**The Babylonian Number
System**

The Babylonians used a base 60, or
sexagecimal, number system which is
preserved in tablets made by pressing into
the soft clay styli with carved cuneiform
script. Our habit of giving 360^{o} to a circle,
60 seconds in a minute and 60 minutes in an
hour are cultural artifacts passed down to
us from the Babylonians. Cuneiform script
is shown at the right. The symbols for 1-9
and 10 - 50 are given in the first two lines
followed by examples of the decimal
(subscript D) numbers 12, 37, 97, 65 and
12709 converted to their sexagecimal
(subscript S) equivalents. Zero was
indicated simply by a space. Information on
this number system comes to us from some
four hundred clay tablets containing lists of
mathematical problems and mathematical
tables of more than half a million engraved in their written cuneiform script which have been
excavated since the first half of the nineteenth century. A particularly well studied tablet is shown
below. It is believed to have been found at Senkereh and was purchased by George Arthur
Plimpton in 1923 and brought to the U.S. but was not deciphered until 1945 by Neugebauer and
Sachs. Designated PLIMPTON 322 in the Plimpton Collection at Columbia University, it is the
oldest surviving document on number theory. It was made in Babylon between 1900 and 1600
B.C. Traces of modern glue can be seen on the left edge but the left fragment is now lost.
Exhibits of these tablets can be found in the great museums of Paris, Berlin and London as well as
the archeological exhibits at Yale, Columbia and the University of Pennsylvania.

Cuneiform writing was difficult to learn. The teacher of cuneiform prepared an example on the left half of a soft clay tablet and the student was instructed to copy that example on the right half.