Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has. ↗
In the book, I make the point that here we have string theory and here we have twistor theory and we don't know if either one of them is the right approach to nature. ↗
My own way of thinking is to ponder long and I hope deeply on problems and for a long time which I keep away for years and years and I never really let them go. ↗
People think of these eureka moments and my feeling is that they tend to be little things, a little realisation and then a little realisation built on that. ↗
The idea is if you use those two shapes and try to colour the plane with them so the colours match, then the only way that you can do this is to produce a pattern which never repeats itself. ↗