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On Mathematics at the Time of the Enlightenment, and Related Topics

  • Paul Henry
Part of the Artificial Intelligence and Society book series (HCS)

Abstract

The end of the eighteenth century, the age of the Enlightenment, is a period of doubt and pessimism about the future of mathematics, a feeling shared by almost all the leading mathematicians of the time. On September 21st, 1781, Lagrange writes to d’Alembert:

I began to sense my ‘force of inertia’ growing little by little, and I am not sure that I will still be able to pursue Geometry ten years from now. It also seems that the mine is almost too deep already, and that unless new veins are discovered, it will have to be abandoned sooner or later. Physics and chemistry now offer riches that are more brilliant and easier to exploit, and the taste of our century also appears to be turned entirely in this direction; it is not impossible that the chairs of Geometry in the Academies will soon become what the chairs in Arabic now are in the universities.” As early as 1699, Fontenelle made a similar prediction, saying that mathematics might well soon become complete, while physics, by its very nature, would be endless. In 1808, in his famous Rapport historique sur le progrès des sciences mathématiques depuis 1789 et sur leur état actuel, Delambre writes: “It would be difficult and perhaps rash to analyze the chance which the future offers to the advancement of mathematics; in almost all its branches one is blocked by insurmountable difficulties; perfection of details seems to be the only thing which remains to be done. (…) All these difficulties appear to announce that the power of our analysis is practically exhausted, as was that of ordinary algebra with respect to transcendental geometry at the time of Leibniz and Newton, and that we need combinations capable of opening up a new field to the calculus of the transcendents and to the solution of the equations which contain them.1

Keywords

Eighteenth Century Geometrical Realism Experimental Philosophy Practical Philosophy Natural Metaphysic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag London Limited 1995

Authors and Affiliations

  • Paul Henry

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