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.

Understanding is, after all, what science is all about — and science is a great deal more than mindless computation.

The basic theory in twistor theory is not to add extra dimensions.

It 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.

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

our present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake up