around 1020, and published it in ...
'' before he died. There are six philosophical papers believed to have been written by Khayyam. One of them, ''On existence'' (), 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'' (), is written in Arabic and deals with
free will Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral respon ...
and
determinism Determinism is the Metaphysics, metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes ov ...
. The titles of his other works are ''On being and necessity'' (), ''The Treatise on Transcendence in Existence'' (), ''On the knowledge of the universal principles of existence'' (), and ''Abridgement concerning natural phenomena'' (). Khayyam himself once said:


Religious views

A literal reading of Khayyam's quatrains leads to the interpretation of his philosophic attitude toward life as a combination of
pessimism Pessimism is a mental attitude in which an undesirable outcome is anticipated from a given situation. Pessimists tend to focus on the negatives of life in general. A common question asked to test for pessimism is "Is the glass half empty or half ...
,
nihilism Nihilism () encompasses various views that reject certain aspects of existence. There have been different nihilist positions, including the views that Existential nihilism, life is meaningless, that Moral nihilism, moral values are baseless, and ...
,
Epicureanism Epicureanism is a system of philosophy founded 307 BCE based upon the teachings of Epicurus, an ancient Greek philosopher. Epicurus was an atomist and materialist, following in the steps of Democritus. His materialism led him to religious s ...
,
fatalism Fatalism is a belief and philosophical doctrine which considers the entire universe as a deterministic system and stresses the subjugation of all events, actions, and behaviors to fate or destiny, which is commonly associated with the cons ...
, and
agnosticism Agnosticism is the view or belief that the existence of God, the divine, or the supernatural is either unknowable in principle or unknown in fact. (page 56 in 1967 edition) It can also mean an apathy towards such religious belief and refer t ...
. This view is taken by
Iranologists Iranian studies ( '), also referred to as Iranology and Iranistics, is an interdisciplinary field dealing with the research and study of the civilization, history, literature, art and culture of Iranian peoples. It is a part of the wider field ...
such as
Arthur Christensen Arthur Emanuel Christensen (9 January 1875 – 31 March 1945) was a Danish orientalist and scholar of Iranian philology and folklore. He is best known for his works on the Iranian history, mythology, religions, medicine and music. Biography Ch ...
,
Hans Heinrich Schaeder Heinz Heinrich Schaeder (31 January 1896 – 13 March 1957) was a German Orientalist and Iranologist. Life Heinz Heinrich Schaeder was born in Göttingen, Germany on 31 January 1896. He was the son of theologist Erich Schaeder, brother of hi ...
,
John Andrew Boyle John Andrew Boyle (10 March 1916 – 19 November 1978), was a British historian, an accomplished linguist, and Oriental scholar. Life and career John was born at Worcester Park, Surrey, England, on 10 March 1916. His father, Andrew Boyle, was ...
,
Edward Denison Ross Sir Edward Denison Ross (6 June 1871 – 20 September 1940) - known as Denison - was an orientalist and linguist, specializing in languages of the Middle East, Central and East Asia. He was the first director of the University of London's School ...
, Edward Henry Whinfield and
George Sarton George Alfred Leon Sarton (; 31 August 1884 – 22 March 1956) was a Belgian-American chemist and historian. He is considered the founder of the discipline of the history of science as an independent field of study. His most influential works were ...
. Conversely, the Khayyamic quatrains have also been described as mystical
