I’ve been thinking about how I might have taught maths to my children if I’d known at the start that the subject was in its infancy.
The problem, as it turns out, is that we’ve been doing it wrong.
We’ve been trying to teach children the principles of algebra, and the problems we are struggling to solve.
Instead, we are teaching children to think in terms of abstract concepts and abstract numbers.
What this means is that the very thing that is the essence of mathematics, and what makes it the foundation of modern science, is a fundamental mistake.
In a way, the problem is not that maths is too difficult, but that the methods we are using to teach it are too simplistic.
I know that I have been teaching maths to some of the most intelligent children in our society for a number of years now.
And it is not just in this context that I think the problem lies.
It is the very idea that mathematics is the same as other subjects, and we have learnt to think of it as a different subject entirely.
Let me start with some simple mathematics.
There are three fundamental properties of a mathematical function: it is a function of its arguments, it is symmetric and it is an object of the form f(x) = x * x + y*.
If we have defined these properties, we can then start to imagine what mathematics would be like without them.
This is an essential insight, for the same reason that we learn the names of the numbers we encounter by simply memorising the symbols we see.
When we begin to imagine mathematics without these three fundamental characteristics, we realise that we are still learning the subject, and that the concepts we have come up with about the subject have nothing to do with how we actually do mathematics.
And what we think of as “mathematics” is in fact the result of our thinking about mathematics.