Research Paper

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Even such patronage would not provide too much stability since local politics and the fortunes of the local military regime decided who at any one time held power. Khayyam himself described the difficulties for men of learning during this period in the introduction to his Treatise on Demonstration of Problems of Algebra (see for example [1]):-
I was unable to devote myself to the learning of this algebra and the continued concentration upon it, because of obstacles in the vagaries of time which hindered me; for we have been deprived of all the people of knowledge save for a group, small in number, with many troubles, whose concern in life is to snatch the opportunity, when time is asleep, to devote themselves meanwhile to the investigation and perfection of a science; for the majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes; and if they see a certain person seeking for the right and preferring the truth, doing his best to refute the false and untrue and leaving aside hypocrisy and deceit, they make a fool of him and mock him.
However Khayyam was an outstanding mathematician and astronomer and, despite the difficulties which he described in this quote, he did write several works including Problems of Arithmetic, a book on music and one on algebra before he was 25 years old. In 1070 he moved to Samarkand in Uzbekistan which is one of the oldest cities of Central Asia. There Khayyam was supported by Abu Tahir, a prominent jurist of Samarkand, and this allowed him to write his most famous algebra work, Treatise on Demonstration of Problems of Algebra from which we gave the quote above. We shall describe the mathematical contents of this work later in this biography.
Toghril Beg, the founder of the Seljuq dynasty, had made Esfahan the capital of his domains and his g...