Omar Khayyam, René Descartes and Solutions to Algebraic Equations

Abstract

Omar Khayyam is the only person who is remembered equally as a great poet and a great mathematician. We describe here the work of Omar Khayyam in the 12th century in solving algebraic equations and describe how his work may have influenced René Descartes in the 17th century. In particular, we discuss his solutions of cubic equations; these equations absorbed mathematicians from 9th to 16th century. Omar made a significant controbution to the finding of positive root through geometrical argument and thus foreshadowed the analytical geometry of Descartes. We give a preliminary background of the equations for non-mathematicians and describe Omar’s classification of cubic equations. His method of solving cubic equations is then described. We also highlight continuing interest in his work, especially by the Omar Khayyam Club in London.^1,2