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

Catalogue, or that they
worked there only after Plato’s death, or that the
Catalogue’s information about
their activity at the Academy is not reliable. Whichever of these explanations
we favor, none of them supports the Academic legend of Plato as the architect
of mathematical science.
3. Mathematics at the Academy
The
 Catalogue names three predecessors of Euclid who had written Elements:
Hippocrates, Leon, and Theudius. The first of these is well known and the last
two are not mentioned at all outside the
 Catalogue. However, that is not the
question. Whoever followed the tradition of writing
Elements, it is obvious that
its originator was Hippocrates. It is very likely that there were attempts to sys-
tematize geometrical knowledge before Hippocrates,
95
but his achievement
was more successful and served as an example to later generations. Is there
anything especially significant in the fact that all the authors of
Elements were
sidered Aristoxenus’ evidence doubtful, the latter did not say that Amyclas was born
in Magna Graecia or that he was an opponent of Plato; therefore I do not see any
problems in identifying Amyclas of Heraclea with the hero of this anecdote.
92
Gaiser.
Academica, 110ff., 443ff.
93
In the case of Amyclas (Amyntas), we cannot be sure, probable as it seems, whether
the same person is meant in all our sources. Philodemus mentions Amyntas of Her-
aclea, Proclus Amyclas of Heraclea, Diogenes ¨Amuklo~ (and not ¨Amukla~ as in
all other sources) of Heraclea, Aelianus Plato’s student Amyclas (
VH III, 19), and
finally, Aristoxenus the Pythagorean Amyclas, Plato’s acquaintance. See Amyclas,
Amyclos, Amyntas,
DPhA 1 (1994) 174f.
94
Menaechmus appears in Eratosthenes as one of the ‘Academic mathematicians’, so
his description in the
Catalogue, Ménaicmo~ @kroat3~ …n Eÿdóxou kaì Plá-
twni dè suggegonø~ (In Eucl., 67.10), very likely goes back to the Platonicus. On
Menaechmus’ alleged discussion with Speusippus (Procl.
In Eucl., 77.7– 79.2 = Las-
serre.
Léodamas, 12 F 4–5), see Bowen, A. C. Menaechmus versus the Platonists:
Two theories of science in the early Academy,
AncPhil 3 (1983) 13–29; cf. Tarán.
Proclus, 237 n. 36f. and below, 5.4.
95
On the Pythagorean compendium, see below, 195 f.

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3. Mathematics at the Academy
101
contemporaries of Plato – one older than him and the two others younger? The
‘Platocentric’ view of ancient philosophy is honored because of its antiquity
and because of the number of celebrities who shared it; however, for a long
time now, the majority of experts has not shared this view, and it has brought
nothing except misunderstanding to the history of Greek science. What is be-
hind it except the natural desire to see genius in everything? Primarily, the ob-
vious fact that from the pre-Euclidean period not a single mathematical writing
is preserved, whereas the
Corpus Platonicum was handed down through the
generations in its entirety. Certainly, Plato knew and valued mathematics and
often used mathematical examples in his reasoning.
96
But was this love mu-
tual? To judge from the
 Elements of Euclid, whom Proclus or his source en-
listed as a Platonist, this was not the case.
97
One can only guess about the con-
tents and nature of the books of Euclid’s predecessors, but it is more reasonable
to base these guesses on the natural tendency of all the sciences of that time to
systematize accumulated knowledge rather than on Plato’s demand for the
axiomatization of geometry
98
or on his more prosaic demand for textbooks for
the Academy.
What is the basis of the current general opinion that geometry and possibly
other mathematical sciences were