Richard Edwards

The “What if?” Habit: How Asking Simple Questions Can Lead to Surprisingly Complex Results

Abstract:

Some of the most useful questions that learners of mathematics can employ begin with “What if...”. Such questions can lead to rich learning opportunities. In this talk, I share the experience of how one student’s “what if” question in a second- semester calculus class led to an exploration of hyper-operations including tetration of complex numbers and brought together the work of Lagrange, Euler, and Lambert. The talk includes interesting mathematical history, beautiful pictures, and reflection on the power of simple questions.

Bio:

Richard "Abe" Edwards is an associate teaching professor of mathematics at Michigan State University. He primarily teaches undergraduate calculus and statistics courses, along with interdisciplinary courses related to the history of mathematics. He regularly leads a study abroad program Europe where students walk in the footsteps of famous mathematicians to learn how mathematics, history, and culture intersect. His research centers on the history of mathematics and its use in teaching, and he is particularly fond of teaching with primary historical sources. He was the recipient of the 2022 Distinguished Teaching Award from the MAA Michigan Section, as well as the 2023 Henry L. Alder award from the MAA.