a major tool for understanding nature and existence. Ancient
Africans used the reality of mathematics to make inferences
from general truths to particular truths and constructed an
order that enabled them to understand life. Mathematics be-
came a tool for achieving perfection, truth, and stability. Th e
entire universe, it was believed, is an arrangement of num-
bers. Th ere are an infi nite number of proofs for the harmony
of mathematics and human existence in ancient Africa.
EGYPT
BY BRADLEY SKEEN
From the early Predynastic Period (ca. 6500–3500 b.c.e.) to
the Greco-Roman Period (332–30 b.c.e.), native Egyptian
civilization made extensive use of practical mathematics in
architecture, astronomy, calendar making, and above all ge-
ometry (the measurement of agricultural fi elds). However,
Egyptians showed little interest in pure mathematics in any
abstract sense. Th e rope stretchers or surveyors who retraced
the boundaries of fi elds aft er the Nile fl ood commonly used
the Pythagorean theorem in their work, but they could not
have stated it in an abstract form or given it a formal math-
ematical proof.
Aside from the incidental representations of numbers
in numerous texts, our knowledge of Egyptian mathematics
comes from two main sources: the Ahmes Papyrus and Mos-
cow Papyrus. Both are small textbooks that would have been
used in scribal schools. Th ey demonstrate techniques to solve
simple mathematical and algebraic equations, but only by
representing specifi c examples from which the student must
infer general rules and procedures, exactly the opposite of the
modern approach to mathematics. Ordinary people would
have been illiterate and also unable to perform any but the
simplest mathematical operations “in their heads.”
Eg y ptia ns used a decima l, or base 10, number system just
as we sti l l do today. Whi le t his system u ltimately derives f rom
the fact that human beings have 10 fi ngers, Egyptians may
have been the originators of this formal mathematical sys-
tem distinct from the older Babylonian mathematical system
that was partially base 10 and partially base 6 (for fi ve fi ngers
and one hand). In hieroglyphs, the oldest form of Egyptian
writing, only the number 1 (a straight upright line represent-
ing a fi nger) and multiples of 10 could be directly shown. Th e
number 10 was indicated by a heel bone, 100 by a snare, 1,000
by a lotus fl ower; 10,000 by a more detailed sketch of a fi n-
ger, 100,000 by a tadpole, and 1,000,000 by a man holding his
hands stretched widely apart, still an innate gesture to indi-
cate a large size. Th ere was no conception of zero as a number.
Other numbers could be written only by giving combinations
of these signs that added up to the number in question, as ifTh e Rhind Mathematical Papyrus, showing mathematical problems and solutions, from Th ebes, Egypt (1550 b.c.e.) (© Th e Trustees of the British
Museum)
numbers and counting: Egypt 799