I would say the universe has a purpose. It's not there just somehow by chance.

Do not be afraid to skip equations (I do this frequently myself).

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.

But I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality.

Some years ago, I wrote a book called the Emperor’s New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations.

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'.

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.