The Mathematicians
The mathematical revolution built up first. Part of the increasing interest in
mathematics came from practical interests, and one can date the gradual
outpouring of commercial math textbooks from the late 1400s. But practical
math was not the source of the innovation in problem-solving techniques which
constituted the core of the new mathematics. The more abstract realms of
mathematics were created as mathematicians made discoveries about general
procedures. Puzzle-solving techniques, such as algorithms for solving higher-
order equations, became topics of discovery in their own right. The takeoff of
math occurred when it became an intellectual game as well as a matter of
practical application. Contact with the network of philosophers turned the
activity of low-status reckoning masters into the high-prestige competition of
the intellectuals who made the claims to matters of greatest importance.
Innovative mathematicians emerged in the philosophical networks. Regio-
montanus came from the network around Cusanus and was patronized by the
Humanist leader Bessarion. Cusanus was not a skilled mathematician in a
technical sense, but his philosophy was permeated with mathematical concep-
tions, and we see here a general intellectual concern raising mathematics into
its orbit. Copernicus came from these same networks in central Europe; he
studied first with a pupil of Regiomontanus at Cracow, and later lived near
Königsberg (from which Regiomontanus originated and received his Latin
name). During 1496–1505 Copernicus studied in Italy, making contact with
the humanistic network, as Cusanus and Regiomontanus had previously; Cop-
ernicus met Ficino’s Platonist followers and overlapped at Padua with the
Aristotelean Pomponazzi and at Bologna with the mathematician Scipione del
Ferro. Not that Copernicus necessarily borrowed his mathematical or astro-
nomical ideas from these contacts; more important is the pattern that creativity
is stimulated by contact with the central focus of intellectual attention.
To the extent that Copernicus’s work was propagated, it was through the
more general intellectual network; his publisher Osiander was a theology
professor at Königsberg, and his assistant Rheticus was visited by Ramus, the
Parisian reformer of school logic.^26 His heliocentric astronomy did not make
much impact for two generations; when it was picked up again in the 1590s
it was by Kepler, a theology student at Tübingen under the theologian Maestlin
(EP, 1967: 4:329–333). What is worth stressing here is that astronomy in this
period was most significant as a vehicle for innovations in mathematics.
Copernicus is as much a part of the initial wave of the mathematical revolution
as he is of the scientific revolution per se;^27 by the time of Kepler, the discov-
ery-making revolution was expanding from the one realm to the other. Astron-
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