Sufi Sufism ( or ) is a mysticism, mystic body of religious practice found within Islam which is characterized by a focus on Islamic Tazkiyah, purification, spirituality, ritualism, and Asceticism#Islam, asceticism. Practitioners of Sufism are r ...
poetry. 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." Edward FitzGerald emphasized the religious skepticism he found in Khayyam. In his preface to the ''Rubáiyát'' he claimed that he "was hated and dreaded by the Sufis", 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."
Sadegh Hedayat Sadegh Hedayat (, ; 17 February 1903 – 9 April 1951) was an Iranian peoples, Iranian writer, translator, satirist, and poet. Best known for his novel ''The Blind Owl'', he was one of the earliest Iranian writers to adopt literary modernism in ...
is one of the most notable proponents of Khayyam's philosophy as agnostic skepticism, and according to
Jan Rypka Jan Rypka, PhDr., Dr.Sc. (28 May 1886 in Kroměříž – 29 December 1968 in Prague) was a prominent Czech oriental studies, orientalist, translator, professor of Iranology and Turkology at Charles University, Prague. Jan Rypka was a participa ...
(1934), he even considered Khayyam an
atheist Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no ...
. 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." Omar Khayyam's poetry has been cited in the context of
New Atheism New Atheism is a perspective shared by some atheist academics, writers, scientists, and philosophers of the 20th and 21st centuries, intolerant of superstition, religion, and irrationalism. New Atheists advocate the antitheist view that the v ...
, such as in '' The Portable Atheist'' by
Christopher Hitchens Christopher Eric Hitchens (13 April 1949 – 15 December 2011) was a British and American author and journalist. He was the author of Christopher Hitchens bibliography, 18 books on faith, religion, culture, politics, and literature. He was born ...
.
Al-Qifti Jamāl al-Dīn Abū al-Ḥasan 'Alī ibn Yūsuf ibn Ibrāhīm ibn 'Abd al-Wahid al-Shaybānī (), called al-Qifṭī (; – 1248), was an Egyptian Arab historian, biographer, encyclopedist and administrator under the Ayyubid rulers of Aleppo ...
() appears to confirm this view of Khayyam's philosophy. In his work ''The 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. He also mentions that he was at one point indicted for impiety, but went on a pilgrimage to prove he was pious. 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. Khayyam on the Koran (quote 84): 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...." Persian novelist
Sadegh Hedayat Sadegh Hedayat (, ; 17 February 1903 – 9 April 1951) was an Iranian peoples, Iranian writer, translator, satirist, and poet. Best known for his novel ''The Blind Owl'', he was one of the earliest Iranian writers to adopt literary modernism in ...
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." In the context of a piece entitled ''On the Knowledge of the Principles of Existence'', Khayyam endorses the Sufi path. Csillik suggests the possibility that Omar Khayyam could see in Sufism an ally against orthodox religiosity. 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 of ''
baqaa Baqaa () is a term in Sufi philosophy which describes a particular state of life with God in Islam; through God, in God, and for God. The related term , literally "land of ''baqāʾ''", is a term for Heaven. It is the summit of the mystical man ...
''. The view of Omar Khayyam as a Sufi was defended by Bjerregaard,
Idries Shah Idries Shah (; , , ; 16 June 1924 – 23 November 1996), also known as Idris Shah, Indries Shah, né Sayyid, Sayed Idries el-Hashemite, Hashimi (Arabic: ) and by the pen name Arkon Daraul, was an Afghans, Afghan author, thinker and teacher in ...
, 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". On the other hand, Iranian experts such as
Mohammad Ali Foroughi Mohammad Ali Foroughi (; early August 1877 – 26 or 27 November 1942), also known as Zoka-ol-Molk ( Persian: ذُکاءُالمُلک), was an Iranian politician, writer, freemason, Azali, and diplomat who served as the Prime Minister of ...
and Mojtaba Minovi rejected the hypothesis that Omar Khayyam was a Sufi. 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 Sufism ( or ) is a mysticism, mystic body of religious practice found within Islam which is characterized by a focus on Islamic Tazkiyah, purification, spirituality, ritualism, and Asceticism#Islam, asceticism. Practitioners of Sufism are r ...
. Aminrazavi 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.". Furthermore, Boyle emphasizes that Khayyam was intensely disliked by a number of celebrated Sufi mystics who belonged to the same century. This includes
Shams Tabrizi Shams-i Tabrīzī () or Shams al-Din Mohammad (1185–1248) was a Persian * * * * Shafi'ite poet, who is credited as the spiritual instructor of Mewlānā Jalāl ad-Dīn Muhammad Balkhi, also known as Rumi and is referenced with great rev ...
(spiritual guide of
Rumi Jalāl al-Dīn Muḥammad Rūmī (), or simply Rumi (30 September 1207 – 17 December 1273), was a 13th-century poet, Hanafi '' faqih'' (jurist), Maturidi theologian (''mutakallim''), and Sufi mystic born during the Khwarazmian Empire ...
), Najm al-Din Daya who described Omar Khayyam as "an unhappy philosopher, atheist, and materialist", and
Attar Attar, also known as ittar, is an essential oil derived from botanical or other natural sources. Most commonly these oils are extracted via hydrodistillation or steam distillation. Attar can also be expressed by chemical means but generally n ...
who regarded him not as a fellow-mystic but a free-thinking scientist who awaited punishments hereafter.
Seyyed Hossein Nasr Seyyed Hossein Nasr (born April 7, 1933) is an Iranian Americans, Iranian-American academic, philosophy, philosopher, theology, theologian, and Ulama, Islamic scholar. He is University Professor of Islamic studies at George Washington University. ...
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 Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian ...
's treatise ''Discourse on Unity'' (), where he expresses orthodox views on Divine Unity in agreement with the author. The prose works believed to be Khayyam's are written in the
Peripatetic Peripatetic may refer to: *Peripatetic school, a school of philosophy in Ancient Greece *Peripatetic axiom, in philosophy *Peripatetic minority, a mobile population moving among settled populations offering a craft or trade. *Peripatetic Jats T ...
style and are explicitly theistic, dealing with subjects such as the existence of God and
theodicy In the philosophy of religion, a theodicy (; meaning 'vindication of God', from Ancient Greek θεός ''theos'', "god" and δίκη ''dikē'', "justice") is an argument that attempts to resolve the problem of evil that arises when all powe ...
. As noted by Bowen these works indicate his involvement in the problems of metaphysics rather than in the subtleties of Sufism. 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 Muhammad (8 June 632 CE) was an Arab religious and political leader and the founder of Islam. Muhammad in Islam, According to Islam, he was a prophet who was divinely inspired to preach and confirm the tawhid, monotheistic teachings of A ...
. In most biographical extracts, he is referred to with religious
honorifics An honorific is a title that conveys esteem, courtesy, or respect for position or rank when used in addressing or referring to a person. Sometimes, the term "honorific" is used in a more specific sense to refer to an honorary academic title. It ...
such as , ''The Patron of Faith'' (), and ''The Evidence of Truth'' (). 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. 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. On the basis of all the existing textual and biographical evidence, the question remains somewhat open, and as a result Khayyam has received sharply conflicting appreciations and criticisms.


