Though calculus is a notoriously difficult and abstract area of mathematics, its applications form the basis for much of modern technology, science and engineering. Prof. Steven Strogatz, applied mathematics, explores this topic further in his upcoming book, “Infinite Powers: How Calculus Reveals the Secrets of the Universe.”
Strogatz explained that the work is composed of three main sections. The first and most central is history, where Strogatz sets out to explain the evolution and development of calculus, from Archimedes to Newton and Leibniz to the modern day.
Next, Strogatz explores a “360-degree view” of the uses of this branch of mathematics and explains the applications of the expansive field of calculus.
Furthermore, he expands upon the fundamental concepts of calculus, from specific differential equations to big-picture ideas like that of infinity.
“What defines calculus is the strategic use of infinity… The book is organized around a thing I call ‘The Infinity Principle’ … it’s this idea that to solve hard problems, you chop them into infinitely many bits, and analyze the bits, and then put them back together,” Strogatz said.
Strogatz wrote the book “for people who didn’t take calculus, or who did take it and didn’t get much out of it … it goes by in a blaze for many people, and they don’t have a great understanding of the subject,” he said.
Despite targeting the everyday reader, Strogatz has not sacrificed the ambitions or passions of his claims.
“What I’m trying to argue in the book is that this is one of the great ideas of all time … it’s something that changed the world, and it’s something that’s very beautiful, powerful and even dramatic,” Strogatz said.
Nowadays, some might argue that learning calculus is not very useful. With the rise of computer algebra systems, the limits, integrals and derivatives that plague freshman calculus are no longer a problem.
“Many cool, modern jobs do use calculus, but many don’t, and many people live perfectly happy lives without doing calculus … understanding quantitative reasoning, how to look at a graph, those are bigger skills that a typical citizen will need in their real life,” Strogatz said.
However, Strogatz argued that the justification for learning calculus has other advantages. Indeed, while not necessary for every occupation, knowledge of higher mathematics does allow one to attain jobs in advanced STEM fields, from quantitative finance to engineering.
Strogatz compared knowledge of mathematics to knowledge of Shakespeare, economics and other fundamentals of being an educated individual. According to Strogatz, if you want to be a part of the conversation, then knowledge of calculus is essential.
For the author himself, writing about calculus has been a challenging yet rewarding process.
“The hardest part [of the writing process] may be trying to figure out … the overall architecture of the book … How much of it was history? How much was explaining the ideas of calculus without history? How much was it about how calculus relates to other things? I wanted it to be about all of those,” Strogatz said.
According to Strogatz, the rewards of the writing process lie in the personal accomplishment that he experiences.
“I tried to do something that I never succeeded in doing before … which was to write a book-length, sustained argument that lasts 300 pages, and that’s not boring or ponderous, that’s really an adventure and an exciting, thrilling ride through a great idea,” Strogatz said.
Having written a dedicated mathematics column for the New York Times for several years, Strogatz has significant experience conveying the joys and wonders of mathematics to the average reader.
Strogatz’s book will be released on Amazon and Kindle on April 2.