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This gave rise to what is now called Fermat’s last theorem, one of the most famous of all mathematical problems and one that was not solved until late in the 20th century. Greek algebra—whether it is like that found in Elements or in Arithmetica—is characterized by a higher level of abstraction than that found in other ancient mathematically sophisticated cultures. Both the choice of problems and method of presentation were unique among the cultures of antiquity, and the Greek influence on future generations of Arab and European mathematicians was profound.

It is essentially a long list of problems. The exception occurs at the beginning of the first volume, in which he attempts to give an account of the foundations of algebra. This is historic because it is the first time that anyone tried to do this. With respect to the number system that he uses, he describes rational numbers—numbers that can be represented as fractions with whole numbers in the numerator and the denominator—and negative numbers. He gives rules for working with negative numbers, and he seems comfortable enough with this system.

The mathematical tradition that developed on the Indian subcontinent during this time is sometimes called Indian mathematics. It was not created entirely in what is now India. Some of it arose in what is now Pakistan, and, in any case, India was not united under a central government during the period of interest to us. There was no India in the modern sense. There are some histories of “Indian” mathematics that use the term Hindu 34 Algebra from India to Northern Africa 35 mathematics, but not all of the mathematicians who contributed to the development of this mathematical tradition were themselves Hindu.

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D-1 152mm Howitzer


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