Speaker: Julian Gould

Title: History of Integration

Abstract: When I took real analysis, learning Lebesgue’ integral was motivated by generality and elegance. The measure theoretic foundation has aesthetic advantages over the Riemann integral, and extends the class of functions that can be integrated. On the other hand, Lebesgue’s motivation for developing his integral was not generality for its own sake. As mathematicians grew to understand just how messy subsets of the continuum can be, deficiencies in Riemann’s theory were brought to light. In this talk, we will discuss the history of the integral from Eudoxus to Lebesgue, with an eye toward the specific concrete problems Lebesgue sought to address. We will also turn a critical eye toward the calculus/real analysis curriculum. Research for this talk is primarily from Lebesgue’s Theory of Integration; Its Origin and Development, by Thomas Hawkins.