By Tony Attwood, chair of The Dyscalculia Centre.
There is a fundamental debate in maths over the question of the origin of maths, and it comes down to two basic points.
One side of the argument says that maths is something fundamental and is part of the universe as we know it. It is natural and “out there”, just as, for example, the elements like hydrogen, oxygen, carbon, iron, etc are “out there” as the fundamental building blocks of the universe itself..
The alternative argument is that maths does not exist of itself, but that it is created when people try to explain what is going on in the world. It is a way of seeing the world that human beings have invented to help along their understanding.
Of course, it is true that whichever way we look at it, maths is an amazingly successful way of describing the universe. It is logical (most of the time) and can be used to explain the world and the universe we see around us.
According to some (and this is an argument that goes back to the Greek philosopher Plato) maths suggests to us that there is an order in the universe, in every way we look at it – and that suggests that if humankind disappeared the maths, as well as the universe, would still be out there.
But others argue that we have constructed maths to describe the universe, so of course maths is uniquely set up to reflect the universe. In other words we make up maths as we go along, and as we discover more and more about the universe around us.
But there is a problem because maths is not very successful at describing all the universe. Take, for example, that whole business of the area of a circle, which most of us learn in school as the area equals pi multiplied by the radius of the circle squared.
Which raises the question, why “pi” - a number that we cannot calculate exactly but which starts as 3.14159265359 and keeps on going on and on and on and... And we might be tempted to ask, if maths is all that natural, why is the relationship between the radius of a circle and the area of a circle dependent on such an odd, never ending number? Wouldn’t it be more reasonable for it to be an obvious number like “5”?
After all, a circle is a perfect construction, and the diameter and radius are perfectly straight lines which touch the centre of the circle. So why is all this “pi” business involved?
This sort of thinking leads to the notion that maths is just a way of reflecting reality in numbers, to make it easier to understand and easier to make predictions about things.
And indeed it can be argued that all mathematical models of reality do ultimately break down. I have written elsewhere about how zero is not a number like other numbers – it doesn't work in the same way. We have to accept it in our way of calculating things, but it doesn't actually work as a number.
To take this further, through the investigation by physicists into the way the universe works at a very small level, we find all sorts of strange things going on, with particles affecting each other instantly over enormous distances in a way that cannot be explained by any form of conventional maths. There is also that problem of objects behaving in totally different ways until we measure the object, which seems irrational. How can measuring an object change it?
Now this argument about maths being a natural part of the universe, or a description invented by humankind to reflect what we find, may seem a bit remote and necessary, especially for a site devoted to dyscalculia. But there is a point here.
If one sees maths as part of the natural order of things, and one sees human beings also as part of the natural order of things, it would seem logical that human beings can understand maths.
But if we see maths as a human invention then it is much more likely that there will be some people who simply find that human creation difficult to understand. After all, why should everyone be able to understand everything that people have invented over time? Certainly we don’t expect everyone to be able to understand all art, or all music, or all foreign languages.
I think that this idea, which many people still hold, that maths is natural and obvious, is the reason why so many people find it difficult to understand why dyscalculics can’t grasp maths as readily as most people.
If, however, the thinking were reversed and maths was seen as much a human creation as works of art are, or the ability to play a musical instrument is, then there would be far less argument about whether dyscalculia were real or not.
To start from the premise that maths is a human-invented construction set out to describe the universe is a perfectly reasonable and valid position, and it has the benefit of taking us into a view of the world where we are as understanding of people who find maths difficult as we are of working with people who can’t sing in tune, find modern art incomprehensible, or find learning a foreign language intolerably difficult.