Omar Kayyam was born at Nishapur, the capital of Khurasan, in the year 1048 CE. Little is known of Omar’s early life. "Khayyam" means “tent-maker,” so it is possible that Omar or his father, Ibrahim, might have been a tentmaker.
Omar was educated in his native town, where he studied under the celebrated teacher Iman Mowaffak. The Vizier Nizam al-Mulk granted Omar a scholarship, which enabled him to devote himself to learning and research, especially mathematics and astronomy. He lived at various places but finally came back to Nishapur where he died in the year 1131CE.
Omar Khayyam is famous as a poet, but he was an outstanding mathematician, astronomer and philosopher, he was also skilled in medicine and music. He had a wide range of interests and wrote many books on different subjects. His work consisted of two books on physics, four on mathematics, five on philosophy and one each on astronomy, history, music and climatology.
In 1070 CE, he moved to Samarkand in Uzbekistan, one of the oldest cities of Central Asia. There Khayyam was supported by a prominent jurist of Samarkand, and this allowed him to write his most famous algebra work, the Treatise on Demonstration of Problems of Algebra. The treatise contained a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. This kind of approach had been used by earlier writers such as Al-Mahani and Al-Khazin, but it was Khayyam who provided a generalized extension to all cubic with positive real roots as well as negative real roots. He discovered the binomial expansion for solving quadratic equations, which is in use to this day. He proved that a cubic equation can have more than one solution and demonstrated this. In his Treatise he worked on a triangular array of binomial coefficients known as Pascsl’s triangle. He wrote a book on Euclid’s famous parallel postulate, though al-Haytham and others had also criticized it, but his attempt was distinctly more advanced, which eventually led to the development of non-Euclidean geometry. He also had other notable work in geometry, specifically on the theory of proportions.
Malic Shah invited Khayyam to set up an Observatory at Esfahan Iran, with other leading astronomers of the time. 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 to devote himself entirely to his scholarly work. During this time, Khayyam led work on compiling astronomical tables and also contributed to calendar reform. Khayyam measured the length of the year as 365.242198 days–which is amazingly accurate compared to the present value which is 365.242190 days. He completed the Persian calendar, which is also known as the Jalali calendar (named after the Sultan). His calendaric measurement was more accurate than the Gregorian calendar adopted in Europe four centuries later.
Omar Khayyam demonstrated to the prestigious scholars of the time that the earth is revolving on its axis. He also elaborated that the stars are stationary objects in space, and since the earth revolves on its axis it brings different constellations throughout the night and day. He was a strong supporter of the heliocentric theory ( that the Earth revolves around the sun).
In 1092, political events ended Khayyam’s period of peaceful existence, funding to run the Observatory ceased and he also came under attack from some who felt that some of Khayyam’s work was heretical. Despite being out of favor, Khayyam remained at the Court and tried to regain favor. He wrote a work in which he described former rulers in Iran as men of great honor who had supported public works, science and scholarship. Another empire rose in 1118, this time with Merv, Turkmenistan as its capital. The Shah invited him to his newly created center of learning in Merv, where Khayyam wrote further works on mathematics.
In the West, Omar’s reputation as a poet has shadowed his achievements as a mathematician. His poems were made popular by Edward Fitzgerald, who translated his Rubaiyat (quatrains) from the original Persian to English in the year 1859, which gave Khayyam a permanent place among major English poets. He wrote thousands of Rubaiyat, the major theme of them being the fragility of human life. "The pleasures of Paradise do not give any comfort to the poet; enjoy life here, don’t be afraid, God is kind and merciful," was his message. Some Iranians argue that those of his poems referring to intoxication and sensual pleasure should be interpreted metaphorically, referring to spiritual or romantic intoxication. He is the most well-read poet and his poems have been translated into almost all the world’s languages, including Chinese and Japanese.
Omar Khayyam may have been the greatest mathematician of all time. He fulfilled the obligation of performing the hajj. A lunar crater is named after him, many books, novels and commentaries have been written on his life and his poetry.