The price of ignorance;Platform;Opinion

24th December 1999 at 00:00
Barry Lewis maintains that anyone without mathematical skills will be left behind as modern companies thrive on using sophisticated maths for commercial advantage.

HOW many people have you met who wear with pride the public image of ignorance in mathematics? Contrast this with the furtive, yet universal, shame of not being able to read. How can this be in otherwise well-educated people?

If there is one thing we have to do in Maths Year 2000 it is to release a virus into society that replicates and takes over its host, producing profound changes in mathematical attitudes and understanding.

Many people think of mathematics as numeracy - the facility to understand and exploit everyday numbers and measures. That's important but only a starting point. It's not difficult to see the commercial advantages of such skills. Multiplication of numbers can be viewed as representing wealth.

A farmer's prosperity is dependent on the crop he can produce. These crops, in turn, depend on the area that is available to him. The area is the product of the length and width of his field, and this is where the mathematical concept of a square comes in: x2. A field that has length and width equal to x, has area equal to x2. So wealth is a square quantity. See practical numeracy morph seamlessly into abstract mathematics.

The mathematics doesn't stop there, either, because the same farmer's prosperity is now measured by a volume: the amount of his harvest. The volume is the product of three lengths and this is where the mathematical concept of a cube comes from: x3.

If we go back to the early 1500s in Italy, we find a group of mathematicians who competed with each other as problem-solvers in the service of merchants and traders. Mercantile society was increasingly concerned with problems of trade, exchange rates, profits and cuts, and these could often be cast as mathematical problems requiring the solution of an equation.

The mathematicians used their mathematical prowess as a form of advertising - and in the competition to impress potential clients they would spend time solving new problems.

Linear and quadratic equations had already been slain by previous mathematical hunters; the prize lay in the cubic equation. The first mathematician to slay this particular dragon could publish the results and secure ever more domination in this competitive market.

This suggests that mathematics is not unlike many other disciplines - music, for instance - which developed under the same sort of patronage and market forces. But mathematics is different. If you look at two manuscript pages of mathematics and of music - a Mozart string quintet and the work of an Indian mathematician, Ramanujan, who worked in England at the beginning of this century - the astonishing thing is that to the first glance they appear so similar.

They are symbols on the page, abstract, stylised and remote - different, yet the same. The treble clef looks for all the world like an integral calculus symbol; the dominant crotchets driving forward the melodic line of the first movement; the continued fraction and its drive to infinity.

Once the quintet plays from the score, we absorb and understand the music - its rhythm, melody, counterpoint and harmonic structure - without necessarily knowing anything about these things. There is a character in Moliere who delights in the discovery that he has been talking in prose all his life. The same thing happens with music: we don't have to understand it to appreciate it.

But not so with mathematics. However well the mathematician plays from the score, we are none the wiser unless we, too, can read and hear the poetry of the mathematics.

That is the challenge for Maths Year 2000 and for us all. We live in an increasingly mathematical world. Modern economies thrive only if they have innovative, world-class companies built on the knowledge, motivation and skills of their workforce. In the new millennium, such companies will be increasingly mathematics-based, in their management, their operation, their marketing and even their products.

Look at financial services, pharmaceuticals and even entertainment. Their infrastructure and their delivery relies on sophisticated mathematics. People without mathematical skills will lose out. This is exclusion.

You probably know what a prime number is: a number divisible only by itself and 1. So the primes are 2,3 5,7... They are the atoms from which all other atomic numbers - that is, the remaining numbers - are made. Euclid, some 2000 years ago, proved that they go on forever. He did this in a particularly ingenius way. Given a collection of prime numbers, he showed that he could construct a new prime number from them, so that they could never end.

Since Euclid's time, mathematical game hunters have tried to bag bigger and bigger primes, a sport made easier by the appearance of powerful, high-speed computers.

A decade ago, an American mathematician, Martin Hellman, stumbled by accident on the so-called Public Key Cryptography. This is an open method of encoding and decoding information that is universally available but, paradoxically, secret and uncrackable. It relies on huge atomic numbers, so gigantic that no computer can find their prime divisions. Publicly, one such division is known, so anyone can encode a message. Privately, so is the other, but no computer can find it.

This is the method behind all our financial transactions on the web. Mathematics has a habit of being driven by the abstract "why", then delivering in a hard-edged commercial and technological "how". We ignore it or dismiss it at our peril.

Barry Lewis is director of Maths Year 2000

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