Reception

The various biographical extracts referring to Omar Khayyam describe him as unequalled in scientific knowledge and achievement during his time. Many called him by the epithet ''King of the Wise'' (). Shahrazuri (d. 1300) esteems him highly as a mathematician, and claims that he may be regarded as "the successor of
Avicenna Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian ...
in the various branches of philosophic learning".
Al-Qifti Jamāl al-Dīn Abū al-Ḥasan 'Alī ibn Yūsuf ibn Ibrāhīm ibn 'Abd al-Wahid al-Shaybānī (), called al-Qifṭī (; – 1248), was an Egyptian Arab historian, biographer, encyclopedist and administrator under the Ayyubid rulers of Aleppo ...
(d. 1248), even though disagreeing with his views, concedes he was "unrivalled in his knowledge of natural philosophy and astronomy". Despite being hailed as a poet by a number of biographers, according to
John Andrew Boyle John Andrew Boyle (10 March 1916 – 19 November 1978), was a British historian, an accomplished linguist, and Oriental scholar. Life and career John was born at Worcester Park, Surrey, England, on 10 March 1916. His father, Andrew Boyle, was ...
"it is still possible to argue that Khayyam's status as a poet of the first rank is a comparatively late development."
Thomas Hyde Thomas Hyde (29 June 163618 February 1703) was an English linguist, historian, librarian, classicist, and orientalist. His chief work was the 1700 'On the Ancient Religion of the Persians'' the first attempt to use Arab and Persian sources ...
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). Western interest in Persia grew with the
Orientalism In art history, literature, and cultural studies, Orientalism is the imitation or depiction of aspects of the Eastern world (or "Orient") by writers, designers, and artists from the Western world. Orientalist painting, particularly of the Middle ...
movement in the 19th century.
Joseph von Hammer-Purgstall Joseph Freiherr von Hammer-Purgstall (; 9 June 1774 – 23 November 1856) was an Austrian orientalist, historian and diplomat. He is considered one of the most accomplished orientalists of his time. Life Born Joseph Hammer in Graz, Duchy of S ...
(1774–1856) translated some of Khayyam's poems into German in 1818, and
Gore Ouseley Sir Gore Ouseley, 1st Baronet Royal Guelphic Order, GCH, Privy Council of the United Kingdom, PC (24 June 1770 – 18 November 1844), was a British entrepreneur, linguist and diplomat. He was born in 1770 and died at Hall Barn Park, Beaconsfiel ...
(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 ''Rubáiyát of Omar Khayyám'' is the title that Edward FitzGerald (poet), Edward FitzGerald gave to his 1859 translation from Persian language, Persian to English of a selection of quatrains (') attributed to Omar Khayyam (1048–1131), dub ...
'' 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 The Pre-Raphaelite Brotherhood (PRB), later known as the Pre-Raphaelites, was a group of English painters, poets, and art critics, founded in 1848 by William Holman Hunt, John Everett Millais, Dante Gabriel Rossetti, William Michael Rossetti ...
. 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". Khayyam's poems have been translated into many languages; many of the more recent ones are more literal than that of FitzGerald. FitzGerald's translation was a factor in rekindling interest in Khayyam as a poet even in his native Iran.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.
Sadegh Hedayat Sadegh Hedayat (, ; 17 February 1903 – 9 April 1951) was an Iranian peoples, Iranian writer, translator, satirist, and poet. Best known for his novel ''The Blind Owl'', he was one of the earliest Iranian writers to adopt literary modernism in ...
in his ''Songs of Khayyam'' (''Taranehha-ye Khayyam'', 1934) reintroduced Khayyam's poetic legacy to modern Iran. Under the
Pahlavi dynasty The Pahlavi dynasty () is an List of monarchs of Iran, Iranian royal dynasty that was the Pahlavi Iran, last to rule Iran before the country's monarchy was abolished by the Iranian Revolution in 1979. It was founded in 1925 by Reza Shah, Reza S ...
, a new
monument A monument is a type of structure that was explicitly created to commemorate a person or event, or which has become relevant to a social group as a part of their remembrance of historic times or cultural heritage, due to its artistic, historical ...
of white marble, designed by the architect Houshang Seyhoun, was erected over his tomb. A statue by
