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8 Th e pluralism of Greek ‘mathematics’
G. E. R. L l o y dGreek mathēmatikē , as has oft en been pointed out, is far from being an
exact equivalent to our term ‘mathematics’. Th e noun mathēma comes from
the verb manthanein that has the entirely general meaning of ‘to learn’.
A mathēma can then be any branch of learning, or anything learnt, as when
in Herodotus (1 207) Croesus refers to the mathēmata – what he has learnt –
from his own bitter experiences. So the mathēmatikos is, strictly speak-
ing, the person who is fond of learning in general, as indeed it is used in
Plato’s Timaeus at 88c where the point at issue is the need to strike a balance
between the cultivation of the intellect and that of the body, the principle
that later became encapsulated in the dictum ‘ mens sana in corpore sano ’.
Yet Plato also recognizes certain special branches of the mathēmata , as
when in the Laws at 817e the Athenian Stranger speaks of those that are
appropriate for free citizens as those that relate to numbers, to the measure-
ment of lengths, breadths and depths, and to the study of the stars, in other
words, very roughly, arithmetic, geometry and astronomy. In Hellenistic
Greek mathēmatikos is used more oft en of the student of the heavens in
particular (whether what we should call the astronomer or the astrologer)
than of the mathematician in general in our sense.
Whether we should think of either what we call mathematics or what
we call philosophy as well-defi ned disciplines before Plato is doubtful.
I have previously discussed the problems so far as philosophy is con-
cerned.^1 Th ose whom modern scholars conventionally group together as
‘the Presocratic philosophers’ are a highly heterogeneous set of individuals,
most of whom would not have recognized most of the others as engaged in
the same inquiry as themselves. Th eir interests spanned in some, but not all,
cases what we call natural philosophy (the inquiry into nature), cosmology,
ontology, epistemology, philosophy of language and ethics, but the ways
in which those interests were distributed among the diff erent individuals
concerned varied considerably.
It is true that we have one good fi ft h-century bce example of a thinker
most of whose work (to judge from the very limited information we have(^1) Lloyd 2006b.