- MESOPOTAMIA 35
(Apepi I). From this information Egyptologists arrived at a date of around 1650
BCE for this papyrus. Ahmose tells us, however, that he is merely copying work
written down in the reign of Pharaoh Ny-maat-re, also known as Amenemhet III
(1842-1797 BCE), the sixth pharaoh of the Twelfth Dynasty. From that informa-
tion it follows that the mathematical knowledge contained in the papyrus is nearly
4000 years old.
What do these documents tell us about the practice of mathematics in an-
cient Egypt? Ahmose begins his work by describing it as a "correct method of
reckoning, for grasping the meaning of things, and knowing everything that is, ob-
scurities. .. and all secrets."^10 The author seems to value mathematics because of
its explanatory power, but that explanatory power was essentially practical. The
problems that are solved bear a very strong resemblance to those in other treatises
such as the Jiu Zhang Suanshu.
The Akhmim Wooden Tablet contains several ways of expressing reciprocals
of integers based on dividing unity (64/64) by these integers. According to Milo
Gardner,^11 the significance of the number 64 is that it is the number of ro in a
hekat of grain. This origin for the numbers makes sense and gives a solid practical
origin for Egyptian arithmetic.5. Mesopotamia
Some quite sophisticated mathematics was developed four millennia ago in the
portion of the Middle East now known as Iraq and Turkey. Unfortunately, this
knowledge was preserved on small clay tablets, and nothing like a systematic trea-
tise contemporary with this early mathematics exists. Scholars have had to piece
together a mosaic picture of this mathematics from a few hundred clay tablets that
show how to solve particular problems. In contrast to Egypt, which had a fairly sta-
ble culture throughout many millennia, the region known as Mesopotamia (Greek
for "between the rivers") was the home of many civilizations. The name of the
region derives from the two rivers, the Euphrates and the Tigris, that flow from the
mountainous regions around the Mediterranean, Black, and Caspian seas into the
Persian Gulf. In ancient times this region was a very fertile floodplain, although
it suffered from an unpredictable climate. It was invaded and conquered many
times, and the successive dynasties spoke and wrote in many different languages.
The convention of referring to all the mathematical texts that come from this area
between 2500 and 300 BCE as "Babylonian" gives undue credit to a single one of
the many dynasties that ruled over this region. The cuneiform script is used for
writing several different languages. The tablets themselves date to the period from
2000 to about 300 BCE.
Of the many thousands of cuneiform texts scattered through museums around
the world, a few hundred have been found to be mathematical in content. Deci-
phering them has not been an easy task, although the work was made simpler by
mutilingual tablets that were created because the cuneiform writers themselves had
need to know what had been written in earlier languages. It was not until 1854
that enough tablets had been deciphered to reveal the system of computation used,
and not until the early twentieth century were significant numbers of mathematical
(^10) This is the translation given by Robins and Shute (1987, p. 11). Chace (1927, p. 49) gives the
translation as "the entrance into the knowledge of all existing things and all secrets."
(^11) See http: //mathworld. wolfram. com/AkhmimWoodenTablet. html.