When I told people that my work with philosophy for children had moved me into mathematics for children, and how we teach it, a lot of them were surprised. They are still surprised when I insist that philosophy and maths are closely related. For many, those two subjects would seem opposite ends of the spectrum: at one end is cold hard mathematics with its truths set in stone, and the other is philosophy, as vague and elusive as a puff of smoke. But this is to misunderstand them both.
Historically, mathematics and philosophy went hand-in-hand for centuries. The mathematician whose name is probably known to the most people, Pythagoras, was a Greek philosopher. And one of the most famous of all philosophers, Descartes, was also a mathematician.
These days, both disciplines have come so far that it would be asking a lot for even a genius to master both. So there probably won’t be another Descartes or Pythagoras, with a foot in both camps. But the two subjects are still linked. One reason why is that they both combine the mental abilities of logic and imagination.
As most of us know from school, we need logic to solve the mathematical problems we are set. When we say to ourselves, ‘The answer to this multiplication must be an even number, because we are multiplying two even numbers together’, that is pure, simple logic. But where does the imagination come in? Well, if you speak to mathematicians who work on the research side, trying to map out parts of the universe of numbers that have not been fully explored, they all maintain that imagination is essential. They mean the imagination to ask ‘What if…?’ and follow a train of thought onto new ground. Or the imagination to conceive of shapes and forms that lesser brains simply boggle at.
The same is true of philosophy. In philosophy, the illogical is not allowed. There are, of course, schools of philosophy which claim that the illogical is a necessary part of thinking. But even this discussion over whether logic is the be-all-and-end-all still puts logic at the heart of things. And as for imagination, yes, the great philosophers have all been hypothetical thinkers, able to picture the world in a multitude of ways.
This is important for the study of maths. Every single school child studies it. To get the maximum from each one, we need to make sure that the imaginative, curious children have the chance to explore maths in that way. Yes, they too need to be drilled and practised on calculation methods. But they need more if they are going to take maths to their hearts.
In the UK, and the US too, taking maths to your heart is quite a comical notion for many. But that’s not the case elsewhere. Many children in East Asia, for example (China, Japan, Korea) claim to love maths. There is no social stigma to liking it, or being good at it. And that is a fact about the whole society, much more than its teaching methods.
Until we in the West take curiosity, imagination, wonder and mystery as essential parts of mathematics, we will lag behind.
We can do this by seeking out questions in maths that are difficult and starting to think about them. And the difficult questions are not only in the difficult areas of maths. Just asking yourself if zero is a number, and trying to prove your answer is enough.
Here are some others to get you started:
What happens if you divide a number by zero?
Does Pi go on for ever? How do we know?
Are there more fractions or more integers (whole numbers)?
How many shapes are there?
How many lines of symmetry does a circle have?
Some of these big questions we can answer. Some we can’t. Some no-one ever will but we don’t know which ones those are.
Philosophy is the missing link that makes maths meaningful, which is why philosophers are very good at sniffing out questions like this. But do you know what? They are not as good as children. Given the chance, children will bamboozle you with queries that strike right at the heart of what numbers actually are. And you won’t be able to answer them sometimes. And that’s great, because it keeps the flame of curiosity alive – for them and you.
**Check out my book The Numberverse: How Numbers Are Bursting Out Of Everything And Just Want To Have Fun.
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