1200s: 3–4–7
1300s: 5–6–0
1400s: 2–3–10
1500s: 17–18–26
1600s: 37–44–23
1700s: 19–39–34Moreover, before 1500, most of the names listed are persons who recorded any
mathematics even without originality; the criterion for listing shifts over in the
1500s to original contributions.- The first use of the equal sign () was in Recorde’s 1551 book on elementary
commercial arithmetic; what would become the modern notation for operations
was popularized in England by Harriot’s 1621 textbook. Neither book contained
any original mathematics. On the history of notation generally, see Cajori (1928). - See Figure 10.1. The other major philosophers are Bacon, Hobbes, Spinoza, and
Locke. If we look not at overlaps between the scientific and philosophical networks
but at personal contacts among their members, we find that all of the major
philosophers are within one link of a significantly creative scientist, and 12 of 14
secondary philosophers are within two links of a scientist. The only major philoso-
pher who is not an active scientist, Locke, is a medical doctor, directly connected
with 2 scientific stars and a host of other scientists. The fact of their working in
science does not imply that the work of these philosophers is itself a significant
contribution; Bacon’s experiments, for example, led to no important discoveries.
Here I use the strong criterion, indicated in note 19, for identifying scientists. I will
often use the term science to include both science and mathematics; it should be
obvious from the context when I am using it in a more restricted sense, exclusive
of the activities of mathematicians. - During 1700–1900, 5 of 13 major philosophers were active in science (Berkeley,
Kant, Schelling, Peirce, James), and 10 of 13 are within one link of an important
scientist. Of secondary philosophers, 14 of 46 are scientists, and 33 are within two
links of one. - We see this by comparing Figure 10.2 (network of Greek mathematicians) with
Figures 3.1 to 3.8 (network of Greek philosophers). Sources for Greek mathema-
ticians (Heath, [1921] 1981; Smith, 1951; Ball, [1908] 1960; Cajori, 1928; Knorr,
1975; Neugebauer, 1957; Boyer, 1985; Kline, 1972; van der Waerden, 1975; DSB,
1981). - This may be traced in the key to Figure 3.4 by noting the figures marked “medi-
cine,” beginning with the merging of the Hippocratic lineage with the network
around Aristotle and the Alexandria schools (71, 75, 76, 108). These connections
are not depicted in Figure 3.4 itself to avoid overcomplicating the diagram. - As we saw in Chapter 8, the creativity of this original Baghdad group derived not
simply from Greek imports but from the cosmopolitan situation which combined
these with materials from Babylonian sects and Indian astronomers, resulting in
al-Khwarizmi’s encyclopedic synthesis in the early 800s. By the generations of
994 •^ Notes to Pages 539–546