Book Review-Infinite Powers By Steven Strogatz

After having been trained in the dark arts of engineering, I considered myself, if not a full-blown expert, at least well versed in calculus: what it is, what the idea can be used for in my engineering specialty, and some of the history about calculus through my classes. I now happily admit to my unreasonable hubris. Steven Strogatz is the master of all that is calculus, what it was, how it came into being, where it is now, and possibly where it is going to be in the future.

My initial arrogance concerning my knowledge on the subject made the initial chapters of the book flow by quickly, I read the historical notes that Strogatz included as a sidelight to the main discussion — something to entertain the less informed of the general reader — I wondered why we would need to know the arcana of ancient mathematics, even I also fancied myself a nerd for history of mathematics? Little did I realize how important these historical notes will be: to drive later discussions as well as to form the foundations of the macro view of calculus.

Strogatz frames the story of calculus in ten chapters, creating the intricate scaffolds that allows the readers to follow the technical developments through history with added notes on the mathematicians that originated the ideas which drove calculus to where it is now. An eleventh chapter serves as his own peering-into-the-crystal-ball statement on what he believes will come in the future. He carefully builds up the structure of the development of calculus and seamlessly build the connections between subjects and shows the open questions that was left at the end of the previous chapters and how the topics covered in the new chapters serves to answers those open questions. It is this attention to the many loose ends and how they were resolved that held my interest.

As Strogatz observed, the teaching of calculus had been subdivided into many subtopics for the sake of convenience, but in so doing, the students had been sold a myth that these subtopics are standalone topic because it suited the purposes of teaching logistics rather than suiting the purposes of gaining a holistic view of what mathematicians throughout history had wrought, continuously.

Chapters 8, 9, and 10 were the chapters that had me holding my breath, for it is in these chapters that Strogatz pulled together all the work from the previous seven chapters, integrated them and brought the story to a denouement, for the moment. It brought together the differential and integral halves of calculus, showed the true powers of the calculus. True to the title of the book, he also forcefully made the point of just how the powerful idea of infinity allowed the method to flourish in the minds of mathematicians, scientists, engineers, and so many more specialties.

One cannot discuss calculus without discussions — many times heated ones — about the two men who are recognized as the progenitor of the largest leaps forward in the calculus: Newton and Leibnitz. Strogatz recognition of each, while nicely put their contributions into the historical context of calculus without delving into the bickering that happened between proponents of either men, which is as it should be, even though the human smallness in me wanted some juicy stories about the two.

Strogatz introduced us to the important women mathematicians which made contribution to the art and science of calculus, their contributions were most often ignored and if recognized, their works were slighted. He gave them credit where it was due, and the book is much better for the recognition.

As I was taking my time reading and enjoying the narrative, I thought about how this book should be made an integral part of the teaching of calculus, a required text taught in parallel with the technical aspects of calculus; a book that answers the “why” and “how did it get this way” questions in parallel with the technical training that answers the “how to do it” questions. I then realized that the reasons that I appreciated this book so much are not the same reasons that the young students in AP Calculus or in college level calculus would appreciate. It took me years of working with the calculus to ask those questions that Strogatz had sought to answer. It takes a certain level of maturity and appreciation for the context of the methods which built up the citadel that is the calculus. I still think that the material in this book has a critical role to play in motivating the understanding of the “how” while also building an appreciation for what our forebears had wrought. As Newton had said: We Stand on the Shoulders of Giants. This book would nicely illumnate that blind spot.

One note of interest. I was reading Mortimer Adler and Charles Van Doren’s book How To Read a Book (Adler 1972) when it was brought to my attention that until the end of the nineteenth century, scientific books were written for the layman, that the habit of having specialists writing only for specialists was necessitated by the increasing complexities that comes with the expansion of knowledge in each scientific topic, so that the necessary knowledge needed to understand scientific books became so broad as to be covered in a single tome. Which I thought was a shame, but I understand how daunting the task of writing science and mathematics books has become. Which makes this tome that much more impressive in that, whether Strogatz realizes it or not, he had accomplished a rare and difficult feat — to communicate this very specialized and complex topic to the general public — a general public that has varying levels of a priori knowledge to draw upon to aid in their comprehension. He has joined the pantheon of authors which serves the knowledge of everyone, if they chose to read the book. He has served the role of the public intellectual by writing this book.

This is a remarkable book from my perspective, it filled in the gaps of my knowledge, technical, historical, and conceptual, without losing my interest nor overwhelmed me.

References

Adler, Mortimer. "How to Read Science and Mathematics." In How To Read A Book, by Charles Van Doren Mortimer Adler, 255-269. New York: Touchstone, Simon and Schuster, 1972.