Making maths a marvel

24th March 2000 at 00:00
The science of numbers and space must be promoted as a thing of wonder to counter its image as boring and irrelevant , says Adam McBride

I WAS disappointed by the lead headline "Maths is not a plus" on the front page of The TES Scotland on March 3. Teachers and practitioners of mathematics are constantly faced with misconceptions and prejudices about their subject. Such a headline is distinctly unhelpful.

The launch of Maths Year 2000 in Scotland, the subject of the report, was an upbeat affair. Unfortunately, perhaps in the spirit of one of Newton's laws of motion, this action has produced an opposite reaction in certain quarters. Although the second part of the article tries to repair the damage, the overall impression for most readers is likely to be negative.

Mathematics does have an image problem. Perhaps mathematicians are partly to blame. We have a good product to sell but we are not succeeding in getting the message across. Our aim should be to convince as many people as possible that the subject is important and relevant.

We have to start early and we can. It is surprising to many people that some of the hardest problems in mathematics rely on concepts that can be explained to pupils in primary school. Fermat's Last Theorem is a case in point: once you have explained what you mean by powers of a whole number, pupils will understand exactly what has to be proved. (The fact that it took the entire mathematical community more than 350 years to find a proof confirms that you often need determination to succeed in life.)

One way of getting an audience interested is to present a modern area of mathematics which impinges on everyday life. Once again, we can go a long way with very simple ideas. Consider codes, by which our lives are ruled. Some are used for identification purposes, such as National Insurance numbers, vehicle registration numbers or ISBNs. Others are used for security, such as pin numbers. How can we send sensitive information from A to B so that no enemy finds out what is going on ?

How safe is it to buy goods via the Internet? Security often relies on the simple fact that it is much easier to multiply two numbers together than it is to start with the answer and try to get the two numbers back again (especially if the numbers have around 200 digits).

What about the weather? Why are forecasts sometimes wrong? Can we predict what the weather will be like in a week or a fortnight or a onth? Some people, like farmers or organisers of outdoor events, may want to know. Mathematicians may call such things nonlinear dynamical systems but the basic idea, namely iteration, is accessible to secondary pupils.

Of course, older areas of mathematics furnish plenty of examples, too. We are constantly being bombarded with statistics, but do we believe what we are being told? Is inflation really going down? Is this financial product really better than all its competitors? We all need some training in statistics, a branch of mathematics, to interpret data or graphs and to avoid being misled.

The subject of statistics is closely related to the theory of probability, which can be used to explain the workings of the National Lottery and other similar activities. The message is that mathematics is relevant to many situations, far more than a lot of people seem to realise.

It might be a salutary lesson for such people to try to list things we take for granted but which require some knowledge of mathematics, often in conjunction with other subjects, to explain how they work. Look, for example, at some of the electronic gadgets around the house. It is quite likely that the liquid crystal displays have been constructed on the basis of mathematical research (possibly in conjunction with chemists). How does an aircraft fly and why is it the shape it is? The answers are supplied by the use of mathematical techniques allied to physics and engineering.

These illustrations make us think of mathematics as a science, but we may also think of it as an art. The subject contains things of great beauty. Look at the geometry of the humble triangle. Who can fail to be amazed by the Euler line or the nine-point circle? If you have never heard of them, find an old geometry book. There is great scope for those of an artistic turn of mind to draw lovely pictures, but there is a lot of serious mathematics, too.

The launch of YM2000 gives us the opportunity to change the general perception of mathematics. It is not an easy subject but a little effort and determination can reap a rich harvest. I hope those who have a negative image of the subject will visit some of the events which will be taking place throughout Scotland in the coming months.

Professor Adam McBride is deputy head of the mathematics department at Strathclyde University and chairman of the Scottish Mathematical Council. He writes in a personal capacity.

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