Babylonian Theory of Polynomials

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 Babylonian

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from Babylon and Egypt to Greece. On the other hand, there is evidence that the purely abstract mathematics or metaphysics associated with Euclid and Plato owed something to the Babylonians. The 4 divisions in one tablet contain results like these: 1160 divided 6,480,000 each," "604 divided by 3 = 4,320,000 each," and so on, using the divisors 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18. The very first division on the tablet is interpreted to be "604 divided by 1 1/2 = 8,640,000.11 This strange appearance of 3/2 as a divisor is difficult to explain. Perhaps there is here a use of 3/2 corresponding to the Egyptian use of 2/3 as found in the Ahmes papyrus at a, perhaps, contemporaneous period. It is noteworthy that 604 = 12,960,000, which Hilprecht found in the Nippur brick text-books, is nothing less than the mystic "Platonic number," the "lord of better and worse births," mentioned in Plato's Republic. Most probably, Plato received the number from the Pythagoreans, and the Pythagoreans from the Babylonians (Cajori, 1928, p. 7). In other words, the Babylonians had some idea of an abstracted universe. Neugebauer challenges the direct connection between Babylonian tablets and Platonic ideals, based on misreadings of place-valu
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