The purpose of this research is to examine the Babylonian theory of polynomials. The plan of the research will be to set forth the historical and cultural context in which the Babylonian approach to developing equation theory emerged, and then to discuss the ways in which the theory could have evolved across ancient cultures toward modern interpretations of the authentic character and importance of equations. As appropriate, reference will be made to the assessments of the Babylonian contribution to the body of mathematical thought as it may have impacted upon subsequent mathematical theory.
One may begin a discussion of the authentic nature of Babylonian theory of polynomials--not by saying what it is but by suggesting what it is not, which is an equivalent of purely theoretical explorations of the mathematical universe that were typical of ancient Greece. That is, the Babylonians were far less purely theoretical than practical in the uses to which they put arithmetic. Anellis (1989) cites the impulse of both Babylonians and Egyptians toward reducing mathematics to utilitarian uses, toward developing concrete representations or projections of mathematical theory in the realm of vulgar reality. In contrast with the emphasis on solving real problems by means of real, irreducible computations, there is the example of the Euclidian universe of pure abstraction on one hand, and the Platonic universe of ideal forms on the other.
This is not to suggest that the Babylonians lacked the ability to abstract and theorize altogether. The cuneiform method of alphabetization, for example, represents an improvement on and generalized cultural evolution of human abstraction capabilities that is at once more flexible and more sophisticated than the highly representational Egyptian method of hieroglyphics. However, according to Wilder (1968), the Egyptians developed a more sophisticated, less cumbersome system than the Babylonians for nu...