ON THE ANALYSIS OF LIBRARY GROWTH
65
the latter was only 25 years older than Archimedes and they were
separated by much of the “known” world of the times (circa 200
B.C.), Archimedes residing in Sicily and Aristarchus on the island
of Samos near modern Turkey. Because of the critical role that
communication plays in mathematical progress, one would expect
that mathematics would experience a renaissance following an
invention which decisively improves communication. In fact, there
is no real mathematics known prior to the Egyptian and Mesopo-
tamian civilizations, although serious mathematics of high cali-
ber is attested in the earliest phases of these civilizations. Much
more information is available about what has happened since
Greek times, and it supports our view. Indeed, if the number of
memorable mathematicians is graphed as a function of the birth
date of the mathematician, then the curve displayed in Figure 4
results. Here a mathematician is “memorable” if he is named in the
index to a standard history of mathematics; the book by Struik
(Ref. 13) has been used for the illustration. Other choices would
not change the shape of the curve. Estimates of world population
are shown in Figure 4 for comparison purposes. Observe that
the number of memorable mathematicians rose rapidly after 700
B.c.—that is, not long after the invention of an alphabet by the
Greeks—and grew exponentially from 300 B,C. until about 1450 a.d.
after which time the growth rate increased dramatically. If the
exponential portion of the memorable mathematician curve is ex-
tended back in time, it suggests that the “first” memorable mathe-
matician lived about 3700 B.C., not long before the first writing
' systems are attested and probably simultaneous with their develop-
ment.
European Universities
The growth curve illustrating the currently extant European
universities as a function of their date of founding (Figure 5)
is interesting. The data came from the Random House Dictionary,
and is given in Table II. Figure 5 shows four distinct phases of
growth, three of which are clearly exponential, with a fourth that
is approximately so. The earliest period, from 1100 to 1210, cor-
responds to such small numbers of universities that statistical
arguments cannot be reliable, and we thus ignore it. The second
period, from about 1210 to 1500, indicates a uniformly exponential
growth doubling approximately every 110 years. After 1500, there
is a 300-year period of roughly exponential growth, which may
mark a transitional phase from the previous period to the next
one, beginning in 1800 and continuing to the present, which shows