This is the first of two posts on the topic of creativity. Do not get too excited. I may not get around to the other.
Most people, I suspect, do not think of mathematics as a creative endeavor. This is understandable. If all you have seen is quadratic equations, ratios and trigonometry, you can be forgiven for finding the creative aspect hard to identify. Indeed creativity is the enemy of success. Pupils who try to find their own way to solve quadratic equations always gain null points in the exam. Just follow the process, and all will be well.
On the other hand, really good mathematics is, necessarily, profoundly creative. If you are going to solve a difficult problem – one which has been around a while – there is no point trying the obvious stuff, because that will all have been tried before. Difficult problems only get solved when a mathematician tries something really left-field, and it still somehow works.
Reading this sort of work takes your breath away. When I read (for example) Dennis Sullivan’s no wandering domains theorem, I am left gasping. Wow. How did that happen? I felt the same way I felt when I saw this picture:
So now I am going to really push the boat out.
Actually in Maths something even more remarkable is happening. Not on has someone done something amazing, breathtaking, awe-inspiring. But it worked – in other words the whole universe has this amazing, breathtaking, awe-inspiring but totally objective thing going on. And that is what really astonishes me, and keeps me doing this whole maths malarkey.