A Concise History of Mathematics

Schouten in 1914), suggested classification of direct quantities on the basis of group theory, thus reaching a position that Cartan, in his quiet, independent way, had also reached.

This brings us to the so-called vector analysis (partaking of both algebra and calculus).

This paper became quite famous after 1913, when Einstein adopted that calculus for his general relativity and gave this calcul absolu the name of tensor calculus.

Abstract spaces spanned by vectors of finite length led to abstract metrical spaces, named after Hilbert.

More and more the ancient concept of mathematics as the theory of quantity was abandoned; more and more it was seen as the theory of structure in general.

We find in his works our modern concept of continuity.

and called the limit for i → 0 the fonction dérivée, y’ ou f’(x).

this paper Gauss dispelled forever the mystery that still surrounded complex numbers by his representation of them by points in a plane.132

In the words of Lazare Carnot, the organisateur de la victoire in the French Revolution, who also worried about Newton’s method of infinitesimals:

“The differentiation of equations consists simply in finding the limits of the ratio of finite differences of two variables included in the equation” (see Section 7 of this chapter).