New Objects and New Methods

Abstract

The eighteenth century had been a dazzling era for its intensive development of techniques which had been introduced in the seventeenth century, especially in analysis and its various applications; and this is equally true of applications to other mathematical disciplines such as geometry and probability theory as to mechanics and astronomy, whose success in the prediction of natural phenomena is well-known1. Strangely, however, the century seemed to end in an impasse. The great mathematicians of the middle of the century departed, Daniel Bernoulli in 1782, Euler and d’Alembert in 1783. Lagrange, at scarcely fifty years of age, judged that the era of progress in pure mathematics was over, and after 1785 he and Monge turned their attention to physics and chemistry, while Laplace was exclusively concerned with mechanics and probability theory. Then came the revolutionary years, which put men of science at the service of the nation and of the war, with the result that the decade 1786–1796 is not marked in France by any significant new mathematical result. Barren periods such as this, connected with social disturbances, have recurred in our time in several countries, but at that epoch, no country apart from France had any active mathematician comparable to those we have just named, which meant that the sterility was universal.