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A detailed comparison of a large number of known Egyptian and Mesopotamian mathematical texts from all periods leads to the conclusion that the level and extent of mathematical knowledge must have been comparable in Egypt and in Mesopotamia in the earlier part of the second millennium BCE, and that there are also unexpectedly close connections between demotic and “non-Euclidean” Graeco-Egyptian mathematical texts from the Ptolemaic and Roman periods on the one hand and Old or Late Babylonian mathematical texts on the other.
When mathematics flourished again in Mesopotamia in the Late Babylonian and Seleucid periods in the second half of the first millennium BCE, possibly in connection with the rise of mathematical astronomy, a great part of the Old Babylonian corpus of mathematical knowledge had been taken over relatively intact. However, for some reason, the transmission of knowledge cannot have been direct, which is shown by an almost complete transformation of the mathematical vocabulary. Similarly in Egypt, after a comparable gap in the documentation, there was a new flourishing of mathematics, documented by demotic and Greek mathematical papyri and ostraca from the Ptolemaic and Roman periods.
Some of the Greek mathematical texts are associated with the Euclidean type of high-level mathematics. Except for those, the remainder of the demotic and Greek mathematical texts show clear signs of having been influenced both by Egyptian traditions, principally the counting with sums of parts, and by Babylonian traditions. An interesting new development was the experimentation with new kinds of representations of fractions, first sexagesimally adapted sums of parts, soon to be abandoned in favor of binomial fractions, the predecessors of our common fractions. The observation that Greek ostraca and papyri with Euclidean style mathematics existed side by side with demotic and Greek papyri with Babylonian style mathematics is important for the reason that this surprising circumstance is an indication that when the Greeks themselves claimed that they got their mathematics from Egypt, they can really have meant that they got their mathematical inspiration from Egyptian texts with mathematics of the Babylonian type. To make this thought much more explicit would be a natural continuation of the present investigation.
Bibliography
| Friberg 2005, vii-viii, 270 | Friberg, Jöran. Unexpected links between Egyptian and Babylonian mathematics. Signapore: World Scientific 2005. |
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For Greece, see Babylonian influences in some of the best known works of Greek mathematicians (1)
Jöran Friberg
URL for this entry: http://www.aakkl.helsinki.fi/melammu/database/gen_html/a0001524.php
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