The Beginnings of Greek Mathematics
With the possible exception of astronomy, mathematics is the oldest and most continuously
pursued of the exact sciences. Its origins lie shrouded in the mists of antiquity. We are often
told that in mathematics all roads lead back to Greece. But the Greeks themselves had other ideas about where mathematics began. A favored one is represented by Aristotle, who in his Metaphysics wrote: “The mathematical sciences originated in the neighborhood of Egypt, because there the priestly class
was allowed leisure.” This is partly true, for the most spectacular advances in mathematics have occurred contemporaneously with the existence of a leisure class devoted to
the pursuit of knowledge. A more prosaic view is that mathematics arose from practical
needs. The Egyptians required ordinary arithmetic in the daily transactions of commerce
and state government to x taxes, to calculate the interest on loans, to compute wages,
and to construct a workable calendar. Simple geometric rules were applied to determine
boundaries of elds and the contents of granaries. As Herodotus called Egypt the gift of
the Nile, we could call geometry a second gift. For with the annual ooding of the Nile
Valley, it became necessary for purposes of taxation to determine how much land had
been gained or lost. This was the view of the Greek commentator Proclus (A.D. 410–485),
whose Commentary on the First Book of Euclid’s Elements is our invaluable source of
information on pre-Euclidean geometry:
According to most accounts geometry was rst discovered among the Egyptians and originated in the measuring of their lands. This was necessary for them because the Nile over ows
and obliterates the boundaries between their properties.
Although the initial emphasis was on utilitarian mathematics, the subject began eventually to be studied for its own sake. Algebra evolved ultimately from the techniques of calculation, and theoretical geometry began with land measurement.
Most historians date the beginning of the recovery of the ancient past in Egypt from
Napoleon Bonaparte’s ill-fated invasion of 1798. In April of that year, Napoleon set sail
from Toulon with an army of 38,000 soldiers crammed into 328 ships. He was intent
on seizing Egypt and thereby threatening the land routes to the rich British possessions in India. Although England’s Admiral Nelson destroyed much of the French eet a
month after the army debarked near Alexandria, the campaign dragged on another 12
months before Napoleon abandoned the cause and hurried back to France. Yet what had
been a French military disaster was a scientic triumph. Napoleon had carried with his
expeditionary force a commission on the sciences and arts, a carefully chosen body of
167 scholars—including the mathematicians Gaspard Monge and Jean-Baptiste Fourier—
charged with making a comprehensive inquiry into every aspect of the life of Egypt
in ancient and modern times. The grand plan had been to enrich the world’s store of
knowledge while softening the impact of France’s military adventures by calling attention
to the superiority of her culture.
The savants of the commission were captured by the British but generously allowed
to return to France with their notes and drawings. In due course, they produced a truly
monumental work with the title D´escription de l’Egypte. This work ran to 9 folio volumes
of text and 12 volumes of plates, published over 25 years. The text itself was divided into
four parts concerned respectively with ancient Egyptian civilization, monuments, modern
Egypt, and natural history. Never before or since has an account of a foreign land been
made so completely, so accurately, so rapidly, and under such dificult conditions.
The D´escription de l’Egypte, with its sumptuous and magnificently illustrated folios,
thrust the riches of ancient Egypt on a society accustomed to the antiquities of Greece
and Rome. The sudden revelation of a nourishing civilization, older than any known
so far, aroused immense interest in European cultural and scholarly circles. What made
the fascination even greater was that the historical records of this early society were
in a script that no one had been able to translate into a modern language. The same
military campaign of Napoleon provided the literary clue to the Egyptian past, for one
of his engineers uncovered the Rosetta Stone and realized its possible importance for
deciphering hieroglyphics.
Most of our knowledge of early mathematics in Egypt comes from two sizable papyri,
each named after its former owner—the Rhind Papyrus and the Golenischev. The latter
is sometimes called the Moscow Papyrus, since it reposes in the Museum of Fine Arts in
Moscow. The Rhind Papyrus was purchased in Luxor, Egypt, in 1858 by the Scotsman
A. Henry Rhind and was subsequently willed to the British Museum. When the health
of this young lawyer broke down, he visited the milder climate of Egypt and became an
archaeologist, specializing in the excavation of Theban tombs. It was in Thebes, in the
ruins of a small building near the Ramesseum, that the papyrus was said to have been
found
