Omar Khayyam

Lecture by Mirza I. Ashraf

Omar Khayyam
(A Muslim Mathematician, Astronomer, Philosopher, and Poet)

Of knowledge, naught remained I did not know,
Of secrets, scarcely any, high or low;
All day and night for three score and twelve years,
I pondered, just to learn that naught I know.

Omar Khayyam Nishapuri (1048-1131), was the most brilliant mathematician, astronomer, and author of important philosophical works of his time. He was a free thinker and a skeptic, but at the same time a poet of Sufi path to wisdom. His unique intellectual genius is the relationship of his poetry with his philosophy, and a relationship of his philosophy with mathematics and astronomy. Generally, his importance in Islamic intellectual tradition is due to his poetry of the Rubaiyyat (quatrains), in which he challenged religious doctrines, alluding to the hypocrisy of the clergies. Casting doubt on almost every aspect of religious belief, he appears to have professed a type of humanism. Because of his rational arguing the secret of creation and human fate, some thinkers in the West refer him as the “Eastern Voltaire.”
With Earth’s first clay They did the Last Man knead,
And there of the Last Harvest sow’d the Seed:
And the First Morning of Creation Wrote
What the last Dawn of Reckoning shall read.

Khayyam believed that man’s presence in this world, entry and exist is predetermined, a condition he bemoans throughout his poetry.
Born into a family of tent-makers in Nishapur, then a Seljuq capital in Khorasan, what is today’s Iran, Khayyam after studying Qur’an and Islamic jurisprudence, achieved proficiency in the sciences of algebra, geometry and astronomy. Throughout his life, he taught algebra and geometry during the day, and in the evening attended the court of the Seljuq Sultan Malik Shah as an adviser. He intelligently makes a whimsical reference to his knowledge of science and his family profession of a tent maker in his quatrain.
Khayyam, who stitched the tents of science,
Has fallen in grief’s furnace and been suddenly burned,
The shears of Fate have cut the tent ropes of his life,
And the broker of Hope has sold him for nothing!
After the death of the Sultan, having lost the favor of an adviser, he set out on Hajj pilgrimage to Mecca and Medina. When he returned to Nishapur, he was appointed as a court astrologer, a rank much lower to his level of knowledge. He was a quiet, humble, reserved person who wished to remain intellectually inconspicuous, as is evident from one of his quatrain:
The secrets which my book of love has bred,
Cannot be told for fear of loss of head;
Since none is fit to learn, or cares to know,
‘Tis better all my thoughts remain unsaid.
He wrote remarkable fourteen treatises identified to date, on the subjects of poetry, philosophy, and mathematics. Since his poetry presents philosophical wisdom, he being initially a man of science and general philosophy has not received the attention he deserved in the scientific field. However, recently his seven-philosophical works have been published.
Omar Khayyam was an important member of the panel that reformed the Persian Jalali calendar which remained in use in Iran and Afghanistan from 11th to 20th centuries. The Jalali calendar, similar to Hindu calendar is based on actual solar transit and is considered more accurate than the Gregorian calendar. Khayyam by adding one day after every four years in the month of February, as a leap year, fixed the Gregorian calendar as we have today.

Omar Khayyam, in his life was very famous as a great mathematician and astronomer. Before Khayyam, Muhammad al-Khwarizmi (780-850) had invented Algebra and most importantly a set of numerical calculations and instructions known by his own name as Alkhwarizm—Latinized Algorithm—which if carried out systematically produces a desired result. Algorithms are critical to software design, modern science, and engineering, enabling computers and smart electronics to sort through masses of digital data and text. Khayyam was familiar with al-Khwarizmi’s great achievement, and in the year 1070 he wrote, Treatise on Demonstration of Problems of Algebra, which was later adopted in Europe. In particular, he derived general methods for solving cubic equations of higher order.

(a) Theory of Parallels: Khayyam wrote Explanations of the Difficulties in the Postulates in Euclid’s Elements, which contains several sections on the parallel postulate on Euclidean definition of ratios, Anthyphairetic ratio (modern continued fraction) and on the multiplication ratios. He made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate.
(b) Geometric Algebra: In solving cubic equation, Khayyam’s celebrated approach and method in geometric-algebra presents the philosophical view of mathematics. His approach can be considered the first systematic study and the first exact method of solving cubic equation.
(c) Binomial Theorem and Extraction of Roots: This particular remark of Khayyam and certain proposition found in his Algebra book have made some historians of mathematics believe that Khayyam had indeed a binomial theorem up to any power, which is based on his ability to extract roots.
(d) Khayyam-Saccheri Quadrilateral: Khayyam, considering the three cases—right, obtuse and acute—that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems about them, he correctly refuted the obtuse and acute cases based on his postulate and hence derived the classic postulate of Euclid.

