34 2. MATHEMATICAL CULTURES I4. Ancient Egypt
Although mathematics has been practiced in Egypt continuously starting at least
4000 years ago, it merged with Greek mathematics during the Hellenistic period
that began at the end of the fourth century BCE, and it formed part of the larger
Muslim culture centered in Baghdad starting about 1200 years ago. What we shall
call Egyptian mathematics in this section had a beginning and an end. It began with
hieroglyphic inscriptions containing numbers and dating to the third millennium
BCE and ended in the time of Euclid, around 300 BCE. The city of Alexandria
in the Nile delta was the main school of mathematics in the Hellenistic world, and
many of the most prominent mathematicians who wrote in Greek studied there.
The great architectural monuments of ancient Egypt are covered with hiero-
glyphs, some of which contain numbers. In fact, the ceremonial mace of the founder
of the first dynasty contains records that mention oxen, goats, and prisoners and
contain hieroglyphic symbols for the numbers 10,000,100,000, and 1,000,000. These
hieroglyphs, although suitable for ceremonial recording of numbers, were not well
adapted for writing on papyrus or leather. The language of the earliest written
documents that have been preserved to the present time is a cursive known as
hieratic.
The most detailed information about Egyptian mathematics comes from a sin-
gle document written in the hieratic script on papyrus around 1650 BCE and pre-
served in the dry Egyptian climate. This document is known properly as the Ah-
mose Papyrus, after its writer, but also as the Rhind Papyrus after the British
lawyer Alexander Rhind (1833-1863), who went to Egypt for his health and be-
came an Egyptologist. Rhind purchased the papyrus in Luxor, Egypt, in 1857.
Parts of the original document have been lost, but a section consisting of 14 sheets
glued end to end to form a continuous roll 3 5 feet wide and 17 feet long remains.
Part of it is on public display in the British Museum, where it has been since 1865
(see Plate 1). Some missing pieces of this document were discovered in 1922 in the
Egyptian collection of the New York Historical Society; these are now housed at
the Brooklyn Museum of Art. A slightly earlier mathematical papyrus, now in the
Moscow Museum of Fine Arts, consists of sheets about one-fourth the size of the
Ahmose Papyrus. This papyrus was purchased by V. S. Golenishchev (1856-1947)
in 1893 and donated to the museum in 1912. A third document, a leather roll pur-
chased along with the Ahmose Papyrus, was not unrolled for 60 years after it reached
the British Museum because the curators feared it would disintegrate if unrolled.
It was some time before suitable techniques were invented for softening the leather,
and the document was unrolled in 1927. The contents turned out to be a collection
of 26 sums of unit fractions, from which historians were able to gain insight into
Egyptian methods of calculation. A fourth set of documents, known as the Reisner
Papyri after the American archaeologist George Andrew Reisner (1867 1942), who
purchased them in 1904, consists of four rolls of records from dockyard workshops,
apparently from the reign of Senusret I (1971-1926 BCE). They are now in the
Boston Museum of Fine Arts. Another document, the Akhmim Wooden Tablet,
is housed in the Egyptian Museum in Cairo. These documents show the practical
application of Egyptian mathematics in construction and commerce.
We are fortunate to be able to date the Ahmose Papyrus with such precision.
The author himself gives us his name and tells us that he is writing in the fourth
month of the flood season of the thirty-third year of the reign of Pharaoh A-user-re