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David Acheson - Five Way Interview

David Acheson is Emeritus Fellow of Jesus College, Oxford, and was the University's first winner of a National Teaching Fellowship in 2004. He was President of the Mathematical Association from 2010 to 2011, and now lectures widely on mathematics to young people and the general public. In 2013, Acheson was awarded an Honorary D.Sc. by the University of East Anglia for his outstanding work in the popularization of mathematics. His books include 1089 and All That (OUP, 2002), The Calculus Story, (OUP, 2017), and The Wonder Book of Geometry, (OUP, 2020). His latest is The Spirit of Mathematics.

Why maths?

There are so many possible answers to this, though I once tried to sum up mathematics at its best in just six words: wonderful theorems, beautiful proofs and great applications. 

Yet I’m inclined to give here a quite different answer, for the best mathematics, at any level, really lasts. While I am no philosopher, it seems to me that so many good things in life are here today and gone, if not  tomorrow, then in, say, 50 years’ time.  

And mathematics at its best just isn’t like that.

Why this book?

About 20 years ago I set out to write an ambitious book for the general public on the three great pillars of mathematics, namely geometry, algebra and calculus. The idea was to go one step further than traditional ‘popular maths’ books, by helping the reader to actually do some mathematics, as well as be inspired by it. And as the years went by, the book got steadily bigger and bigger, and eventually split into three.

The first to be actually finished was The Calculus Story, in 2017, followed three years later by The Wonder Book of Geometry. In a sense, then, the new book, with its slant towards algebra, completes a trilogy. 

Yet, even as I was writing it, I could feel the book gradually turning into something rather different, and that it was really going to be about mathematics at its best using only simple materials. And that is why, in the end, it narrowly missed out on some dubious title like ‘Fun with Algebra’, and became instead The Spirit of Mathematics.

Would we be better teaching what you might call ‘popular maths’ to school children, only adding in most of the detailed ‘how’ for those who are going to require it further at A-level/university?

I sometimes wonder if mathematics has almost become too successful for its own good. So many people want it – or at least need it – but they want or need different parts of it and for different purposes. This presents schools with a big problem, and I certainly wouldn’t claim to have the solution.

Another reason why I am hesitant about answering the question is that I have virtually no experience of actually teaching in a school. When I last ‘taught’ 6th-formers, for instance, I was on stage at the Piccadilly Theatre in London, in a big maths show, demonstrating the mathematics of vibrating strings with my electric guitar.

For what it’s worth, however, I do believe that schools would do best to help pupils develop a ‘big picture’ of mathematics, guided largely by its history, alongside the gradual acquisition of the most elementary mathematical skills. And I would suggest that they do this, too, almost from the very beginning, in primary school. 

This is because I have always believed that there is much to be said for the dictum: ‘if you have no idea where you’re going, don’t be too surprised if you never get there.’

What’s next?

I plan to write a book on dynamics, but, once again, aimed at the general public, and with a fairly strong historical slant, as with The Calculus Story.

What’s exciting you at the moment?

The book that I’m writing at present. Unfortunately, I can’t tell you anything about it, because I never talk about the book I’m actually working on.

This is not out of some absurd fear that my ideas might get stolen, but because of an almost pathological fear that those ideas might end up simply as ‘hot air’. For talking about writing a book is infinitely easier than actually doing it. 

In short, I’m with the humorist Peter de Vries, who once said, so memorably: ‘I love being a writer. What I can’t stand is the paperwork.’

Image by Geraint Lewis


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