Document Type



Mathematics (Pitzer)

Publication Date



Derivative, Peirre de Fermat, Karl Weierstrass, Mathematics, History


Historically speaking, there were four steps in the development of today's concept of the derivative, which I list here in chronological order. The derivative was first used; it was then discovered; it was then explored and developed; and it was finally defined. That is, examples of what we now recognize as derivatives first were used on an ad hoc basis in solving particular problems; then the general concept lying behind them these uses was identified (as part of the invention of calculus); then many properties of the derivative were explained and developed in applications both to mathematics and to physics; and finally, a rigorous definition was given and the concept of the derivative was embedded in a rigorous theory. I will describe the steps, and give one detailed mathematical example from each. We will then reflect on what it all means -for the teacher, for the historian, and for the mathematician.


Please note that this paper won the Carl Allendoerfer Award in 1984.

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© 1983 Mathematical Association of America. All Rights Reserved.