Mathematics in Ancient Times 
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Remember back just a few short years ago when you were learning your multiplication tables. I know, it's a painful memory, right? Some of us had trouble memorizing any of the tables and most of us had trouble remembering specific parts; for instance the times table for the number 9. Now I want you to imagine you lived in ancient Mesopotamia and had to memorize their multiplication tables. If you thought our base 10 number system was difficult, try to imagine, if you can, a multiplication table for a number system that was base 60! Very simply put, what this means is that the Babylonians' multiplication table did not stop at 9, rather at 59! When trying to imagine this, it is important to remember that the Babylonians did not use the numbers we have today, they had symbols. The subject that we call Babylonian Mathematics is actually what we know about the mathematics in Mesopotamia and is relatively new information. The sources of the mathematical information that have been discovered and translated are cuneiform tablets. Several hundred of these mathematical tablets have been recovered. Twothirds of the recovered tablets are considered "Old Babylonian" dating between 18001600 B.C.! Based on these and other discoveries it is said by most studying mathematics that the Babylonian's far outstripped the Egyptians in Mathematics. Numerous tables give the squares of numbers 1 to 50, and also the cubes, square roots, and cube roots of the numbers! Separate and distinguished from the table tablets are tablets that deal with algebraic and geometrical equations. These most often presented a sequence of related numerical problems together with the relevant calculations and the answers. This could be compared to text books of today with the many examples of algebraic and geometrical equations with complete instructions and answers given to show students how to work the problem. While none of these tablets gave what we would consider today as "general rules," the consistency with which the problems were treated suggests that the Babylonians, again unlike the Egyptians, had a theoretical approach to mathematics, and in many cases the problems seemed to be intellectual exercises. Sound familiar to anyone? Just as an example of the advanced number system that they developed, there are scores of clay tablets indicating that the Babylonians of 2000 B.C. were familiar with our formula for solving the quadratic equation! The Babylonians can claim priority in several discoveries, most notably the Pythagorean Theorem. Usually credit for this theorem is given to later mathematical schools. Their sexagesimal notation enabled them to calculate fractions as readily as with integers and led to extremely highly developed algebra. However, nowhere in their number system could they rationalize negative solutions to quadratics. Credit must be given where credit is due thought. The Babylonian number system was by far the most advanced and easily worked of its time. The Babylonians were empiricists and observers who worked with tables that presented the facts in an orderly fashion.

Contributed by S. Anderson 
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