The mathematical theory of continuity is based, not on intuition, but on the logically developed theories of number and sets of points.

Voltaire called the calculus "the Art of numbering and measuring exactly a Thing whose Existence cannot be conceived."See Letters Concerning the English Nation p. 152

In making the basis of the calculus more rigorously formal, Weierstrass also attacked the appeal to intuition of continuous motion which is implied in Cauchy's expression -- that a variable approaches a limit.

Thus the required rigor was found in the application of the concept of number, made formal by divorcing it from the idea of geometrical quantity

Most of his predecessors had considered the differential calculus as bound up with geometry, but Euler made the subject a formal theory of functions which had no need to revert to diagrams or geometrical conceptions.

Carnot, one of a school of mathematicians who emphasized the relationship of mathematics to scientific practice, appears, in spite of the title of his work, to have been more concerned about the facility of application of the rules of procedure than about the logical reasoning involved.