1. Life History of Omar Khayyam
Political Environment:
Umar Khayyam’s real name was Ghiyath al-Din Abul Fateh Umar Ibn Ibrahim
al-Khayyam. He was born in Nishapur, the capital of Khurasan. The commercially rich
province was at that time under Seljaq rule. The Seljuq Turks were tribes that invaded
southwestern Asia in the 11th
century and eventually founded an empire that included
Mesopotamia, Saria, Palestine, and most of Iran. The Seljuq occupied the grazing
grounds of Khorasan and then, between 1038 and 1040, they conquered all of north-
eastern Iran. The Seljuq ruler Toghril Beg proclaimed himself sultan at Nishapur in 1038
and entered Baghdad in 1055. Toghril Beg made Esfahan the capital of his domains and
his grandson, Malik-Shah Jalal-al-Din, was the ruler of that city from 1073. Some
western scholars have termed the regime a difficult unstable military empire, which also
had religious problems as it attempted to establish an orthodox Muslim state. This was
not an empire in which thise of learning, even those as learned as Khayyam, found life
easy unless they had the support of a ruler at one of the many courts. Umar Khayyam was
lucky in this regard since he was invited by Malik-Shah to go to Esfahan to set up an
Observatory there.
Other leading astronomers were also brought to the Observatory in Esfahan and
for 18 years Khayyam led the scientists and produced work of outstanding quality. It was
a period of peace during which the political situation allowed Khayyam the opportunity to
devote himself entirely to his scholarly work. In 1092 political events ended Khayyam’s
period of peaceful existence. Malik-Shah died in November of the year, a month after his
vizier (Minister) Nizam al-Mulk had been murdered on the road from Esfahan to Baghdad
by the terrorist movement called Assassins. Malik-Shah’s second wife took over as ruler
for two years she had argued with Nizam al-Mulk so now whom he had supported found
that support withdrawn. Funding to run the Observatory ceased and Khayyam’s calendar
reform was put on hold. Khayyam also came under attack from the orthodox Muslims
who felt that Khayyam’s questioning mind did not conform to the faith. Despite being out
of favour on all sides, Khayyam remained at Court and tried to regain favour. Malik-
Shah’s third son Sanjar, who was governor of Khorasan, became the overall ruler of the
Seljuq Empire in 1118. Sometime after this Khayyam left Esfahan traveled to Merv (now
Mary, Turkmenistan) which Sanjar made the capital of the Seljuq Empire. Sanjar created
a great centre of Islamic learning in Merv where Khayyam wrote further works on
mathematics.
2. Khayyam stayed in Merv a short while and traveled to Nishapur to stay there. But,
in 1095, Nishapur erupted with religious strife, persecuting those who espoused mash’s
ideas. Khayyam, a prime target, recognized the danger and left Nishapur for mecca. He
did not return until the unrest had subsided. He lived in Nishapur until his death. He died
in Nishapur at the age of over 80, but not before he was to write his wishes,
Ah, with the Grape my fading Life provide,
And Wash my Body whence the life has died,
And in a winding sheet of Vine-leaf wrapt,
So bury me by some sweet Garden-side.
(LXVII of Rubaiyat)
Umar Khayyam was undoubtedly a great mystic poet, a great monotheistic writer,
extremely rational and an extremely argumentative poet. He was opposed to the orthodox
‘ulama’ and was opposed to all institutionalized regulations of religion. To him several
institutions of religion were meaningless. Sufism was uncalled-for, and excessive fervor
for religion was something detested. He was for natural religion and for a natural and
humanitarian approach to it. His Ruba’iyat was for a clean and simple man. He was
forgiveness of man for all his errors and his sympathy went deep into his heart.
But above all he was an optimist and not a pessimist. To him beauty, truth, life,
welfare had a special appeal. He was for all humanity. But he believed in the
transmigration of souls which is against the fundamental beliefs of Islam. Looking at just
a few of the accomplishments of Umar Khayyam one cannot help but be astonished. His
mind was quite obviously ahead of the time. From creating the Al-Tarkhal-Jalali, a
calendar with unbelievable accuracy, to writing, “Maqalat fi al-Jabr al-Muqabila. “ a
book on algebra that stated that cubic could not be solved by ruler and compass methods
but require the use of conics, which would not be proven until seven hundred and fifty
years later. A poet that excelled not only in prose, but whose ability in language flowed
freely from written word to the language of mathematics and science.
Education
Little is known of Umar’s early life. The epithet Khayyam signifies “tant-maker”
it is possible that Umar or his father, Ibrahim the Tent maker, one time exercised that
trade. It has also been suggested that he could have belonged to the Khayyami tribe of
Arab origin who might have settled in Persia.