Abolhassan Sadighi Abolhassan Sadighi () (5 October 1894 – 11 December 1995) was an Iranian sculptor and painter and was known as Ostad Sadighi (English: Master Sadighi). He was a student and disciple of Kamal-ol-molk. The statue of Ferdowsi in the Ferdowsi squa ...
was erected in
Laleh Park Laleh Park (Pârk-e Laleh, formerly called Park-e Farah after Farah Diba), is a large recreation area of the Iranian capital Tehran. ''Laleh'' (لاله) is the Persian language, Persian word for tulip, which is also a Tulip#Iran, popular symbol ...
,
Tehran Tehran (; , ''Tehrân'') is the capital and largest city of Iran. It is the capital of Tehran province, and the administrative center for Tehran County and its Central District (Tehran County), Central District. With a population of around 9. ...
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 In architecture, ''pavilion'' has several meanings; * It may be a subsidiary building that is either positioned separately or as an attachment to a main building. Often it is associated with pleasure. In palaces and traditional mansions of Asia ...
to the United Nations Office in Vienna, inaugurated at
Vienna International Center The Vienna International Centre (VIC) is the campus and building complex hosting the United Nations Office at Vienna (UNOV; in ). It is colloquially also known as UNO City. Overview The VIC, designed by Austrian architect Johann Staber, was b ...
. In 2016, three statues of Khayyam were unveiled: one at the
University of Oklahoma The University of Oklahoma (OU) is a Public university, public research university in Norman, Oklahoma, United States. Founded in 1890, it had existed in Oklahoma Territory near Indian Territory for 17 years before the two territories became the ...
, one in Nishapur and one in Florence, Italy. Over 150
composer A composer is a person who writes music. The term is especially used to indicate composers of Western classical music, or those who are composers by occupation. Many composers are, or were, also skilled performers of music. Etymology and def ...
s have used the ''Rubaiyat'' as their source of inspiration. The earliest such composer was Liza Lehmann. 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 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 A silent film is a film without synchronized recorded sound (or more generally, no audible dialogue). Though silent films convey narrative and emotion visually, various plot elements (such as a setting or era) or key lines of dialogue may, w ...
in 1922. US General
Omar Bradley Omar Nelson Bradley (12 February 1893 – 8 April 1981) was a senior Officer (armed forces), officer of the United States Army during and after World War II, rising to the rank of General of the Army (United States), General of the Army. He wa ...
was given the nickname "Omar the Tent-Maker" in World War II. The diverse talents and intellectual pursuits of Khayyam captivated many Ottoman and Turkish writers throughout history. Scholars often viewed Khayyam as a means to enhance their own poetic prowess and intellectual depth, drawing inspiration and recognition from his writings. 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. Figures like
Abdullah Cevdet Abdullah Cevdet Bey (‎9 September 1869 – 29 November 1932) was a Young Turk intellectual and physician of Kurdish origin. He was one of the founders of the Committee of Union and Progress (CUP) and wrote articles with pen name of "Bir Kür ...
, Rıza Tevfik, and
Yahya Kemal Yahya may refer to: * Yahya (name), a common Arabic male given name * Yahya (Zaragoza), 11th-century ruler of Zaragoza * Yahya of Antioch / Yahya ibn Sa'id al-Antaki / Yaḥya ibn Saʿīd al-Anṭākī, 11th century Christian Arabic historian. * ...
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. Similarly, Turkish leftist poets and intellectuals, including
Nâzım Hikmet Mehmed Nâzım Ran (17 January 1902 – 3 June 1963), Note: 403 Forbidden error received 10 October 2022. commonly known as Nâzım Hikmet (), was a Turkish people, Turkish poet, playwright, novelist, screenwriter, director, and memoirist. ...
, Sabahattin Eyüboğlu, A. Kadir, and Gökçe, appropriated Khayyam to champion their socialist worldview, imbuing his voice with a humanistic tone in the vernacular. Khayyam's resurgence in spoken Turkish since the 1980s has transformed him into a poet of the people, with numerous books and translations revitalizing his historical significance. Conversely, scholars like Dāniş, Tevfik, and Gölpınarlı advocated for source criticism and the identification of authentic quatrains to discern the genuine Khayyam amidst historical perceptions of his sociocultural image.


