developments, in turn, forced indigenous groups to pay atten-
tion to the passage of seasons and to develop systems of keep-
ing track of those changes to procure food. Tracking change
required mathematics and some form of calendrical system,
but archaeological evidence for such practices does not ap-
pear until around 900 c.e.
Early architectural engineering suggests the creation of a
form of mathematical measurement system. For example, in
Shabik’eschee Village in New Mexico, as many as 18 pit houses
were discovered. Th ese small, sunken structures were prob-
ably household compounds. Usually round or square in fl oor
plan and made with mud and clay, these structures were oft en
a foot or more deep. Th e entryways of some of these structures
have been found to be oriented toward the north-south axis,
suggesting some form of astronomical observation. Pit houses
were discovered throughout the Southwest and were one of
the earliest permanent structures in North America.
Ora l t rad it ions of ma ny i nd igenous g roups i nd ic ated t hat
certain numbers were revered. For example, among the Ojib-
way, an Algonquian-speaking people centered in the Lake
Superior region, including the present-day areas of Michigan,
Wisconsin, Minnesota, and parts of Canada, the number 4
appears in several versions of their creation and migration
myths that date back to ancient times. In one version of their
creation myth the Good Spirit creates four beings who will
become the fi rst people. Another version tells of the Maker,
who sends four men to create the world. Th ere are also four
grandfathers and four colors of man (red, yellow, black, and
white). Th is reverence for the number 4 is also seen in Ojib-
way birch bark scrollwork.
In ancient Mesoamerica the earliest evidence of a num-
bering system appeared in the Preclassic Period (ca. 1800
b.c.e.–150 c.e.), carved on upright stone monuments called
stelae. In the present-day region of Veracruz, Mexico, at an
Olmec (1200–400 c.e.) site called Tres Zapotes, a series of
bars and dots appear on the back of one such monument,
Stela C. Th ese bars and dots also appear on later Maya (1000
b.c.e.–1521 c.e.) monuments. Th e bar-and-dot counting sys-
tem was based on a vigesimal system, or a base 20 system,
which corresponds to the number of digits on the hands and
feet. A dot corresponds to one unit, and a bar corresponds
to fi ve units. On Stela C, the dot and bar correspond to the
numbers 7.16.6.16.18, which archaeologists and epigraphists
(scholars who study inscriptions) have determined to be a
specifi c date, the third day of September in the year 32 b.c.e.
Using similar numbering systems on many later Mayan mon-
uments, it has been determined that this counting system re-
lates to a Mesoamerican calendrical system called the Long
Count; along with a ritual and solar calendar, this system was
used throughout Mesoamerica.
Th e Long Count calendar, unlike the ritual and solar cal-
endar, which was cyclical, was a linear count from a specifi c
origin point. Each number corresponds to a multiple of 20,
except for the last. For example, in the Long Count date on
Stela C, the 7 corresponds to the number of Bak’tuns, or the
cycle of 144,000 days that have passed. In this way, the Maya
and other Mesoamerican groups could confi gure large num-
bers. Th e Maya also invented the concept of zero, which was
represented by a shell or Maltese cross. Certain numbers had
specifi c signifi cance in Mesoamerica, such as the number 13,
which is the common number for the layers of the heavens
and also important in the ritual calendar. Th e numbers 18
and 20 also have calendrical signifi cance, as they are the com-
mon confi guration of the solar calendar. Finally, the numbers
9 and 7 are both associated with the underworld in myth.See also agriculture; architecture; art; astrono-
my; calendars and clocks; climate and geography;
crafts; economy; education; language; religion and
cosmology; sacred sites; trade and exchange; weights
and measures; writing.FURTHER READING
Carl B. Boyer, A History of Mathematics (Princeton, N.J.: Princeton
University Press, 1985).
Michael P. Closs, ed., Native American Mathematics (Austin: Uni-
versity of Texas Press, 1986).
Toyin Falola and Akanmu Adebayo, Culture, Politics, and Money
among the Yoruba (New Brunswick, N.J.: Transaction Publish-
ers, 2000).
John Fauvel, Mathematics in the Ancient World (Milton Keynes,
U.K.: Open University Press, 1987).
Richard J. Gillings, Mathematics in the Time of the Pharaohs (New
York: Dover, 1982).
Th omas Heath, Th e Th irteen Books of Euclid’s “Elements” (Mineola,
N.Y.: Dover, 1956).
Th omas Heath, A History of Greek Mathematics, vol. 1 (Mineola,
N.Y.: Dover, 1981).
Jacob Klein, Greek Mathematical Th ought and the Origin of Algebra
(Mineola, N.Y.: Dover, 1992).
David Matz, Ancient World Lists and Numbers: Numerical Phrases
and Rosters in Greco-Roman Civilizations (Jeff erson, N.C.: Mc-
Farland, 1995).
Aidan Meehan, Celtic Knots (London: Th ames and Hudson, 2003).
Karl W. Menninger, Number Words and Number Symbols: A Cul-
tural History of Numbers, trans. Paul Broneer (Ca mbridge,
Mass.: M.I.T. Press, 1969).
O. Neugebauer and A. Sachs, Mathematical Cuneiform Texts (New
Haven, Conn.: Yale University Press, 1945).
Gay Robins and Charles Shute, Th e Rhind Mathematical Papyrus:
An Ancient Egyptian Text (New York: Dover, 1990).
Peter Strom Rudman, How Mathematics Happened: Th e First 50,000
Ye a r s (Buff alo, NY: Prometheus Books, 2006).
G. J. Toomer, “Mathematics and Astronomy.” In Th e Legacy of
Egypt, 2nd ed., ed. John R. Harris (Oxford. U.K.: Clarendon
Press, 1971).
B. L. Van der Waerden, Science Awakening (New York: John Wiley,
1963).
Claudia Zaslavsky, Africa Counts: Number and Pattern in African
Cultures, 3rd ed. (Chicago: Lawrence Hill Books, 1999).806 numbers and counting: further reading