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Keywords: Mathematics, biography, history of ideas Title: Infinite Powers Author: Steven Strogatz Publisher: Atlantic Books ISBN: 978-1786492944 Media: Book Verdict: Recommended — and not just for math geeks

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Asked to think about the invention of calculus, most of us will think of Isaac Newton and Gottfried Liebniz, but as Steven Strogatz makes clear there is a rich pre-history of calculus that goes back to Archimedes and other ancient Greeks. Indeed, this is a very wide-ranging book that covers not just the people but also the fundamental ideas that they developed and refined and which in the end contributed to the body of math we now think of as calculus.

For those not mathematically inclined there is always the worry that a book like this is going to be hard going or filled with strange mathematical notation of the type they left behind at school. But one of the beauties of this book is that it manages to convey complex mathematical ideas in a very relaxed and informal way. The concepts are here, but not the notation or the learning by rote examples that people remember from school. In fact the book reverses the school-type methods and focuses on ideas and concepts and not on mechanistic application of rules to solve questions. It makes this an ideal book to read alongside a calculus course at school and college — the two approaches really complement each other.

The ideas of infinity and change are fundamental to calculus — and these are the threads that connect Archimedes to Fermat and to Newton and Leibniz and the others who worked towards the development of the tools and techniques that have made the modern world. And that's not just said for effect — our very idea of the universe, from Einstein to string theory, are expressed in the language of calculus. Calculus is not just a set of mathematical tools, it's a philosophical approach that is connected in some very deep way to the structure of the world around us.

These ideas are explored in a highly readable and enjoyable way. Steven Strogatz is an able writer as well as a leading mathematician specialising in dynamic and complex systems. His love of the subject is on display here, and also his desire to bring math to the public. He is a great communicator with a mission to make complex ideas understandable and relevant to the general public.

Highly recommended — especially for those who've always wanted to dip a toe into calculus but have been afraid to. And for those of us who've done calculus courses before, there are still plenty of new ideas and new connections that you'll pick up from the book.