Every head of the Academy from Plato through Arcesilaus (excepting only
Polemon) is known as a mathematician (albeit a minor one); the same is true
of Aristotle’s school through Strato, whose pupil was the great heliocentric
astronomer Aristarchus. Aristotle, though critical of the mathematical philoso-
phy of the Platonic Forms, nevertheless is important for having laid out
explicitly the formal procedures of mathematical proof. When the scientific
center at the Alexandria Museum was founded about 300 b.c.e., it was staffed
largely by the later generations of these networks. After 200 b.c.e. we find that
the creativity of both the philosophical network and the mathematical thins
out; thenceforward, what important activity there was tended to take place in
separation from the other. Yet again in late antiquity, when the Academy was
formally reestablished around 400 c.e., mathematics revived there, although
without much creativity.
Whatever is distinctive about Greek philosophy and creative about its
mathematics in its classical period seems to have come from their association
with each other. Ancient medical science also flourished in much the same
network milieu as the Athenian and Alexandrian mathematical scientists; and
its scientific innovativeness tended to fade too at about the same time, by 200
b.c.e. In later centuries the best-known physicians were those connected with
philosophy, from the Skeptics and Methodists down to the generation of Sextus
Empiricus and Galen.^17
Medieval Islam not only acquired Greek cultural capital but also has an
even more extreme network connection of philosophy with mathematics and
science. Virtually all of the major Islamic and Jewish philosophers (9 of 11)
are within two steps of the scientific network, and 5 of 11 are themselves
scientists (al-Kindi, al-Farabi, Ibn Sina, Averroës, Maimonides). Among secon-
dary philosophers, 18 of 41 are close to the scientific network, and 8 of them
overlap. As with the Greeks, the first-rate scientific stars are usually not the
most important philosophers (only Ibn Sina in medicine fits that description),
but 2 of them are secondary philosophers (the mathematician-logician Thabit
ibn Qurra and the astronomer al-Tusi). In Spain the connection between the
networks is especially complete: all 4 of the major Islamic and Jewish philoso-
phers and 5 of 7 secondaries are no more than one tie away.
Most of the Islamic scientists in Figures 8.1 through 8.5 constitute a single
network, which began in Baghdad with the translators at the House of Wis-
dom, and was later transplanted to Iran, Cairo, and Spain.^18 This network had
two bases: court support for astronomers and astrologers; and medical doctors,
with their independent base in endowed hospitals. The astronomers’ and the
doctors’ networks intertwined at Baghdad, brought into rivalry and contact
with the indigenous network of Islamic theologians; the result was to create
the hybrid role of the Greek-oriented falasifa (the “Arab philosophers” most
546 • (^) Intellectual Communities: Western Paths