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Arthur Benjamin: When mathematics is magic

In conversation with ‘mathemagician’ Arthur Benjamin

To those on the outside, the words ‘mathematics’ and ‘fun’ won’t often appear in the same sentence. Most people outside the world of science and technology probably reach adulthood with a lack of nostalgia or affection for a subject whose sole purpose of existence was to be endured rather than enjoyed, and have as a result become ‘maths-phobic’. For Arthur Benjamin, author of ‘The Magic of Maths’, this is nothing short of a tragedy, because his chosen subject is one that describes both the physical and abstract world around him.

Maths professor at Harvey Mudd College in California, Benjamin says that he has always “gotten along well with numbers, for as long as I can remember. For me, mathematics has always being a fun mental challenge. And I found that as a kid it was an indispensable tool for me to simply play games better, whether it was Monopoly or backgammon, poker or bridge. But then, as I went on to university I began to see more applications for mathematics, and today as a college professor one of the things that I enjoy most is sharing my passion for the subject.” Working with maths, he says, “you get a lot of ‘light bulb’ moments. And when you see the bulb go on in others, that’s a great experience.”

The degree of Benjamin’s passion for the subject is revealed by the fact that he calls himself a ‘mathemagician’; it’s a word he clearly likes. When you watch a magician perform, you witness reactions of awe and disbelief, enthusiasm and wonder. “When you see a mathematician lecturing to a group of students, you should get exactly the same reaction.” In his book, as early as chapter 3, he is investigating a phenomenon that all children encounter as their first moment of mathematical magic: the nine times table. “So you can do magic tricks with this number and you can get the magician’s audience response. But my question is not so much what, but why?

“Unlike so many other subjects, the facts are true because of reasoning and not because the facts are merely established. You don’t often get to say in mathematics that something is the way it is, simply because that is the way it is. There is something fundamentally important going on here.”

Language of technology

“I’m hoping that this book will be the one that everybody wished that they had at school when they were studying mathematics. And that’s because not only do I try to present important aspects of mathematics in a clear way, but also I am trying to communicate the fun, the beauty and the magic that is so seldom taught in school these days.”

The reason for this lack of engagement is because “everyone is so preoccupied with testing that they focus on teaching a smaller body of material.” What this means is that “the joy of mathematics has been tossed aside. I want students and former students not only to learn the mathematics, but to love the mathematics.”

Mathematics, says the author, is a fundamental language for expressing the properties of everything. But for engineers it is “the home language. Mathematics is the language of science. It’s the language of technology. It’s what allows us to invent, create and improve things. It allows us to make things more efficient, and we couldn’t do that without such an accurate language.”

More than that, while maths is a “serious subject”, as Benjamin’s book attests, “it really doesn’t have to be taught in a dry and serious way”. This worries the author, particularly as his personal observations have led him to believe that “mathematics is not being taught in schools and universities by people who are themselves passionate about the subject. This is something that gets passed on. On the other hand, the countries that seem to be producing the next generation of mathematicians - such as China and India - are the countries that value the subject most. Not just in terms of remuneration of teachers, but in absolute terms of how important the subject is. The people who go on to become maths teachers in countries like Singapore and South Korea are among the best and brightest in their respective societies. And yet in countries such as the United States and the United Kingdom, those who are really good at maths are in some ways discouraged from actually teaching.” One of the reasons ‘The Magic of Maths’ is such an important book is because it sets out to supplement the curriculum by opening people’s eyes to the idea that arithmetic is a critical aspect of a subject that is rarely taught properly.

The biggest problem with the way that maths is taught today is that it is confined to rule-based thinking. “We are taught that it is a discipline where rules are learnt for the sake of learning rules.” That will, Benjamin concedes, teach you something about how mathematics works. But it won’t teach you anything about why it is so important or what is going on. “Imagine if we taught music in a way that students were compelled to write the notes accurately and neatly, but at no point were invited to consider the beauty of music.”

All things being equal

Unless you have a maths degree, the balance of probability is that sooner or later you will reach a point in ‘The Magic of Maths’ where you can go no further. It might be a book that describes the author’s affection for the subject as having magical properties, but it is not a magic book. By which I mean you will not become a genius simply by reading it. But even the novice, through various re-readings will come to realise that you know more about calculus or infinity than you thought.

You will also have reached a more elevated understanding of why a subject that seems abstruse to outsiders is a matter of everyday magic. *

The Magic of Maths’ by Arthur Benjamin is published by Basic Books, £10

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