Khayyam completed his elementary education in Balkh under Muhammad
Mansur. By the age of seventeen he was well-versed in the sciences of his time. He spent
the next nine years in Samarqand and Bukhara becoming acquainted with the philosophy
of the mashai’s, especially with the works of Ibn-i Sina studied under the celebrated
3. teacher the Iman Mowaffak. In Samara he completed his treatise on algebra. In addition
to being educated in his home town of Naishapur, Umar Khayyam studied in Bukhara,
Balkh and Isphahan. While at Samarqand he was patronized by a signatory, Abu Tahir,
Philosophy, Jurisprudence, history, mathematics, and astronomy were among the subjects
mastered by this brilliant man. He was also skilled in medicine and music. His corpus of
works, consisting of two works in physics, four in mathematics, five in philosophy, and
one each in geography, astronomy, history, and music reflect his wide range of interest in
the sciences and the arts.
Umar was from his boyhood a keen and commendable student. His memory was
unusually sharp. He could memorize any difficult lesson or book, and once he learnt
something he would never forget it. It is said that once, in Isfahan, he studied a large
arithmetical book seven times and when he returned to Nishapur he reproduced the whole
book from his memory without any mistake. He had unusual command of the languages
of Persian and Arabic. He was a good recite of the Qur’an and he could recite the Qur’an
in the seven approved recessions.
Contributions to Mathematics and Astronomy:
In the medieval period of Islam, from about 9th
to 14th
centuries, the Muslims led
the world in their pursuit of knowledge. The Islamic world at this time was the most
scientifically advanced region of the globe, while also making important contributions in
philosophy and literature. The Islamic influence on the development of modern science is
evident in the many Arabic-based words that remain in the English scientific vocabulary,
mostly due to the fact that being unfamiliar with the subject matter; Latin translators were
unable to change all words into Latin. Examples include algebra, algorithm, chemistry,
alchemy, zircon, atlas, almanac, earth, monsoon, alcohol, aorta, pancreas, colon,
cornea, and diaphragm.
Muslims also made significant advancements in mathematics. Umar Khayyam
was one such mathematician. After his studies were completed, he started teaching at the
Nishapur College and soon became as a mathematician and as an astronomer. His
classification of algebraic was fundamental to the advancement of algebra as a science
for example, just as his work on the theory of parallel lines was important in geometry.
In 1074, Khayyam was asked by Abu Ali Hassan ibn-i Ali (Nazam al-mulk), on
behalf of the Saljuq sultan Jalal al-Din Malikshah to revise the Iranian calendar which
had been in use since the time of the last Sassanian monarch, Yazdagird III. Heading a
committee of five, including Abu Hatim Muzaffar Isfazari, Abu Abbasi Lukari, Abu al-
Rahman Khazeni, and Marymun ibn-I Najib Busti, Khayyam completed the mission in
five years. The revised calendar, called the “Jalali calendar” went into operation in on
4. March 15, 1079. Specifically, he measured the length of the year as 365.24219858156
days. It shows that he recognized the importance of accuracy by giving his result to
eleven decimal places. As a comparison, the length of the year in our time is 365.242190
days. This number changes slightly in the sixth decimal place, e. g., in the nineteenth
century it was 365.242196 days. “
Umar’s revision of the Old Persian solar calendar was discontinued when
Islamic orthodoxy gained power, but in 1925 it was again introduced in Iran.
One of the accomplishments of the Persian mathematician Umar Khayyam was to give
geometrical constructions for the roots of a cubic as the intersections of two conics. Of
course, this approach had been used earlier by Menaechmus and others to solve certain
special cubic (notably in relation to the problem of “duplicating the cubic”), but
Khayyam generalized it to cover essentially all cubics (albeit with individual cases so as
to avoid negative numbers).
This is usually cited as evidence of how Khayyam contributed to reconciling the
two fields of geometry and algebra that had been so assiduously separated by the Greeks
and thereby casting Khayyam as a forerunner of Descartes. There is certainly truth in this
view, because Khayyam was definitely far more inclined than the Greeks to treat his
geometrical line segments as numerical quantities rather than strictly as spatial
magnitudes. In fact, he developed a numerical version of Euclid’s (Eudoxus) theory of
proportion that comes very close to Dedekind’s definition of irrational numbers. In
Commentaries on the difficult postulates of Euclid’s book Khayyam made a contribution
to non-Euclidean geometry, although this was not his intention. In trying to prove the
parallels postulate he accidentally proved properties of figures in non-Euclidean
geometries. Khayyam also gave important results on ratios in this book, extending
Euclid’s work to include the multiplication of ratios.
