Algebra: Sets, Symbols, and the Language of Thought (The by John, Ph.D. Tabak

By John, Ph.D. Tabak

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Extra resources for Algebra: Sets, Symbols, and the Language of Thought (The History of Mathematics), Revised Edition

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It could be argued that Chinese and Mesopotamian mathematicians were not really interested in these applications, either—that they simply used practical problems to express their mathematical insights. Perhaps they simply preferred to express their mathematical ideas in practical terms. Perhaps, as it was for their Greek counterparts, it was the mathematics and not the applications that provided them with their motivation. There is, however, no doubt about how the Greeks felt about utilitarian mathematics.

Greek mathematicians soon moved away from Pythagorean concepts and toward a geometric view of mathematics and the world around them. How much of this was due to the discoveries of the Pythagoreans and how much was due to the success of later generations of geometers is not clear. In Greek Algebra 25 Suppose a/b = √2. Now solve for b to get a/√2 = b Finally, square both sides. a2/2 = b2 This completes the proof. Now we have to read off what the last equation tells us. First, a2 is evenly divisible by 2.

Mahavira exercises his algebraic insights on two other classes of problems. In one section of the book he studies combinatorics. Combinatorics, which generally requires a fairly extensive knowledge of algebra, deals with the way different combinations of objects can be chosen from a fixed set. It is the kind of knowledge that is now widely used in the study of probability.  .  . 2 · 1 where we have written his result in modern notation. This is an important formula that is widely used today. 42 ALGEBRA The second class of algebra problems is geometric in origin.

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