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

Platon, Theaetet und die antike Mathematik
(1932), Darmstadt 1969 (esp. Nachtrag); idem.
Grundprobleme, 250ff. Neugebauer.
ES, 152, expressed his opinion very definitively: “I think that it is evident that Plato’s
role has been widely exaggerated. His own direct contributions to mathematical
knowledge were obviously nil … The often adopted notion that Plato ‘directed’ re-
search fortunately is not borne out by the facts.”
6
Gaiser, K.
Platons ungeschriebene Lehre, Stuttgart 1963, 293ff.; idem. Philodems
Academica, Stuttgart 1988; Lasserre, F. The birth of mathematics in the age of Plato,
London 1964; idem.
Léodamas, 516f.; Fowler, D. H. The mathematics of Plato’s
Academy. A new reconstruction, Oxford 1987, 342ff.; Hösle, V. I fondamenti dell’
aritmetica e della geometria in Platone, Milan 1994. I. Mueller is also ready to admit
that Plato was a “general mathematical director, posing problems to the mathema-
ticians” (Mathematical method and philosophical truth,
The Cambridge companion
to Plato, ed. by R. Kraut, Cambridge 1992, 175).

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Chapter 3: Science in the Platonic Academy
84
there is a grain of historical truth in these legends, we need a critical analysis of
ancient evidence of the place of the exact sciences in Plato’s Academy.
One of the classic examples of the tradition in question is the story about the
famous solution to the Delian problem of the duplication of the cube, preserved
by Plutarch, Theon of Smyrna (first part of the second century AD), and several
later commentators.
7
It should be noted that for ancient mathematics the Delian
problem was not unlike Fermat’s theorem for modern mathematics: in the
course of the seven hundred years from Hippocrates to Pappus, a great many fa-
mous mathematicians tried to find a solution to it.
8
Thus, the tradition connect-
ing it with Plato makes him seem like the originator of one of the central prob-
lems in ancient mathematics. The versions of the story found in Plutarch and
Theon can be generally summed up in the following way. The people of Delos,
tormented by a plague that Apollo had sent upon them, asked Plato to solve the
problem of duplicating a cubic altar. The Delphic oracle had posed them this
problem – the plague would leave the island if the Delians succeeded in giving
it a solution. Plato, having reprimanded the Greeks for their contempt of ge-
ometry, commissioned the famous ‘Academic mathematicians’ Archytas, Eu-
doxus, and Menaechmus to find a solution.
9
Their approach employed mech-
anical devices, and Plato rebuked them for ruining the value of geometry by
having sunk to the level of crude mechanics.
According to general opinion, the common source of Plutarch and Theon
was Eratosthenes’ dialogue
Platonicus.
10
The plot of this dialogue is clearly lit-
erary fiction: the problem of the duplication of the cube arose in the mid-fifth
century, and was not set for Plato by the Delians. Hippocrates had reduced it to
7
Plut.
De E ap. Delph. 386 E; De gen. Socr. 579 B–C; Quaest. conv. 718 E–F; Marc.
14, 9–11; Theon.
Exp., 2.3–12; Eutoc. In Archim. De sphaer., 88.3–96.9; Asclep.
Tral.
In Nicom. Intr. arith., 61; Philop. In APo comm., 102.12–22; Anon. Proleg., 11.
See Riginos, A. E.
Platonica. The anecdotes concerning the life and writings of
Plato, Leiden 1976, 141ff. (no. 99–100); Dörrie, H. Der Platonismus in der Antike,
Vol. 1. Stuttgart 1987 (Baustein 7.2–5); Geus, K.