Khayyam’s Cubic Solution
Khayyam was then led to solve the following cubic, x+200x = 20x +2000
finding a positive root by considering the intersection of a rectangular hyperbola and a
circle.
5. (School of mathematics and Statistics University of St. Andrews, Scotland)
(http://www.montgomerycollege.edu/Departments/StudentJournal/volume1/Robert_Gree
n.pdf)
Given the cubic x + ax = b.
Draw the parabola x = ay
Draw circle diameter AC = b/a on x-axis
Let the circle and parabola meet at P
Draw line from P perpendicular to
The x-axis meeting it at Q.
Solution to the cubic is AQ
He has been considered to be the first to find the binomial theorem and determine
binomial coefficients.
Contributions to Literature
Known only for his mathematical calculations since the 16th
century, Khayyam
gained overnight fame and increasing appeal when, in 1859, Edward FitzGeral published
his translation of Quatrains. According to convention, in quatrains the first, second and
last lines are rhymed. While the third line rarely follows the rhyme of the other lines.
Thus a rubai (plural rubaiyat) has the form aaba. Each line expresses a complete thought.
6. Familiar with the personality of Khayyam and his masha’ philosophy, Fitzgerald
versified those of Khayyam’s quatrains that he felt his Western audiences would read and
appreciate. As a result, many generations, including Iranians, have read and enjoyed his
renditions of Khayyam’s Rubaiyyat into English verse. With his beautiful verses he
proved himself to be a poet of great excellence. The major themes of Khayyam’s
Ruba’iyyat are:
1. The secret of creation
2. The agony of existence
3. Predestination (life planned by the maker)
4. Time and tide (life created by Time)
5. Rotating particles (life consisting of particles)
6. Acquiescence to the fortuitous (life happening as an accident)
7. Seizing the moment
The subjects that Khayyam includes in his Ruba’iyyat are diverse and
intellectually provocative. In addition, Khayyam often combines philosophy with social,
ethical, and aesthetical concerns, providing his quatrains with depth as well as a spectrum
of areas of interest. In quatrain Khayyam examines the futility of existence, the tyranny
of time, the shortness of life, and the helplessness of man.
It is very difficult to determine the number of poems and verses that ‘Umar
Khayyam composed, but the number of Ruba’iyat that is, the quatrains, is more than
twelve hundred. However, there are many claimants to the composition of these, and
nobody is absolutely sure who actually composed them. But they were passed on as the
Ruba’iyat-I ‘Umar Khayyam.
Contribution to philosophy
As mentioned, Khayyam has five works on philosophy. In them, especially in
the 1047 “Risala fi Kulliyat al-wujud,” he follows the teaching of the masha’
philosophers, particularly his own “teacher” Ibn-i-Sina. In “Al-javab al-Salasa Masa’il
Zaruratu Tazad fi al-Alam Wa al-Jabr wa al-Baqa,” he becomes more original as he
explains cause and effect as aspects of determinism. Khayyam’s major contributions to
philosophy are the 1080 “Risalat al-Kawn wa al-Taklif,” which was written in response
to the questions of Abunasr Muhammad ibn-I Abdulrahim Nasavi, to Ibn-I Sina’s student,
and the 1097 “ Risala fi Kulliyat al-Wujud.”
Contribution to physics
7. Umar Khayyam also provided insight in other areas of science. He wrote two books in
Metaphysics, “Risala Dar Wujud” and “Nauruz Namah.”
Bibliography
Online Research
1. Umar Khayyam,
http://www.kirjasto.sci.fi/khayyam.htm
2. Central Asia and Iran
http://www.geocities.com/sitabhra/khayyam/bashiri.html
3. Umar Khayyam: much more then a poet,
http://www.montgomerycollege.edu/Departments/studentJou
rnal/volume1/Robert_Green.pdf
4. Rubaiyat of Umar Khayyam,
http://www.iranchamber.com/literature/khayyam/rubaiyat_khayya
m1.php
5. Biography of Umar Khayyam, http://www-gap.dcs.st-and.ac.uk/
%7 Ehistory/Mathematicians/Khayyam.htm
6. Umar Khayyam on cubic Equations,
http://mathpages.com/home/kmath448.htm
7. Umar Khayyam’s Mathematical insight,
http://mathpages.com/home/kmath448.htm
8. The Epicurian Humanism of Umar Khayyam,
http://humanists.net/pdhutcheon/humanist%20articles/omar
%20Khayyam.htm
9. The internet Classic Archive, The Rubaiyat of Umar Khayyam,
http://calssics .mit.edu/Khayyam/rubaiyat.html
10. Fitzgerald, Edward. “Umar Khayyam, the Astronomer poet of
Persia,” 1868 and 1872.