The Moving Finger quatrain

The quatrain by Omar Khayyam known as "The Moving Finger", in the form of its translation by the English poet Edward Fitzgerald is one of the most popular quatrains in the
Anglosphere The Anglosphere, also known as the Anglo-American world, is a Western-led sphere of influence among the Anglophone countries. The core group of this sphere of influence comprises five developed countries that maintain close social, cultura ...
. It reads: The title of the novel '' The Moving Finger'' written by
Agatha Christie Dame Agatha Mary Clarissa Christie, Lady Mallowan, (; 15 September 1890 – 12 January 1976) was an English people, English author known for her 66 detective novels and 14 short story collections, particularly those revolving ...
and published in 1942 was inspired by this quatrain of the translation of ''
Rubaiyat of Omar Khayyam ''Rubáiyát of Omar Khayyám'' is the title that Edward FitzGerald (poet), Edward FitzGerald gave to his 1859 translation from Persian language, Persian to English of a selection of quatrains (') attributed to Omar Khayyam (1048–1131), dub ...
'' by Edward Fitzgerald.
Martin Luther King Martin Luther King Jr. (born Michael King Jr.; January 15, 1929 – April 4, 1968) was an American Baptist minister, civil rights activist and political philosopher who was a leader of the civil rights movement from 1955 until his a ...
also cites this quatrain of Omar Khayyam in one of his speeches, " Beyond Vietnam: A Time to Break Silence": In one of his apologetic speeches about the
Clinton–Lewinsky scandal The Clinton–Lewinsky scandal was a sex scandal involving Bill Clinton, the president of the United States, and Monica Lewinsky, a White House intern. Their sexual relationship began in 1995—when Clinton was 49 years old and Lewinsky ...
,
Bill Clinton William Jefferson Clinton (né Blythe III; born August 19, 1946) is an American politician and lawyer who was the 42nd president of the United States from 1993 to 2001. A member of the Democratic Party (United States), Democratic Party, ...
, the 42nd president of the US, also cites this quatrain.


Other popular culture references

In 1934
Harold Lamb Harold Albert Lamb (September 1, 1892 – April 9, 1962) was an American writer, novelist, historian, and screenwriter. In both his fiction and nonfiction work, Lamb gravitated toward subjects related to Asia and the Middle East. Lamb was an advo ...
published a historical novel ''Omar Khayyam''. The French-Lebanese writer
Amin Maalouf Amin Maalouf (; ; born 25 February 1949) is a Lebanese people in France, Lebanese-born French"A ...
based the first half of his historical fiction novel ''
Samarkand Samarkand ( ; Uzbek language, Uzbek and Tajik language, Tajik: Самарқанд / Samarqand, ) is a city in southeastern Uzbekistan and among the List of oldest continuously inhabited cities, oldest continuously inhabited cities in Central As ...
'' on Khayyam's life and the creation of his Rubaiyat. The sculptor
Eduardo Chillida Eduardo Chillida Juantegui (Basque: ''Eduardo Txillida Juantegi''; 10 January 1924 – 19 August 2002) was a Spanish Basque sculptor notable for his abstract works. Early life and career Born in San Sebastián (Donostia) to Pedro Chillida an ...
produced four massive iron pieces titled ''Mesa de Omar Khayyam'' (Omar Khayyam's Table) in the 1980s. The
lunar crater Lunar craters are impact craters on Earth's Moon. The Moon's surface has many craters, all of which were formed by impacts. The International Astronomical Union currently recognizes 9,137 craters, of which 1,675 have been dated. History The wo ...
Omar Khayyam Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī (18 May 1048 – 4 December 1131) (Persian language, Persian: غیاث الدین ابوالفتح عمر بن ابراهیم خیام نیشابورﻯ), commonly known as Omar ...
was named in his honour in 1970, as was the
minor planet According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor ...
3095 Omarkhayyam discovered by
Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
astronomer
Lyudmila Zhuravlyova Lyudmila Vasilyevna Zhuravleva (, ; born 22 May 1946) is a Soviet, Russian and Ukrainian astronomer, who worked at the Crimean Astrophysical Observatory in Nauchnij, where she discovered 213 minor planets. She also serves as president of the Cr ...
in 1980.
Google Google LLC (, ) is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial ...
has released two
Google Doodle Google Doodle is a special, temporary alteration of the logo on Google's homepages intended to commemorate holidays, events, achievements, and historical figures. The first Google Doodle honored the 1998 edition of the long-running annual Bu ...
s commemorating him. The first was on his 964th birthday on 18 May 2012. The second was on his 971st birthday on 18 May 2019.