The statue of Khayyam in Persian Scholars Pavilion,
United Nations Office in Vienna, Austria

4. ASTRONOMER: Like most of Muslim mathematicians of the medieval Islamic period, Khayyam was also an astronomer. Invited by sultan Malik Shah he helped build an Observatory. Before Khayyam, ibn al-Haytham (900-1040), author of the Book of Optics, wrote about empirical science, optics, light, and the skies to create perhaps the most scientific and accurate view of the physical universe until Copernicus and Galileo. But it was Al-Biruni (973-1048) who had proved four centuries before Galileo that the earth is round, rotates on its axis and moves around the sun. Al-Biruni showed through a diagram how lunar eclipses occur.

5. HELIOCENTRIC THEORY: Khayyam demonstrated that the earth rotates on its axis by presenting to his contemporaries a model of the stars in his planetarium. Edward Fitzgerald’s anachronistic rendering of Khayyam’s poetry, in which the first lines are mistranslated with a heliocentric image of the Sun fling “the Stone that puts the Stars to Flight,” depicts that Khayyam believed in heliocentrism.
Awake! for Morning in the Bowl of Night
Has flung the Stone that puts the Stars to Flight:
And Lo! The Hunter of the East has caught
The Sultan’s Turret in a Noose of Light.

Statue of Omar Khayyam at his home town Nishapur

Khayyam’s philosophical treatises were written in the Peripatetic tradition when philosophy in general and rationalism in particular was under attack in twelfth century in the world of Islam. He, therefore, had to defend himself against the charge of being a philosopher.
“A philosopher I am,” my enemies falsely say,
But God knows I am not what they say;
While in this sorrow-laden nook, I reside
Need to know who I am, and why Here stay.
In his work On Being and Necessity, Khayyam defining philosophy along the Peripatetic line argues that there are three real issues to be discussed in philosophy—which are standard Aristotelian questions— ‘is it?’ ‘what is it?’ and ‘why is it?’
For “Is” and “Is-not” though with Rule and Line
And “Up-and-down” by Logic I define,
Of all that one should care to fathom, I
Was never deep in anything but—Wine.
For Khayyam, these questions have a wider range of philosophical implication as the subject of philosophy is essentially the response to three questions: “whether something is,” “what it is,” and “why it is what it is.”
Omar Khayyam frequently mentions Avicenna as his master. He taught for decades the philosophy of Avicenna, especially The Book of Healing, in his hometown of Nishapur, till his death. He is the most important thinker to have continued Avicennian philosophy, and at the same time the last solitary philosopher to have raised his voice during the period of philosophical suppression in the Islamic world. When one examines all of Khayyam’s philosophical treatises together, one finds him as essentially Avicennian or Aristotelian philosopher with particular acumen in the mathematical and natural order, on the one hand, and mysticism, on the other. His whole work is based on the Necessary Being, the One, who is Reality who in religious language is called “God.” He believed that all that exists, exists by virtue of the One Necessary Being.
Khayyam’s philosophy of mathematics draws attention to three basic mathematical ideas. The first is “mathematical order,” that the Divine origin of all existence not only emanates the being, by virtue of which all things gain reality, but it is also the source of order that is inseparable from the very act of existence. To speak of a being is also to speak of order, which the science of mathematics studies in turn as do certain other disciplines. The second is a “mathematic-philosophical” question with which Khayyam was concerned is the significance of postulates in geometry and the necessity for the mathematician to rely upon philosophy in order to prove the postulates and principles of his own science. He associated motion with the world of matter and wanted to keep it away from the purely intelligible and immaterial world of geometry. Third important issue for Khayyam is the “difference between natural body and mathematical body.” The natural body is in the category of substance with which the natural science deals and it stands for itself, while the mathematical body is of the category of accident which is the concern of mathematics that does not subsist by itself in the external world.
Though Khayyam, the philosopher could also be understood through his Rubaiyyat, but in Fitzgerald’s translation the quatrains convey, at least superficially, hedonistic, fatalistic, and this worldly philosophy combined with much skepticism about religious teaching. He is to be best understood through his philosophical works in the light of intellectual and social conditions of his time. The philosopher-scientist Khayyam was not the same Khayyam who is the author of the quatrains. Khayyam in his time as well as today, is famously known as Hakim meaning a philosopher-sage, and a spiritual-pragmatist. In fact, his Rubaiyyat are to be viewed as a philosophical commentary on the human condition.
For Khayyam, there are two discourses, each of which pertains to one dimension of human existence: philosophical and poetic. Philosophically, Khayyam was the last Aristotelian in the world of Muslim thinkers. He defended rationalism against the rise of orthodoxy and made an attempt to revive the spirit of rationalism which had remained prevalent in the first four centuries in the Islamic world. Poetically, he represents a voice of protest against what he regards to be fundamentally unjust world. People, even today, find in him a voice they love to hear, and many centuries after he had died his Rubaiyyat in original Persian language and translations in many other languages, are being seen a venue for those who are experiencing the same trials and tribulations as Omar Khayyam had.

