1 The Birth of Science - MSRI

2
Hellenistic Mathematics
2.1 Precursors of Mathematical Science
The term “mathematics” is seldom defined by historians of the subject: for
instance, Boyer’s History of Mathematics explicitly avoids the task, saying
merely that “much of the subject [ . . . ] is an outgrowth of thought that originally
centered on the concepts of number, magnitude and form.” 1 Were
we to take this as the basis for a definition, mathematics would not only
go back to paleolithic times — and indeed long before, since one can talk
about the “mathematical abilities” of various animals, and research has
been done on the issue — but it would also encompass systems such as
the Neapolitan “smorfia”, 2 which, one must admit, also deals with questions
centered on the concept of number.
But mathematical science, in the particular sense in which we have defined
“science”, arises in the Hellenistic period. Of course Hellenistic mathematics
does not come out of nothing. In the preceding history of mathematics
one can, to a rough approximation, distinguish two periods. The
first, extremely long, includes among others the “mathematics” of Old
Babylonia and of Egypt under the Pharaohs. The second consists of a period
of approximately two and a half centuries in which classical Greece
created what we will call “Hellenic mathematics”, to distinguish it from
Hellenistic mathematics.
The first period started with the appearance of the ability to count, in page 51
1 [Boyer], p. 1.
2 The smorfia is a series of rules for extracting from dreams information that is supposedly help-
ful in predicting winning lottery numbers.
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