More detail regarding these papyri will be found following the bibliographical notes.Īddition. About a dozen of these, often referred to in a study of the history of mathematics, are briefly listed below, not in order of their importance but alphabetically, with their abbreviations that will be used throughout the essay.
Of all the ancient papyri and ostraca that have been recovered from ancient Egypt and are preserved in universities, museums, and other institutions, relatively few are of a mathematical nature. It is a matter of semantics and to help resolve it, one should note what Ernst Mach wrote in 1898: “There is no problem in all mathematics that cannot be solved by direct counting, but with present implements, many operations can be performed in a few minutes, which without mathematical methods, would take a lifetime.” And Comte wrote: “There is no inquiry which is not finally reducible to a question of numbers.” Acceptance of these statements would perhaps justify saying that Egyptians at the time of the pharaohs did have mathematics, in their own particular way. When it appeared that Egyptian arithmetic was based solely upon a complete knowledge of the “two-times” table and an ability to find two-thirds of any number, integral or fractional that their geometry dealt almost wholly with areas and volumes and that problems were solved by a kind of literal algebraic reasoning, the question arose whether this can be called mathematics. One had to wait for a Champollion and a Rosetta Stone before interpretation of hieroglyphs, and the cursive hieratic writing and numbers, became possible. Pharaonic mathematics has been available to the student and the historian for barely a century, although it originated nearly four thousand years ago.
The historian would be wise not to judge too hastily the very few genuinely mathematical papyri and ostraca that have come down to us, by making critical comparisons with the more numerous and detailed works of the Greeks, which have been known and studied for over two thousand years. In the long period of ancient Egypt, some three millennia, mathematics meant first arithmetic, then some elementary geometry, then varied problems that by modern standards had an algebraic flavor. When one refers to mathematics in the time of the pharaohs, the significance of the word “mathematics” inevitably comes into consideration. TABLES FOR THE ADDITION OF UNIT FRACTIONS, AND THE G RULE
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