around 1070–1079 CE
Exact solution procedure for cubic equations
Omar Khayyam's Maqalah fi al-jabr wa-al muqabalah (On the Proofs of the Problems of Algebra and Muqabala) was most likely written between the years 1070–1079 CE. It considers several types of algebraic problems, but is best known for geometric solutions to six classes of cubic equations. This treatment represents the first systematic study of—as well as the first exact solution procedure for—general classes of cubic equations.
While Khayyam is best known in the Western world as the author of the collection of poems known as the Rubáiyát, he was also a mathematician and worked as an astronomer for the court of Sultan Malik-Shah I (1055–1092). His work Al-jabr was composed in Samarkand under the patronage of Samarkand's governor, Abu Tahir Abd al-Rahman ibn 'Alaq.