OMAR KHAYYAM
Renowned for his poetry as well as astronomy and mathematics, Omar Khayyam made outstanding contributions to the development of algebra.
Khayyam was born in AD 1048 in Nishapur, Persia, which is in modern-day Iran.
His talent in mathematics and astronomy quickly shone. Khayyam taught these subjects throughout his lifetime.
Khayyam wrote his first book on algebra at the age of twenty-two. He is best known in mathematics for his work on cubic equations.
Khayyam carried out much of the early work establishing the link between geometry and algebra.
He wrote commentaries on Euclid’s Elements, in particular attempting to prove the parallel axiom.
He died in Nishapur in 1131.
A MASTER OF ALGEBRA
Khayyam’s work was crucial to the development of algebra as a discipline in modern times.
In his Treatise on Demonstration of Problems of Algebra and Balancing, published c.1070, Khayyam gave extensive examples of how conic sections such as circles and hyperbolas can be used to provide the solutions to cubic equations.
These are equations involving a cubic (x3) term, of the form ax3 + bx2 + cx + d = 0. If b and c are both 0, then solving the equation amounts to taking a simple cube root. But, in general, the solution is much more complicated.
Khayyam’s insight was to break cubics down into problems that involved finding the intersection between two conic sections. Then by plotting the conic curves and finding their crossing points, he was able to solve the equation geometrically.
DID YOU KNOW?
The word “Khayyam” means tentmaker, which may have been his forefathers’ profession.