Omar Khayyam

Omar Khayyam

The Persian astronomer, mathematician, and poet Omar Khayyam (1048-ca. 1132) made important contributions to mathematics, but his chief claim to fame, at least in the last 100 years, has been as the author of a collection of quatrains, the “Rubaiyat.” 

His treatise on algebra (On Proofs for Problems Concerning Algebra) includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. As a scholar, he is most notable for his work on cubic equations and his calendar reform.


Early Life

Omar Khayyam was a Persian mathematician, philosopher, poet and astronomer born in 1048 in Nishapur (modern day Iran). He obtained his early education from a scholar named Sheikh Mohammad Mansuri and later from one of the most renowned scholars of khorasan province. He started his career with teaching algebra and geometry. In his spare evening time, Khayyam also fulfilled his duties as advisor to Malik Shah I and the nights were dedicated to astronomical studies and the Jalali calendar.

After the murder of Malik Shah, he was no longer required as advisor so he decided to fulfill his religious duties and thus went for performing his Hajj pilgrimage. After his return he got the job of the court astrologer and he was granted permission to return to Nishapur where he taught medicine, astronomy and his passion which was mathematics.


Astronomical and Mathematical Works

Khayyam’s most famous works include his highly influential mathematical treatise called ‘Treatise on Demonstration of Problems of Algebra’ which he completed in 1070. This treatise highlighted the basic algebraic principles that were ultimately shifted to Europe. He laid the foundation of the Pascal’s triangle with his work on triangular array of binomial coefficients. In 1077 another major work was written by Khayyam namely ‘Sharh ma ashkala min musadarat kitab Uqlidis’ meaning ‘Explanations of the Difficulties in the Postulates of Euclid’. It was published in English as “On the Difficulties of Euclid’s Definitions. In this book he contributed to non-euclidean geometry even though this was not his original plan. It is said that Omar Khayyam was originally trying to prove the parallels postulate when he proven the properties of figures in the non-euclidean geometry.

His geometrical work consisted of his efforts on the theory of proportion and geometrical algebra topics such as cubic equations. Khayyam was the first mathematician to consider the ‘Saccheri quadrilateral’ in the 11th century. It was mentioned in his book the ‘Explanations of the difficulties in the postulates of Euclid’. It wasn’t until 6 centuries later when another mathematician, Giordano Vitale made further advances on Khayyam’s theory. Other books by Khayyam include his book named ‘Problems of Arithmetic’, a book on music and algebra.

Khayyam, like the other Persian mathematicians of the time was also an astronomer. The Sultan Jalal ud Din Malik Shah Saljuqi requested him to build an observatory with a team of scientists. He was part of the team that made several reforms to the Iranian calendar which was made the official Persian calendar to be followed by the Sultan on March 15th 1079. The Jalali Calendar became the base for other calendars and is also known to be more accurate than the Gregorian calendar.


Omar Khayyam as a Poet

Omer Khayyam is the writer of more than a thousand ‘Rubaiyat’ or verses. He rose to fame as a poet through the translations of Edward Fitzgerald in 1859 known as ‘Rubáiyát of Omar Khayyám’. His poetry is also translated to other languages other than English.

There is a manuscript tradition attributing poetry, mostly in the form of quatrains (rubaiyat) to Omar Khayyam. There are more than 100 manuscripts containing such poetry, but all of them are comparatively late, the earliest such source that can be dated with confidence was written in 1460, and the bulk dates to the 17th to 19th centuries. Bodleian MS. Ouseley 140, a manuscript written in Shiraz in 1460, contains 158 quatrains on 47 folia. The manuscript belonged to William Ouseley (1767-1842) and was purchased by the Bodleian Library in 1844.


One of his most liked verses are the following:

The Moving Finger writes, and, having writ,

Moves on: nor all thy Piety nor Wit

Shall lure it back to cancel half a Line,

Nor all thy Tears wash out a Word of it.