Omar Khayyam
Native spelling: غیاثالدین ابوالفتح عمر بن ابراهیم خیام نیشابوری
1048–1131, Nishapur, Persia, Nishapur, Persia
Persian mathematician, astronomer and poet who classified cubic equations and solved them geometrically as intersections of conic sections, critiqued Euclid's parallel postulate in a way that foreshadowed non-Euclidean geometry, and reformed the Persian calendar.
Ghiyath al-Din Abu'l-Fath Umar ibn Ibrahim al-Nisaburi al-Khayyami, known as Omar Khayyam, was born on 18 May 1048 in Nishapur, then a major city of Persia in the region of modern Iran, and died there on 4 December 1131. His epithet 'al-Khayyam', 'the tent-maker', may reflect his father's trade. He studied in Nishapur and Samarkand under the turbulent but intellectually rich conditions of the Seljuk Empire, and his reputation eventually won him the patronage of the Seljuk sultan Malik-Shah I and his vizier Nizam al-Mulk, who supported the observatory Khayyam directed in Isfahan.
Khayyam's central mathematical achievement was a systematic classification of cubic equations and a method for solving them geometrically, by finding the intersection points of conic sections such as a parabola and a circle. He did not obtain general algebraic (radical) formulas for the roots of cubics — those would only come from Italian algebraists more than four centuries later — but his classification and geometric constructions represent the most advanced treatment of cubic equations achieved before that point. He also worked with expansions of binomial coefficients for positive integer powers, a precursor of what later became known in Europe as Pascal's triangle, and he wrote a treatise on Euclid's parallel postulate, attempting to prove it from the other axioms and, in doing so, producing criticisms that anticipated the eventual discovery of non-Euclidean geometries.
In 1074 Malik-Shah commissioned Khayyam, together with a panel of astronomers, to reform the Persian calendar; the result was the Jalali calendar, a solar calendar accurate enough to accumulate only about one day of error over roughly five thousand years, more precise in practice than the Gregorian calendar that would later be adopted in the West. Khayyam also compiled astronomical tables (a Zij) and wrote philosophical works in the tradition of Avicenna. Although his scientific writing was largely forgotten outside specialist circles for centuries, he achieved enormous posthumous fame as a poet through Edward FitzGerald's 19th-century English translation of his quatrains, the Rubaiyat of Omar Khayyam.
Workplaces: Isfahan observatory, under Seljuk patronage, Nishapur and Samarkand
Iran