Preference for sensual pleasures and glorification of love
Omar Khayyam’s one thousand Rubaiyyat, which are based on a poetry of a series of quatrains, sparkling with witty epigrammatic observances of life, is filled with exquisite oriental imagery. Although scores of other European scholars had prepared their version of Khayyam’s quatrains, it was Edward Fitzgerald (1809-1883), an Irish poet, who adapted and lovingly translated in 1895 the best of his Rubaiyyat weaving them in a single, magical poem. His quatrains became so popular that from 1895 to 1900 were published 25 times. Khayyam, who was basically a man of science, rebelled against the bigotry and fanaticism around him and sought escape in the pleasures of poetry and philosophy. His Epicurean audacity of thought and speech caused him to be regarded askance in his own time and country.

Then to the Lip of this poor earthen Urn
I lean’d, the Secret of my Life to learn:
And Lip to Lip it murm’d – “While you live,
Drink! – for, once dead, you never shall return.”

Ah, fill the Cup:- what boots it to repeat
How Time is slipping underneath our Feet:
Unborn Tomorrow, and dead Yesterday,
Why fret about them it today be sweet!

How long, how long, in infinite Pursuit
Of This and That endeavor and dispute?
Better be merry with the fruitful Grape
Than sadden after none, or bitter Fruit.

But Khayyam was too honest of heart as well as of mind. Having failed (however mistakenly) of finding any Providence but Destiny, and world but this, he set about making the most of it; preferring rather to soothe the soul through the senses into acquiescence with things as he saw them, than to perplex it with vain disquietude after what they might be. It has been seen, however, that his worldly ambition was exorbitant; and he very likely takes a humorous or perverse pleasure in exalting the gratification of sense above that of the intellect, in which he must have taken great delight, although it failed to answer the Questions in which he, in common with all men, was most vitally interested. His quatrains are full of witty thoughts with dual meanings.

And, as the Cock crew, those who stood before
The Tavern shouted—Open then the door!
You know how little while we have to stay,
“And once departed, may return no more.”

Khayyam’s poetry is filled with a live-for-today philosophy, a preference for sensual pleasures and glorification of love that have made his Rubaiyyat delightful reading for many generations of admirers. He uses the concept of “wine and intoxication” throughout his poetry in three distinct ways: the intoxicant wine, the mystical wine, and the wine of love. The esoteric use of wine and drinking in Persian Sufi literature, refers to the state of ecstasy in which one is intoxicated with Divine love. But Khayyam was not a mystic in traditional sense. He uses wine in the profound sense of Sophia or wisdom that provides a sage with philosophical wisdom, allowing one to come to terms with temporality of life and to live in the here and now.

Those imprisoned by the intellect’s need to decipher
Humbled; knowing being from non-being, they proffer
Seek ignorance and drink the juice of the grape
Those fools acting as wise, scoffer.

Khayyam, the mathematician-astronomer, fails to find any purpose for human existence within an orderly and complex universe.

Yesterday this day’s madness did prepare;
Tomorrow’s silence, triumph, or despair:
Drink! For you know not whence you came, nor why:
Drink! For you know not why you go, nor where

Here with a Loaf of Bread beneath the Bough,
A Flask of wine, a Book of Verse—and You
Beside me singing in the Wilderness—
And Wilderness is Paradise anew.

Many readers of Khayyam consider that Khayyam is the timeless Sufi voice. Sufis believe that within mankind there is an element, activated by love, which provides the means of attaining to true reality, called mystical meaning. Khayyam relates this concept beautifully:

When the Original Cause determined my being
I was given the first lesson of love.
It was then that the fragment of my heart was made
The Key to the Treasury of Pearls of mystical meaning.

In his poetry, Khayyam uses the imagery of bowl (kuza) and clay for man. He believed that man is made from the “dust and to dust he shall return.”
For in the Market-place, one Dusk Day,
I watch’d the potter thumping his wet Clay:
And with its all obliterated Tongue
It murmur’d — “Gently, Brother, gently, I pray.”

With them the seed of Wisdom did I sow,
And with my own hand wrought to make it grow;
And this was all the Harvest that I reap’d—
“I came like Water, and like Wind I go.”