Should we popularise mathematics? If so, how? by Ian Stewart

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Should we popularise mathematics? If so, how?

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Summary: In support of his book Mathematics of Life, Ian Stewart looks at the pros and cons popularising mathematics, through books and other means.
Date: 26 May 2011

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In support of his book Mathematics of Life, Ian Stewart looks at the pros and cons popularising mathematics, through books and other means.

Should we popularise mathematics? If so, how? by Ian Stewart

To many people the combination of 'popular' and 'mathematics' in the same sentence is a contradiction in terms. However, sales of popular mathematics books show that there is a strong demand for books that explain what mathematicians are, or have been doing, in terms that are comprehensible without a PhD - or, indeed, without even a GCSE in mathematics. But even if there's an audience, we can ask whether such books achieve anything beyond preaching to the converted.

Even if they don't, there are good reasons to keep the converts happy. We surely ought to hang on to them; they are the lifeblood of the subject. They influence their friends and their children, and their devotion to mathematics deserves to be rewarded. Anyway, in purely commercial terms, you try to sell footballers' autobiographies to people who enjoy football, so it makes sense to aim mathematics books at people who enjoy mathematics.

A colleague at the University of Liverpool gives about 200 talks every year to school pupils, showing the mathematical magic tricks and surprising puzzles. He particularly likes to show them counterintuitive results, such as the fact that you only need 23 people in a room for it to be more likely than not that at least two have the same birthday.

He tells me that the students split into two distinct groups. One group finds the counterintuitive results stimulating. Pupils in the second group react by rejecting the mathematics: if it gives such unbelievable results, it must be nonsense. Once turned off, they cease to be receptive to any further approaches. So it seems that the benefits of popularisation may not be as obvious as we popularisers would like to imagine.

There is also the tricky question of how far the mathematics can legitimately be simplified. To make ideas comprehensible, most of the detail has to be removed, and the story has to be made as simple as possible. Albert Einstein allegedly added but not more so, although this precise form of words is not recorded. Be that as it may, he was right. There is a fine line between simplifying a complex idea, and misrepresenting it completely. Enthusiasm can easily carry us across that line as we seek to attract a new audience, but we shouldn't lose sight of what we're aiming to achieve, and making mathematics palatable by distorting it is not a sensible objective.

I have a great admiration for people who go out into the suburbs and put mathematical and scientific ideas over to very difficult audiences - people who don't have a natural interest in the subject. In popularisation terms, this is converting the heathen, not preaching to the converted. However, it would be a brave publisher who produced a book aimed solely at such an audience. Publishing is not a branch of philanthropy. I'm not saying that it wouldn't be a good thing if they did, but the reality is that very few can. They'd lose money and go out of business.

It is possible, though, to reach new audiences while avoiding being too ambitious, and this is where popularisation can have a real impact. One way to do this is to write about new and important applications of mathematics. The most distressing feature of the popular image of mathematics, as far as mathematicians are concerned, is that it grossly underestimates the vital role that mathematics plays in society. Most people think the subject died centuries ago, that what they did at school is all there is, and that none of it is useful. After all, how often do you see a mathematician in the movie credits, or buy a gadget that puts mathematics to good use?

Aside from Good Will Hunting and A Beautiful Mind, maths and the movies are largely unrelated. But nearly everyone owns gadgets that do maths. Mobile phones wouldn't work unless they could put messages into a specially coded form that prevents errors creeping in as the message is transmitted. CD players would lose track of the music every time the car hit a bump in the road. Aircraft heading for Tenerife wouldn#t know where they were without a lot of maths. Car SatNav depends on random number generators and trigonometry. And ultrasound scans of your coming grandchild would be impossible without a lot of mathematics.

In school lessons, you can't be taught much of the maths involved, because it's too advanced. Schools have to teach to a syllabus, and the main emphasis is on showing you how to do the sums. That's where popularisation comes into its own: it can show you the main ideas, and explain what they're good for, without expecting you to pass an exam.

Mathematics is everywhere, if you look. It is even becoming vital in biology, the science that traditionally you went into if you didn't like mathematics. It tells us how to provide better cancer treatments, how to keep ecosystems healthy, why tigers have stripes, why evolution is possible, and whether there is one Tree of Life or several.

I think that's so interesting that to be honest I don't really care whether anyone who reads about it is already a convert, or a new member of the mathematical congregation. But I do especially value the new members.

Ian Stewart is author of Mathematics of Life, and Emeritus Professor and Digital Media Fellow at the University of Warwick.