Omar Khayyam is a strange figure - in our eyes - to enter the mathematical arena. But once there he strides across its stage with colour, romance and flamboyance.
He is probably best know for his great poetry the Rubaiyat which was translated into English by Edward Fitzgerald and is considered a classic; here are some lines:
With them the Seed of Wisdom did I sow, And with my own hand labour’d it to grow: And this was all the Harvest that I reap’d—- “I came like Water, and like Wind I go.”
Kahyyam was a man of many talents renowned for his astronomical and mathematical skills during his own time. Born in Iran, he spent most of his life in the great city of Isfahan where he helped to set up an observatory. He made a detailed and highly accurate measurement of a year and helped to devise a calendar which was used in Iran until 1925.
He is probably best known for his work on cubics - he gave the first complete treatment of cubic equations and a geometric solution of a cubic. This latter work preceded (by almost half a millenium) that of Descartes which established an inspiring and practical bridge between the long standing divide between geometry and algebra. A cubic equation is one in which the highest power is 3:
If the equation can be factorised, then it can be solved. Here are two examples giving very different (apparently) results:
x^3-1=0 can be factorised as (x-1)(x^2+x+1)=0
so that x takes the single value x-1
x^3-3x^2+2x=0 can be factorised as x(x-1)(x-2)=0
so x can take the values x=,0,1 or 2
He realised that a cubic equation could have more than 1 solution, but it was left to others to prove that it always has 3 - sometimes those solutions are not real numbers.
We must end on another verse of his poetry:
The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.