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.
Roger PenroseIt is always the case, with mathematics, that a little direct experience of thinking over things on your own can provide a much deeper understanding than merely reading about them.
Roger PenroseAs you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.
Roger Penrose