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

History of Geometry and the books of the Academics,
especially when the subject was Plato and his students. The passages about
Plato and Philip could scarcely belong to Eudemus, but they might have been
inserted into the
 Catalogue by a Neoplatonic redactor. Indeed, in the context of
the
 Catalogue, which lists particular achievements in mathematics, Philip’s
characteristics look rather odd: his foremost merit in mathematics is that he
studied problems that he believed to be connected with Platonic philosophy!
Such an assessment can hardly come from Eudemus. It is more natural, rather,
to expect it from Philip’s Academic colleagues or from their Neoplatonic fol-
lowers.
47
Evaluating the little that is known about Philip’s scientific work, one
should admit that in the field of
mathe¯mata Philip scarcely had any other
achievements that could do honor to the Academy.
48
Plato occupies a central place in the second half of the
 Catalogue, and such a
perspective, of course, brings it closer to the papyrus passage. But even then, it
mentions only one mathematician as a pupil of Plato and says nothing about the
posing of the problems. What is said about his contribution to the development
of mathematics is supported with a reference to his dialogues, but not to his role
as an ‘architect of science’. The author (or redactor) of the
 Catalogue uses more
subtle means to express what is directly said in Philodemus: all the mathema-
ticians of Plato’s time worked under his methodological supervision. This ef-
fect is achieved mainly by situating all these mathematicians in the text be-
tween Plato and Philip, the latter being described as a devoted student working
in accordance with Plato’s instructions. Because of this circular arrangement,
Plato’s figure overshadows those of his contemporaries. This impression is re-
inforced by the constant emphasis on the close relationship between Plato and
47
The similarity of characteristics the
Catalogue attributes to Philip and Euclid points
to a Neoplatonic redactor rather than to an Academic author. See below, 182.
48
See below, 102 f.

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Chapter 3: Science in the Platonic Academy
92
the mathematicians: some ‘lived at the time of Plato’, others ‘communicated
with him’ or ‘were his students’, and still others ‘were friends of his students’,
etc. Since for our present analysis it is not very important whether this perspec-
tive derives from the early or from the later Platonists, I would propose the fol-
lowing approach to the second part of the
Catalogue. If, in spite of its clear bias,
it does not specifically mention that someone was a pupil of Plato or that he
worked at the Academy, this fact was unknown in the late fourth century BC. It
seems very unlikely that Porphyry or Proclus would have omitted such a fact,
had they found it in an Academic or Peripatetic source.
The first three mathematicians of Plato’s time mentioned here are Leodamas
of Thasos, Archytas, and Theaetetus. Nothing is said about their connection
with the Academy or about their personal relationships with Plato. Since the
chronology in this part of the
 Catalogue is very accurate, one can suggest that
Leodamas was the oldest of the three, or at least that he was not younger than
Archytas. It is with him that Lasserre begins his collection of sources concern-
ing the ‘Academic mathematicians’, although there is absolutely no evidence
that Leodamas worked at the Academy.
49
The only thing linking him with Plato
is Favorinus’ (second century AD) statement, repeated with some hesitation by
Proclus, that Plato taught him a method of analysis
50
and the pseudo-Platonic
11
th
letter addressed to a certain Leodamas. But then why should not Archytas
be included in this collection as well? After all, there is much more evidence
concerning him: we have Plato’s authentic 7
th
letter that mentions the help he
gave to Plato, Eratosthenes’ evidence, and the fact that Archytas (but not Leo-
damas!) occurs in several lists of Plato’s students.
51
Certainly, Archytas, unlike
Leodamas, was too independent a figure to be easily turned into an Academic
mathematician (moreover, he was known as a Pythagorean). But this is not easy
to do with Leodamas himself, either. Even if Leodamas was the same age as
Archytas (born ca. 435/430),
52
then at the time the
Meno was written (ca.
385/380) – the first dialogue where Plato shows an interest in mathematics and
gives, in particular, a description of the method ëx ûpoqésew~ (86e–87c),
49
Fritz, K. von. Leodamas,