in France in 1836. Competition among journal editors for notable pieces, and
the rush of mathematicians to anticipate opponents in publication, must have
heightened emotional energy, while the specialized journals focused attention
inward on the mathematical community in its own right (Boyer, 1985: 561;
Collins and Restivo, 1983). Cauchy, who controlled the official publication of
the Académie, was famous for rushing into print, and for unsavory tactics to
anticipate or block his competitors. Mathematicians from peripheral countries
or low-status positions, such as the Norwegian Abel and the École Normale
Supérieure student Galois, were scandalously treated when they attempted to
get their work published in Paris during 1826–1832. Nevertheless, their work
came to light through the support of the editors of the new journals, who no
doubt were looking for material to launch their enterprises with a splash.^2
Two results of these conditions were a movement toward rigor and the
takeoff into pure abstraction. The mathematicians of the previous century
in exploring analysis had left behind the deductive proofs of the Euclidean
method; they argued by induction from particular examples, from intuition or
physical cases. General theorems were often guessed at and left without proof.
Without any inquiring into their validity, new concepts were used such as the
convergence of series and integrals, differentials of higher order, infinitesimal
increments, and procedures which amounted to discarding terms and dividing
by zero (Kline, 1972: 392–394, 616–618, 1024; Kitcher, 1984: 235). Rigor
was disregarded in part because mathematics was interpreted physically; as
long as empirically useful results were obtained in the sciences, proofs were
considered needless subtleties. Socially this attitude was a product of the lack
of differentiation between the activity of the mathematician and the physicist
or even the engineer. D’Alembert and others held that the traditional field of
mathematics had now turned into mechanics, and the attitude of disregarding
rigor continued among applied mathematicians such as Fourier and Poisson
into the 1820s and 1830s. Even those mathematicians who, like Euler, were
caught up in the game of inventing algorithms had confidence in the manipu-
lation of symbols without inquiring deeply into their meaning; the “machin-
ery” of mathematics was socially convincing because it gave repeatable results.
The shift to rigor was driven by the hyper-competitiveness exemplified by
Cauchy, and by the academicization of mathematics brought about by the
Polytechnique and the German universities. Unlike the virtuoso math of the
academies, that taught in the schools was more systematic; scholasticism and
pedantry contributed to a more careful statement of fundamentals (Grabiner,
1986). Even though the Polytechnique was intended for the training of engi-
neers, it underwent a goal displacement typical of academic organization and
began to treat the standards of mathematics as ends in themselves. Rigor is
the form which bureaucratization takes inside the community of mathemati-
698 •^ Intellectual Communities: Western Paths