Leonid Zhmud The Origin of the History of Science in Classical Antiquity

 taught at the Academy? There is no reliable
historical evidence of this,
99
and we actually know very little about what
exactly was taught at the Academy. Most reconstructions rely on the Platonic
dialogues, and in particular on book VII of the
 Republic, where a solid program
of mathematical education is put forward (for those between the ages of 20 and
30). Nevertheless, an expert like Krämer notes that we have no knowledge of a
stable program of education at the Academy like the one described in the
 Re-
public and in the Laws. “Anyway, the educational curriculum outlined in the
Republic VII and the Laws XII cannot be directly transferred to the reality of
the Academy.”
100
96
The mathematical passages from the dialogues are collected in Brumbaugh, R. S.
Plato’s mathematical imagination, Bloomington 1954; Frajese, A. Platone e la ma-
tematica nel mondo antico, Rome 1963.
97
Knorr, W. R. On the early history of axiomatics: A reply on some criticism,
Theory
change, ancient axiomatics and Galileo methodology, ed. by J. Hintikka et al., Dor-
drecht, 1981, 194ff.; idem. What Euclid meant: On the use of evidence in studying
ancient mathematics,
Science and philosophy in classical Greece, ed. by A. C.
Bowen et al., New York, 1991, 141ff.; Mueller, I. On the notion of a mathematical
starting point in Plato, Aristotle, and Euclid, ibid., 59–97.
98
In practice, this demand meant the construction of the ‘philosophical base’ for math-
ematical definitions: Taylor, C. C.W. Plato and the mathematicians,
PhilosQ 17
(1968) 193–203.
99
The famous inscription @gewmétrhto~ mhdeì~ eısítw is a late literary fiction: Saf-
frey, H. D. AGEWMETRHTOS MHDEIS EISITW: Une inscription légendaire,
REG 81 (1968) 67–87.
100
Krämer,
op. cit., 5.

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Chapter 3: Science in the Platonic Academy
102
To judge from Plato’s dialogues, the mathematical element in his work in-
creases toward the end of his life. Might we conclude that during the last decade
of his life mathematics was especially intensively taught at the Academy? Al-
most none of the younger Academics show any special interest in geometry.
101
As for the older Academics, at the time of Plato’s death, Speusippus, Xeno-
crates, Heraclides, Philip and Aristotle were long past the students’ age. They
were more suited to teaching than to learning mathematics. Their writings
imply that they received some mathematical education, but did this take place at
the Academy? It is difficult to imagine Plato himself teaching mathematics, but
if he did not, then who did, and what kind of mathematics?
102
Cherniss devel-
oped his idea about the teaching of mathematics at the Academy only because it
was necessary to support his thesis that Platonic metaphysics was
not taught
there.
103
What, then, was taught at the Academy if not mathematics? The easiest
answer to this is dialectic; the most honest answer is that we do not know.
Whether Plato adopted his educational program from the Pythagoreans or
the Sophists is not so important;
104
the significant point is that his predecessors
realized it in practical teaching and produced generations of brilliant mathema-
ticians such as Theodorus, Hippocrates, Archytas, Theaetetus, and Eudoxus
and his pupils. In Plato, we come across this program only in the dialogues and
even there only as a preparation for the study of dialectic (
Res. 531d), which
was for him far more important than any other science. He handed this attitude
down to his students: despite all their fertility in the field of the philosophy of
mathematics,
105
none of them left any mark in the exact sciences. To judge, for
instance, from the large fragment from Speusippus’