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Omar Khayyam

Omar Khayyam Photo

The famous Persian philosopher, astronomer, poet and most importantly, mathematician, Omar Khayyam was born on 18th May 1048, in Nishapur, Persia. At birth, he was named Ghiyath ad-Din Abu l-Fath Umar ibn Ibrahim al-Khayyam Nishapuri. It is believed that his father was a tent maker since the name al-Khayyam translated in Persian means “tent maker”.  His early schooling was conducted under Imam Mowaffaq Nishapuri, a highly respected teacher from the province of Khorasan.  Under Nishapuri’s tutelage, Khayyam studied philosophy and sciences.

In his early 20’s, Khayyam wrote a book on algebra and after moving to Samarkand in 1070, he published his most acknowledged work, the “Algebra Treatise” which was greatly respected by the English mathematician John Wallis. Khayyam was an extremely hard working polymath and in order to make ends meet, taught philosophy and algebra during the day, served as an advisor to the Seljuq sultan, Malik Shah I, in the evening and pursued astronomy by night at the Esfahan Observatory.

During this time, he created various astronomical tables along with the famous Jalali calendar which in 1075 was established as the official Persian calendar by Malik Shah I. After the sultan was assassinated in 1092, Khayyam took refuge in Medina and Mecca under the guise of pilgrimage. It was quite sometime later that he was allowed to return to Nishapur by Malik Shah’s third son, who by then had become ruler of the Seljuq dynasty. After his return, Khayyam continued teaching astronomy, mathematics, and philosophy.

Greatest Contributions

One of the most respected and iconic achievement of Omar Khayyam even to this day is his – “Treatise on Demonstration of Problems of Algebra.” He wrote this when he was just 22 and it is a compilation of principles of algebra. These principles were readily taken up and practiced by almost all noted mathematicians of the west. But what really created a stir were his systematic methods of solving cubic equations.

In Treatise on Demonstration of Problems of Algebra, Khayyam focused specifically on what is now known as Pascal’s triangle, a triangular array of the binomial coefficients. In algebra, he proved the existence of two solutions for every equation and in geometry, his contribution was the theory of proportions. Omar Khayyam played a major role in developing the non-Euclidean side of geometry, especially the parallel postulate.

Another one of his masterpieces, “Explanations of the Difficulties in the Postulates in Euclid’s Elements” was published in 1077, where he proved properties of figures in non-Euclidean geometry and included the multiplication ratios.

Khayyam was the first mathematician to research in detail the Khayyam-Saccheri quadrilateral; it is a quadrilateral with two equal sides, perpendicular to the base. The famous Al-Zamakhshari called Khayyam “the philosopher of the world”, since apart from general philosophy; Khayyam also made his mark in the philosophy of mathematics. He demonstrated great insight into the subject by arguing on the ideas of the distinction between natural and mathematical bodies and the importance of axioms in geometry and mathematical order.

Apart from making significant contributions to the Islamic calendar reform, heliocentric theory and improving upon the geometrical method of solving cubic equations, Khayyam achieved greatness throughout the world for other reasons as well. Not only was he a brilliant astronomer, but in the West, he is highly revered for his poetic writings as well. The great English poet Edwards FitzGerald translated and adapted Khayyam’s quatrains into The Rubaiyat of Omar Khayyam, published in a late 19th century and are still going strong.

Death and Legacy

Omar Khayyam died on 4th December 1131 at the ripe old age of 83 in Nishapur, Khorasan. He is buried in the famous Khayyam Garden at the mausoleum of Imamzadeh Mahruq. Omar Khayyam’s own mausoleum, a masterpiece of Persian architecture, was completed in 1963 by Hooshang Seyhoun.

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