The history of mathematics is but a thin ribbon across
the fabric of general history, that is, of the cultural
history of events, insights, and ideas. Yet there are
major problems of general history that are meaning-
fully refracted in the history of mathematics, and one
such problem, on which we shall concentrate, is the
problem of explaining the decline of ancient civili-
zation in the West. On the other hand, it may happen
that mathematics is materially involved in a problem
in general history, and yet cannot contribute to its
illumination; one such problem, on which we intend
to comment, is the problem of the rise and spread of
phonetic writing. Finally, there are intriguing situa-
tions in which the judgment of mathematics on the
eminence of an era is different from that of other fields
of knowledge, even of physics proper, and in several
brief preliminary sections we shall rapidly review a
few problems of this kind from periods beginning with
and following upon the Renaissance.
But before beginning our reviews we wish to state
that the problems to be encountered will be formulated
in broad, summary, and even simplistic terms. This is
to be expected. As a mode of rational cognition mathe-
matics appears rather early and is quite central, but
as a mode of intellectual activity it is rather primitive.
For this reason mathematics is effective because of its
strength rather than its delicacy, even when involved
in sensibilities. Therefore, when participating in the
analysis of problems from general history, the history
of mathematics is at its best when the problems are
stated in large, manifest, even crude fashion rather than
in a localized, esoteric, and delicate manner.
