Two problems:
1. You are in an airport and are walking from the main departure lounge to a rather distant gate. On the way there are several moving walkways. There is a small stone in your shoe, which is annoying enough that you decide that you must remove it. If you want to get to the gate as quickly as possible, and if there is no danger of your annoying other passengers, is it better to remove the stone while on a moving walkway or while on stationary ground, or does it make no difference?
2. You want to give £1,000 to somebody as a 21st birthday present. The person in question is just about to turn 16. A savings scheme offers a guaranteed interest rate of 3 per cent for the next five years, provided you save the same amount at the beginning of each year. What should this amount be so that you end up with £1,000?
And which of those two questions did you find more engaging? If you are like almost everybody, you will already be thinking about the first, but the second will make your heart sink.
Recently, the government has expressed a wish that all schoolchildren should study mathematics up to the age of 18, a view that appears to have cross-party support. As a mathematician, I am a firm believer in the benefits, both direct and indirect, that mathematical understanding can bring. However, I am also aware that many intelligent people thoroughly dislike mathematics, give it up at the age of 16, and have absolutely no regrets afterwards. Will two further years of mathematics really make a difference to such people, other than turning them off the subject even more?
One method that is sometimes proposed for making subjects more appealing is to make them ‘relevant’. In mathematics, this supposed relevance often takes the dismal form of ‘word problems’ such as this: two apples and three pears cost £1.80,
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