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One has not even a slight idea of what mathematics is, one does not suspect its extraordinary scope, the nature of the problems that it proposes and solves, until one knows what a function is, how a given function is studied, how its variations are followed, how it is represented by a curve, how algebra and geometry aid each other mutually, how number and space illustrate one another, how tangents, areas, volumes are determined, how we are led to create new functions, new curves, and to study their properties. Precisely these notions and methods are needed to read technical books in which mathematics is applied. They are indispensable to whoever wishes to understand the rapid scientific movement, the manifold scientific applications of our times which day by day tend to modify more profoundly our fashion of thinking and of living.

Jules Tannery
French mathematician, 1848 1910
Notions de Mathematiques, 1903