Gallery

File:005-a-Ruby-kindles-in-the-vine-810x1146.jpg, "A Ruby kindles in the vine", illustration for FitzGerald's ''
Rubaiyat of Omar Khayyam ''Rubáiyát of Omar Khayyám'' is the title that Edward FitzGerald (poet), Edward FitzGerald gave to his 1859 translation from Persian language, Persian to English of a selection of quatrains (') attributed to Omar Khayyam (1048–1131), dub ...
'' by Adelaide Hanscom Leeson (c. 1905). File:At the Tomb of Omar Khayyam - by Jay Hambidge.jpg, "At the Tomb of Omar Khayyam" by
Jay Hambidge Jay Hambidge (1867–1924) was an American artist who formulated the theory of "dynamic symmetry", a system defining compositional rules, which was adopted by several notable American and Canadian artists in the early 20th century. Early life an ...
(1911). File:Persian Scholar pavilion in Viena UN (Omar Khayyam).jpg, The statue of Khayyam in United Nations Office in Vienna as a part of Persian Scholars Pavilion donated by
Iran Iran, officially the Islamic Republic of Iran (IRI) and also known as Persia, is a country in West Asia. It borders Iraq to the west, Turkey, Azerbaijan, and Armenia to the northwest, the Caspian Sea to the north, Turkmenistan to the nort ...
. File:Bucureşti - Omar Khayam 3.jpg, Statue of Omar Khayyam in
Bucharest Bucharest ( , ; ) is the capital and largest city of Romania. The metropolis stands on the River Dâmbovița (river), Dâmbovița in south-eastern Romania. Its population is officially estimated at 1.76 million residents within a greater Buc ...
File:Madrid - Ciudad Universitaria, Monumento a Omar Jayyam 1.jpg, Monument to Omar Khayyam in Ciudad Universitaria of
Madrid Madrid ( ; ) is the capital and List of largest cities in Spain, most populous municipality of Spain. It has almost 3.5 million inhabitants and a Madrid metropolitan area, metropolitan area population of approximately 7 million. It i ...


See also

* '' Nozhat al-Majales''


Notable films

* ''Omar Khayyam'' (1957 film) * '' The Keeper: The Legend of Omar Khayyam''


Noted Khayyamologists

*
Badiozzaman Forouzanfar Badiozzaman Forouzanfar or Badi'ozzamān Forūzānfar (, also as "Badiʿ al-Zamān Furūzānfar"; born 12 July 1904 in Boshrooyeh, Ferdows County – died 6 May 1970 in Tehran, born ''Ziyaa' Boshrooye-i'' ) was a scholar of Persian literat ...
*
Abdolhossein Zarrinkoob Abdolhossein Zarrinkoub ( Luri/ Persian: , also Romanized as ''Zarrinkoob'', ''Zarrinkub'', ) (March 21, 1923 – September 15, 1999) was a scholar and professor of Iranian literature, history of literature, Persian culture and history. He was ...


Notes


References


Further reading

* * * *


External links

* * *
PDF version
)
Umar Khayyam
in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...
''
The illustrated Rubáiyát of Omar Khayyám
at the
Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...
{{DEFAULTSORT:Khayyam, Omar 1048 births 1131 deaths 11th-century Iranian astronomers 11th-century Persian-language poets 11th-century Persian-language writers 12th-century astronomers 12th-century Iranian astronomers 12th-century Iranian mathematicians 12th-century Persian-language poets 12th-century Persian-language writers Algebraists Astronomers of the medieval Islamic world Iranian philosophers Mathematicians from Nishapur Medieval Iranian physicists Philosophers from Nishapur Poets from the Seljuk Empire Scholars from the Seljuk Empire Iranian atheists