Infinite Powers: The Story of Calculus

"I learned so much from this book, mostly about the history not just of calculus but of our subject, mathematics, in general. The other thing I really like about it is that it explains calculus in a way that you’re not really ever taught at school. Calculus is the subject of change and understanding how things vary with each other. Strogatz takes this really intuitive view of it. He breaks things down to their simplest components and shows you why these rules—that you learn almost as rote in school—work. For me, some of the ideas in the book I’d seen before, which is to be expected with such a well known subject areas, but the surprising thing was that a lot of them I hadn’t. I really enjoyed learning something new about my subject. For example, I didn’t know how far back calculus went. I had read that people were doing something similar to calculus before Newton and Leibniz, but Steve argues in the book that everything people were doing all the way back to Archimedes was actually calculus—just in a slightly less formal way. Newton and Leibniz formalized the mathematics of calculus, but people had been using these proto-calculus tools for millennia. It’s a really, really great book. “Everything people were doing all the way back to Archimedes was actually calculus—just in a slightly less formal way” The other thing he does is make calculus really accessible by using lots of nice, neat analogies, and also by showing the applications of calculus. He talks about how calculus was used to help better understand the dynamics of HIV infections in the body. It wasn’t, as most doctors thought, that HIV was just lying dormant for many years in a person before it suddenly accelerated and became AIDS. It was actually that the body’s immune system was fighting this constant battle against HIV. HIV particles were being produced incredibly rapidly and just as rapidly the body was killing them off, to leave you at this sort of steady state. And then, eventually, the immune system loses its battle. He talks about how some very simple ideas from calculus effectively earned two scientists a Nobel Prize for their work on HIV. As a mathematical biologist, that’s a story I didn’t know, and one I’ll probably borrow and put in my mathematical modelling course. Motivation is a really important part of wanting to learn anything. We often lack it in math, because it seems that we’re so divorced from the real world. But throughout the book Steve just makes point after point and shows application after application where calculus can be used. And it’s true. I was talking about the weather before: the equations that I was talking about are differential equations that are written in calculus. Almost any place you want to do some modelling of the real world, you need to use calculus. No, he isn’t. It really is fundamental. The subtitle of the book is ‘the language of the universe.’ We talk about math more generally being the language of the universe but calculus is a large part of that."

"In this book, Steven Strogatz takes us on a magisterial journey through the history of mathematics, charting the development of one of the greatest achievements in human thought. Strogatz is Professor of Applied Mathematics at Cornell University and one of the most highly cited mathematicians in the world. He writes popular science books that make challenging material accessible and are a joy to read. Infinite Powers is a wonderful motivational book for anyone taking a course in calculus. For those readers who remember calculus with dread from maths classes of yore, here is a text that explains just why the material has always had such a key place in our curricula. It charts a history of ideas that sought to make sense of the world through mathematics—to develop methods that find the deep laws and patterns that govern nature and enable us to build everything from computers to jet engines, televisions to microwaves. Support Five Books Five Books interviews are expensive to produce. If you're enjoying this interview, please support us by donating a small amount . The book explains how key developments in the work of Pythagoras, Archimedes and other mathematicians from the classical era laid the foundations for calculus, how these ancient scholars developed some of its most important concepts, from infinity to the ratio underpinning pi. The text is suffused with examples to lead the reader through the key concepts and developments that eventually led to the methods of Newton and Leibniz. Here he recounts the battle of ideas, the different personalities behind modern calculus. Strogatz brings the story of the calculus right up to date with its applications in contexts as various as modelling HIV epidemics to the differential equation that predicted antimatter, understanding how DNA coils to AI and data compression. Everyone who reads this book and has access to a microwave should use his shredded cheese method to calculate the speed of light. Such is the power of the infinitesimal calculus! Read more about Infinite Powers. Science is a profoundly human endeavour. The stories of triumph and success in science, alongside the failures and despair are, compelling. They demonstrate that scientists are human. They demonstrate the power of the scientific method but also invite us to think how things can go wrong. The human story of science is a fantastic way to inspire us all."