965–1035, this elementary algebra had been developed to the high points of world
mathematics at the time, al-Buzjani’s Diophantine equations and al-Karaji’s theory
of algebraic calculation and algebra of polynomials, breaking with geometrical
representations into an arithmeticized algebra. The Spanish network began around
965 with migrants from the Pure Brethren, numerological cosmologists branching
from the Baghdad scientific network. Within a few generations this spread to the
Jews (initially via numerology); it blossomed simultaneously into creative astron-
omy (e.g., al-Bitruji’s revision of the Ptolemaic system in the late 1100s) and the
work of the major Jewish and Muslim philosophers. The scientific-philosophical
network was disrupted in the eastern region around 1100. It was reestablished by
Jewish travelers back from Spain: Abraham Ibn Ezra and Maimonides, who linked
to the network around the Jewish doctor and astronomer Abu-l-Barakat and
onward to the major astronomer al-Tusi and his lineage. The Jews played the role
of cosmopolitan transmitters twice, not only to Christian Europe but also to the
high point of Iranian Muslim science.
- If we use the loose criterion of writing on some aspect of natural science, we would
have to include 8 of 11 major philosophers (72 percent) and 19 of 48 secondary
(40 percent) in medieval Christendom. By a stricter criterion (formulating princi-
ples in astronomy or physics, collecting naturalistic observations, or making at
least crude calculations), we still find 45 percent of major and 23 percent of
secondary Christian philosophers active in science. For comparison let us use a
strong criterion: contributing actively to astronomy, mathematics, medicine, or
naturalist observation. In Greece, 14 of 28 major philosophers were themselves
scientists; in medieval Islam (including Jews), 5 of 11; in Europe, 1600–1900, 10
of 19. The percentages are similar in all four places: Greece, 50 percent; Islam/Jews,
45 percent; Christendom, 45 percent; Europe, 53 percent. Throughout the West,
the most influential philosophers tend to be more interested in science than less
influential philosophers. Among secondary philosophers, the percentages of over-
lap are lower everywhere: Greece, 28 percent (19 of 68); Islam, 20 percent (8 of
41); Christendom, 23 percent (11 of 48); and Europe, 28 percent (17 of 60). If we
extend the perimeter to two links from the scientific network, the pattern is similar
everywhere: for major philosophers, Greece, 82 percent; Islam, 82 percent, Chris-
tendom, 73 percent, Europe, 89 percent; for secondaries, Greece, 50 percent,
Christendom, 44 percent, and Islam, 44 percent though here Europe stands out
with 76 percent within the periphery of scientists.
- Eminence among scientists and mathematicians is measured in the same way as
for philosophers: by the relative amount of space devoted to them in histories of
those periods.
- In China, of 25 major philosophers, 6 (24 percent) were involved in some way in
mathematical science, for the most part very tangentially. Among secondary phi-
losophers, 7 of 61 (11 percent) were involved in astronomy, and only one of them,
Liu Hsin in the Han dynasty, was an important astronomer. An additional 6 names
of astronomers overlap the list of minor philosophers, making up less than 2
percent of the total. Extending the network outward, we find a mathematical
Notes to Pages 548–549^ •^995
