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  • Print publication year: 2003
  • Online publication date: March 2008

13 - Mathematics

from Part II - Disciplines


Considered broadly, mathematical activity in the eighteenth century was characterized by a strong emphasis on analysis and mechanics. The great advances occurred in the development of calculus-related parts of mathematics and in the detailed elaboration of the program of inertial mechanics founded during the Scientific Revolution. There were other mathematical developments of note – in the theory of equations, number theory, probability and statistics, and geometry – but none of them reached anything like the depth and scope attained in analysis and mechanics.

The close relationship between mathematics and mechanics had a basis that extended deep into Enlightenment thought. In the Preliminary Discourse to the famous French Encyclopédie, Jean d’ Alembert distinguished between “pure” mathematics (geometry, arithmetic, algebra, calculus) and “mixed” mathematics (mechanics, geometrical astronomy, optics, art of conjecturing). He classified mathematics more generally as a “science of nature” and separated it from logic, a “science of man.” An internalized and critical spirit of inquiry, associated with the invention of new mathematical structures (for example, non-commutative algebra, non-Euclidean geometry, logic, set theory), represents characteristics of modern mathematics that would emerge only in the next century.

Although there were several notable British mathematicians of the period–Abraham De Moivre, James Stirling, Brook Taylor, and Colin Maclaurin among them – the major lines of mathematical production occurred on the Continent, a trend that intensified as the century developed. Leadership was provided by a relatively small number of energetic figures: Jakob, Johann, and Daniel Bernoulli, Jakob Hermann, Leonhard Euler, Alexis Clairaut, Jean d’Alembert, Johann Heinrich Lambert, Joseph Louis Lagrange, Adrien Marie Legendre, and Pierre Simon Laplace.