If a KS4 or KS5 student asked you to suggest a book on mathematics to read, what would you recommend? You would no doubt want to choose something that was accessible, challenging, stimulating and, perhaps, most importantly, inspirational.

My choice would be “Infinite Powers” by the Cornell University mathematician, Steven Strogatz, which was published last year. I do have a slight bias here as the book is about the area of mathematics which I think is the most interesting and has had the greatest impact, namely Calculus. The second paragraph of the book’s Introduction suggests that Strogatz would agree with me on this point: It’s a curiosity of history that the world was changed forever by an arcane branch of mathematics. How could it be that a theory originally about shapes ultimately reshaped civilisation? “Infinite Powers” seeks to answer this question.

The book starts by looking at the ideas about infinity, in particular, the work of Archimedes. Strogatz describes some of the ideas that Archimedes had around calculating the area of a parabolic segment using techniques that, in modern terminology, we would simply call passing to the limit. Strogatz also makes the interesting point that, as the Greeks regarded mathematics as something existing completely separate from the real world, they were never able to make the connection between curves and rates of change; that had to wait several centuries for Newton (and Leibniz!).

In Newton’s case, his work was carried out in isolation at his mother’s home in Lincolnshire following the closing of universities due to the bubonic plague. Periods of social distancing can therefore be very productive, no matter how difficult they may appear at present.

The heart of the book is the development of differentiation and integration, and how these ideas have been ever since (for example, in the iPhone). Strogatz has clearly worked hard to make sure his explanations are understandable for someone with a moderate mathematical ability but willing to spend the time carefully thinking about what they are reading.

And this is, of course, what we as teachers should be expecting and encouraging our students to do. Indeed, the first Teachers’ Standard requires the setting of high expectations which “inspire, motivate and challenge”. Encouraging any student to look at Infinite Powers, or many of the other fine popular maths book by Hannah Fry and others, seems to me a perfect way to fulfil this standard.

Finally, returning to my earlier point about the importance of Calculus, if you disagree with my view of the importance of Calculus, then I simply refer you to the physicist, Richard Feynman - he advised someone to learn the subject as “it’s the language God talks”.

By Nick Owen