Review: Infinite Powers

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When I tell people that I’m an engineer, my wife likes to follow up that comment with, “He does math all day long.” A common response is, “Oh, you must really like math. I didn’t enjoy it in [insert level of schooling here].” To keep the conversation moving I agree, and while I do like math, I didn’t always. Until I started studying calculus, math bored me. Algebra existed as a set of rules; geometry, though my introduction to proofs, seemed too abstract. But when I first solved a derivative, my indifference turned to frustration and intrigue. My plan to take only enough math to get an engineering degree changed to a serious contemplation of switching career paths to applied mathematics (with an eye towards physics grad degrees). Ultimately, I stuck with the engineering curriculum but ended up studying higher level mathematics, and to this day, I still read about and love math. Part of my studies now involves going back and filling in what I missed during previous years. One of the voices to which I turn is Dr. Steven Strogatz, and his latest book, Infinite Powers, fills in details about calculus that I lacked. His explanations don’t rely on the familiar equations but, instead, root themselves in history, in logic, and in excellent prose. Infinite Powers transforms calculus from equations into meaning.

TL;DR

In Infinite Powers, Dr. Steven Strogatz teaches us how to use our microwaves to calculate the speed of light. I’m not kidding. That’s all the recommendation this book needs. Highly Recommended.

Review Infinite Powers by Steven Strogatz
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From the Publisher

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus – how it works and why it makes our lives immeasurably better.

Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.

As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

The Story

In Infinite Powers, Dr. Strogatz starts with Archimedes from ancient Greece and carries on to some of today’s most unique challenges. It is the story of calculus told as a continuum of human learning. Often, the public thinks that scientific breakthroughs happen when lone geniuses discover something new, but in reality discoveries occur when people improve upon the work of others. In Infinite Powers Dr. Strogatz traces the methods Archimedes used to Newton and Leibniz, who are the inventors or discoverers1 of calculus. Along the way, we learn about contributions from Fermat, Galileo, Descartes, Arabic, and Chinese mathematicians. But we don’t stop at the discovery era. Infinite Powers continues on to Fourier and Sophie Germain2. We even get to see how calculus is being used today to treat HIV patients, to create microwaves, and, near to my own heart and pocketbook, help the 787 fly.

The Writing

Math possesses a strong language of its own rooted in symbols and logic. While I view this as a strength, I also know others view the equations, Greek letters, and symbols to be inscrutable. Others have said that math texts tend to be dry reads. For anyone who thinks this, “Infinite Powers” is the book for you. While equations do exists, they are few. Dr. Strogatz takes the time to explain, in detail, what each of the symbols means. But the majority of the book reads more like a history text than a mathematical treatise. While it doesn’t spoon feed the reader, it doesn’t bog down in jargon. Clarity and simplicity are the descriptors I have already used talking about this book with friends. Dr. Strogatz does an excellent job describing what the math is actually doing. The reader will NOT be able to do any calculus after reading it, but he/she will understand how powerful a tool it is.

There are graphs and pictures throughout the book. In my advanced reader’s copy (ARC), the graphs didn’t show up. So, I cannot speak to their quality; however, with my background and the detail of Dr. Strogatz’s descriptions, I could picture what his intent was with the graphs. That should be an indicator of success for the prose of this book.

Ugh, Math, Really?

Bear with me here as I get on my soapbox for a minute. One of the other responses that I get when I’m introduced as an engineer is, “You must be really good at math.” And compared to most people, yes, I am good at math. But I’m good at math for one reason only, I’ve been practicing it in one form or another for the last 23 years. In the martial arts, there’s a saying that a black belt is simply a white belt who didn’t quit. To me, that’s all that math is. I’m good at math and calculus because I didn’t quit doing math. The general public often thinks that math requires a certain mindset or, even, a certain person. No, it requires practices and tenacity. The reason that I stuck with math is because of teachers in high school that showed the same enthusiasm that Dr. Strogatz shows in this book. Teachers and professors who care that students understand a subject make this world a better place. After reading “Infinite Powers,” I have no doubt Dr. Strogatz is a teacher than inspires students. I can’t help but wonder what could happen if a book like this gets into the hands of someone who thinks they have to be good at math to understand it.

Math as Art

Though we use math in the sciences, I’ve come to view it more as an art. The mathematician, engineer, chemist, or whoever must know and understand the tools math gives us in order to solve problems, and like a painter picks and chooses the right brush to add to the painting, the problem solver picks and chooses the correct mathematical tool. It’s a creative process that, instead of being hung in a gallery or museum, zips down the road, flows through our veins, or launches a satellite into space. Dr. Strogatz demonstrates the versatility and creativity that we are capable of when using calculus. Whether putting satellites in space or determining how viruses spread, calculus is a tool for delving into nature’s mysteries. Infinite Powers stirred that creative sense, that feeling of awe at being able to see into the universes internal mechanisms. At the same time, it reminded me of the ingenuity of the human animal to seek out and explore the world around us. Dr. Strogatz conveys the beauty that one can find in math, and I felt that thrill of discovery again as I read this book.

Infinity

Originally, I requested this book because I thought it was about infinity. That mathematical concept that looks like an 8 fell asleep, ∞. Instead, it was about calculus; so, I went into the first few chapters with the wrong expectations. Dr. Strogatz discusses infinity but not enough to satisfy me. And throughout the book, he does reference back to the topic of infinity, but it feels more like a forced attempt to tie the later chapters to the theme. I’m still hoping that Dr. Strogatz gives us a book about infinity in the same detail and manner that he gave us a book about calculus.

Conclusion

Dr. Steven Strogatz’s “Infinite Powers” details the history and development of calculus. Dr. Strogatz’s ability to relate complex mathematical concepts in clear and precise language is at peak form in this book. For anyone curious about calculus, this book provides answers in delightful, easy to understand prose that will awaken your curiousity.

8 out of 10!


1. There exists real discussions in the mathematical community whether humans invent math or simply uncover it. In the book, Dr. Strogatz gives his opinion. As for me, I’m easily swayed by arguments on both sides; so, I take the cowards path and remain undecided. Click here to return.

2. To get on my soapbox, I didn’t know anything about Sophie Germain prior to reading this book. With a quick and not at all thorough internet search, I say with confidence that this woman is criminally under-known outside mathematical circles.Click here to return.