encouraged on the Catholic side and sought after by the Protestant standard-
bearers from the House of Palatine, and was visited by reformers such as
Comenius. Descartes was inducted into science through the Dutch network of
mathematicians and experimenters, Stevin, Snel, and Beeckman. Of crucial
importance, Descartes was sponsored by Mersenne’s circle, the center of or-
ganized scientific correspondence; Mersenne arranged debates to publicize
Descartes’s philosophy and treated him as the intellectual leader of the new
movement.
Descartes played this role not because of preordained genius, but because
by the accidents of geography he fell into the maximally effective combination
of network connections. His beginnings were undistinguished, a boy from the
minor provincial nobility in a small town in Poitou; but he was sent to the
college newly founded nearby at La Flèche, the spearhead of Jesuit educational
expansion in France, where he was a fellow pupil with Mersenne. Then came
various travels as a military freelancer, which happened to bring him into
contact with the Dutch scientists. This may have struck a chord because of
Descartes’s background connection with Viète, the greatest French mathema-
tician of the previous generation.^34 Soon after, in 1619, Descartes had his
famous dreams in which he envisioned a great system of mathematical phi-
losophy.
In mathematics, Descartes plays the role of synthesizer of prior achieve-
ments. He builds on Viète’s work, but pushes it to explicit statement on a
higher level of abstraction.^35 The work of Cardano and Viète in the theory of
equations is turned into a machinery; the use of geometric methods for algebra,
and vice versa, becomes formulated as a normal technique. As he does in prose
style, Descartes sets the standard for mathematical notation. His originality is
in his synthesis; most of the techniques of equational notation were scattered
in commercial textbooks, while many of the advanced problem-solving tech-
niques were still expressed verbally by leading mathematicians. Descartes
brings it all together and transmutes it into an essentially new thing, a philo-
sophical mathematics.
Descartes’s contribution to the scientific revolution is also a matter of
synthesis. Like Bacon, he was a propagandist for the future development of
science; he believed that he could show the method by which all scientific
problems could eventually be solved. Descartes proposed to do this by deriving
science from the techniques of mathematics. The result was that he downplayed
the empirical side of science. This was not through lack of familiarity, the
counterpart to Bacon’s unfamiliarity with forefront mathematics, but because
Descartes’s principal network resource was his mathematics, which he wished
to use to build a philosophy of complete certainty. His method, beginning with
clear and distinct ideas and proceeding through regular deductive steps to in-
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