Lived from 1048 to circa 1122. His full name was Ghiyath al-Din Abu’l-Fath Umar ibn Ibrahim Al-Nisaburi al-Khayyami. A literal translation of his name “al Khayyami” means ‘the tentmaker’ - in reference possibly to the trade of his father.
Khayyam studied philosophy at Naishapur, as well as mathematics and astronomy. In 1070 he moved to Samarkand in Uzbekistan where he wrote his most famous algebra work, Treatise on Demonstration of Problems of Algebra. Malik Shah, the grandson of the founder of the Seljuq Dynasty, sent an invitation to Khayyam to set up an Observatory at Esfahan, the capital. One of Khayyam’s tasks was to compute the length of one year which he came up as 365.24219858156 days. He was not accurate, but he wasn’t far off. About eight hundred years later, the most accurate computation given was 365.242196 days; today we know it is 365.242190 days.
Shortly after Malik Shah’s third son, Sanjar, had become the ruler of the Seljuq empire, Khayyam left Esfahan and travelled to Merv (now known as Mary in Turkmenistan), which had been declared the new capital of the Seljuq empire. In one of his algebra journals, he described some of the mathematical work he was mulling over:
The Indians possess methods for finding the sides of squares and cubes based on such knowledge of the squares of nine figures, that is the square of 1, 2, 3, etc. and also the products formed by multiplying them by each other, i.e. the products of 2, 3 etc. I have composed a work to demonstrate the accuracy of these methods, and have proved that they do lead to the sought aim. I have moreover increased the species, that is I have shown how to find the sides of the square-square, quatro-cube, cubo-cube, etc. to any length, which has not been made before now. the proofs I gave on this occasion are only arithmetic proofs based on the arithmetical parts of Euclid’s “Elements”.
Among other things, Khayyam is well known for solving a complex cubic equation; when he had found the solution, he stated that it required the use of conic sections and that it could not be solved by ruler and compass methods - something that would not be proved for another 750 years.
In his Commentaries on the difficult postulates of Euclid’s book, Khayyam also made contributions to non-euclidean geometry though accidentally.
Perhaps among all things, however, Khayyam is today best known for his poetry - made more famous when, in 1859, Edward Fitzgerald translated it from Farsi into English; it was so popular that it went through five editions. It was a collection of short, four-line poems all known as the Rubaiyat. It has been translated into English, French, German, Italian, Russian, Chinese, Hindi, Arabic, and Urdu.
Some good links for further info on Omar Khayyam:
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Khayyam.html
http://www.blissbat.net/rambles/rubaiyat_fitz_fifth.html