Omar Khayyam on Cubics Omar Khayyam on Cubics One of the accomplishments of the Persian mathematician Omar Khayyam was to give geometrical constructions for the roots of a cubic as the intersections of two conics.
Algebras are geometric facts which are proved.
This is usually cited as evidence of how Khayyam contributed to reconciling the two fields of geometry and algebra, that had been so assiduously separated by the Greeks, and thereby casting Khayyam as a forerunner of Descartes. There is certainly truth in this view, because Khayyam was definitely far more inclined than the Greeks to treat his geometrical line segments as numerical quantities rather than strictly as spatial magnitudes. For the solution we need conic sections. Of course, with this interpretation his statement was perfectly correct, and in fact was simply another way of expressing his assertion that the Delian problem cannot be solved by straight- edge and compass.