Infinite Powers

by Steven Strogatz (Houghton Mifflin Harcourt, 2019)

Calculus for Everyone

Infinite Powers explores calculus and its history for a popular audience. Steven Strogatz has succeeded both in applied mathematics and in public communication, and the book ranges freely between basic but powerful examples (such as the caloric value of bread slices plotted as a linear function), historical vignettes, and broad perspective. He situates calculus as a human innovation that has carried forward the work of many, ever since the ancient Greeks formalized geometry.

Knowing About vs. Knowing How

This book is an excellent resource for motivating the study of higher mathematics, whether "higher" means algebra, trigonometry, or calculus. Yet a continual tension in the community college math classroom is the distinction between knowing about a topic and becoming personally fluent in its use. The book has surely sparked curiosity in many prospective students, but performing algebraic manipulations smoothly and consistently is a different ballgame from reading about how symbolic algebra opened doors to human advancement. The hard work of gaining the skill is left to the reader as an exercise.

An Inflection Point

At this inflection point for AI, I find that my students have a newfound clarity, if not about their role with regard to technology (someone who knows about it? someone who wields it fluently? someone who builds it?), then at least clarity that the question is worth asking. Strogatz, writing in 2019, predicts that AI will be able to generate proofs of ancient puzzles and even display insight, shedding light on the meaning of a puzzle as well as its solution. As the development of symbolic algebra expanded the frontiers of human thinking, so is the development of AI. Infinite Powers can inspire students to ask where they stand; the classroom is where they build the fluency to answer.