The Age of Enlightenment. The merits and achieve-
ments of this age are subject to most diverse and diver-
gent interpretations. For instance, Carl Becker, in a
small but unforgettable book, The Heavenly City of
the Eighteenth-century Philosophers (1932), proposed
that, on the whole, the intellectual attitudes of the age
were medieval rather than modern, Voltaire or no
Voltaire. Notwithstanding assertions by some historians
of science, the advancement in physical science was
rather circumscribed. For instance, the eighteenth
century did not achieve much in the theory of elec-
tricity, at any rate not before Henry Cavendish and
C. A. Coulomb, who were active towards the end of
the century after the sheen of the Enlightenment had
already been dimmed. Also, optics virtually stood still
for over a century. After the lustrous works of Newton,
Christiaan Huygens, and others in the seventeenth
century almost nothing memorable happened in optics
till the early part of the nineteenth century when
Thomas Young, Étienne-Louis Malus, Augustin Fresnel,
William Hyde Wollaston, and Joseph von Fraunhofer
began to crowd the field. Furthermore, Immanuel
Kant's famous Critiques came toward the end of the
eighteenth century, after the “true” Enlightenment had
begun to fade; and Kant's predecessors in metaphysics
earlier in the century had been not a whit better than
Kant had depicted them.
But the eminence of mathematics in the era of
Enlightenment is clear-cut. It was a very great century.
Mathematicians like G. W. Leibniz, Jacob and John
Bernoulli, A. C. Clairaut, L. Euler, J. le R. D'Alembert,
P. L. M. de Maupertuis, J. L. Lagrange, and P. S. de
Laplace made it as distinctive a century as any since
Pythagoras among the Greeks, or even since the age
of Hammurabi in Mesopotamia. Also the age had one
feature that made it simply unique. It fused mathe-
matics and mechanics in a manner and to a degree
that were unparalleled in any other era, before or after.
Also, in mathematics, far from being a “medieval” age
as in Carl Becker's conception of the eighteenth cen-
tury, it was a very “modern” age. Monumental as
Newton's Principia (1686) may have been, it is Lag-
range's Mécanique analytique (1786) that became the
basic textbook of our later physical theory. Lagrange's
treatise is old-fashioned, but readable, Newton's treatise
is “immortal,” but antiquarian, and very difficult.
It is not easy to follow in depth the growth of this
mathematics in relation to other developments of the
era. Socioeconomic motivations do not account for its
high level, and there are no explanations from general
philosophy that are convincing. Immanuel Kant, for
instance, shows no familiarity at all with the advanced
mathematics of his times.
