Colloquium

"The Fundamental Theorem of Calculus: History, Intuition, Pedagogy, Proof"

by

Dr. V. Frederick Rickey

Professor Emeritus of Mathematics, West Point

Distinguished Teaching Professor of Mathematics Emeritus, Bowling Green State University

Abstract: The Fundamental Theorem of Calculus (FTC) was a theorem with Newton and Leibniz, a triviality with Bernoulli and Euler, and only took on the meaning of "fundamental" when Cauchy and Riemann defined the integral. FTC became part of research mathematics in the 19th century, but waited until the 20th century to take hold in classroom mathematics. We will discuss the transition from clear intuition to rigorous proof that occurred over three centuries. Most importantly, we shall explain why both parts of the FTC are vital.

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