New advice suggests children should
study maths until they leave school. Don't be scared though, numbers are
wonderful, fascinating things
Maths is justified in this country because it is useful. Sparks said his proposals were necessary because young people need a better grasp of maths to compete in the job market, where an understanding of technology and numeracy are increasingly important.
I agree. But maths should also be studied for the same reasons we study Shakespeare – it is our intellectual and cultural heritage. Maths makes us more creative and gives us a deeper understanding of the way things really are.
Most other developed nations have non-specialist maths courses beyond GCSE and Sparks said that we need to follow suit in order to compete on the global market. The British have traditionally seen maths as an uncool subject, unlike countries such as France, Germany and America – where geekdom is revered rather than derided – and it would be wonderful if by increasing maths education the subject loses its stigma here.
In all countries, however, the need to pass exams and the emphasis on number-crunching often makes us forget how fascinating maths can be. Here is a list of 10 morsels that, I hope, give a taste of the pleasures to be had.
If we're all going to be doing a lot more maths in the future – we might as well enjoy it.
1 Pi is the ratio of the circumference of a circle to its diameter – in other words, the ratio of the length around a circle to the length across it. It is the most famous number in maths, and the one whose name is most susceptible to puns. Pi's deliciousness, however, comes from the cacophony of its digits. It begins 3.14159 and then continues for perpetuity in disarray, obeying no order and following no pattern. How such a simple ratio – the simplest ratio of the simplest shape – is also the most unruly and irregular is a mystery that still provokes awe and wonder.
2 Maths didn't begin with circles, however. It began with the triangle. The first deductive proof in mathematical literature was the Greek thinker Thales's calculation of the height of the Great Pyramid. He used "shadow reckoning", in which the height of a tall object is calculated by measuring the length of its shadow and considering both height and shadow as sides of a triangle. Triangles thus enabled us to measure the distance to places, such as the top of a pyramid, without needing physically to reach that place. Triangles would later be used to discover the height of Everest, and the distance to planets and stars.
3 Now imagine a person leaves Everest base camp on Monday at 9am to climb to the summit, which he reaches the following Monday at 9am, and as soon as he reaches the top of it he returns, arriving at base camp just one day later. The descent is much faster than the ascent and both journeys involve stops and varying speeds depending on terrain. Is there a spot where he is at the same altitude on the mountain at the same time of day?
4 Before you answer, flick through this newspaper. It contains many numbers – dates, financial sums, temperatures, percentages and so on. Even though I am writing this before most of the other stories are written I will bet my house that about 30% of the numbers in the paper today will begin with a one, about 17% will begin with a two, and only about 5% begin with a nine. In fact, I bet that the percentages are the same in every newspaper published today, not just in the UK but in the whole world. The bizarre preponderance of numbers beginning with a one is called Benford's Law and is not entirely understood, even by mathematicians. Maths always challenges your preconceptions.
5 Another example. When the shuffle feature on iPods was launched, in which music tracks are played in a random order, several consumers complained that it didn't work since often tracks from the same album were played in succession. Surely this was the opposite of randomness, they harrumphed! Yet the study of probability teaches us that clusters of similar tracks are indeed very likely, in the same way that when you flip a coin, you will get surprisingly long runs of heads or tails. In response, Steve Jobs said he would change the algorithm: "We're making [it] less random to make it feel more random."
6 Humour is not an acclaimed feature of mathematics, yet mathematicians are often very funny. Alice's Adventures In Wonderland, the benchmark for wit in children's fiction, was written by an Oxford maths don, Charles Dodgson, AKA Lewis Carroll, and The Simpsons is written by a team heavy with maths and computer-science graduates. As masters of logic, we have a love of illogic. Just like comedians and satirists, absurdity is our stock-in-trade. The quickest way to prove that a statement is true is to show that the opposite of the statement is nonsensical.
7 It's funny to realise that only 200 years ago negative numbers were considered so controversial that an algebra book was published by a top Cambridge scholar in which he called them "a jargon, at which common sense recoils". The book included no negative numbers at all, although the minus sign was allowed in equations. William Frend banished negative numbers because they had no physical interpretation. What, for example, is a negative book? Maths, however, is the study of structures and rules – and it is very ironic that the more abstract it has become the better it is at finding applications in the real world.
8 One fantastic application of a mathematical idea is jangling in your pocket: the 50p piece. For a shape to be permissible as a coin it has to have constant width, so it can be usable in slot-operated machines, which read a coin's value by measuring width. Circles obviously have a constant width. In the 60s the Decimal Currency Board wondered if there were other shapes that had a constant width in order to help blind and partially sighted people tell the difference between different denominations. The "equilateral curve heptagon" used for the 50p does have that shape – its height is always the same at whatever point you rest it on its edge. This remarkable property means that if you made two rollers each with a 50p piece shape as a cross-section, you could roll an object on the top of them and it wouldn't bob up and down.
9 Money management is more than fiddling with 50p pieces. Numeracy keeps us aware, for example, of exponential growth. A £1 investment earning 20% a year compounded interest will grow to £6 in a decade, to £9,000 in 50 years and to £82m in a century.
10 What I like about maths is how it requires the creative solution of problems. Let's return to our climber on Everest. Yes, there is a spot where the climber is at the same altitude on the mountain at the same time of day, and here's an intuitive proof: the climber leaves basecamp for the ascent at 9am on a Monday and takes a week. He descends from the summit at 9am and takes a day. Now superimpose both trips on the same day, as if two climbers are heading towards each other, one from the top and one from the bottom. Their paths must cross – at that moment they share the same altitude at the same time.
• Alex Bellos is the author of Alex's Adventures in
Numberland.
