This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

I was indeed very slow as a youngster.

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

Ordinary photons do have spin, they have a notion of helicity so they spin around their direction on motion.

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.

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.

Well I didn't actually see the Matrix but I've seen other movies where with similar sorts of themes.

As for morality, well that's all tied up with the question of consciousness.

If you didn't have any conscious beings in the world, there really wouldn't be morality but with consciousness that you have it.

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

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.

As 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.

I'm pretty tenacious when it comes to problems.

So what I'm saying is why don't we think about changing Schrodinger's equation at some level when masses become too big at the level that you might have to worry about Einstein's general relativity.

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.

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

Well, I don't know if I can comment on Kant or Hegel because I'm no real philosopher in the sense of knowing what these people have said in any detail so let me not comment on that too much.

And these little things may not seem like much but after a while they take you off on a direction where you may be a long way off from what other people have been thinking about.

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.

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.

Some people take the view that the universe is simply there, and it runs along - it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe.

Some people take the view that we happen by accident. I think that there is something much deeper, of which we have very little inkling at the moment.

There is a certain sense in which I would say the universe has a purpose. It's not there by chance.

If the computer-guided robots turn out to be our superiors in every respect, then will they not find that they can run the world better without the need of us at all? Humanity itself will then have become obsolete.

In mathematics we have long since drawn the rein, and given over a hopeless race.

In mathematics the art of proposing a question must be held of higher value than solving it.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

Mathematics is as old as Man.

I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account.

As the existence of a corps of professors of mathematics is peculiar to our navy, as well as an apparent, perhaps a real, anomaly, some account of it may be of interest.

Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.

I read one or two other books which gave me a background in mathematics other than logic.

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

Life has obliged him to remember so much useful knowledge that he has lost not only his history, but his whole original cargo of useless knowledge; history, languages, literatures, the higher mathematics, or what you will - are all gone.

How is an error possible in mathematics?

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

I could never accept findings based almost exclusively on mathematics. It ain't ignorance that causes all the trouble in this world. It's the things people know that ain't so.

If a man's wit be wandering, let him study the mathematics.

Reading music is something that's inherently hateful to me. It makes music like mathematics.

The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.

Mathematics is the art of giving the same name to different things.

You can not apply mathematics as long as words still becloud reality.

My interest in the sciences started with mathematics in the very beginning, and later with chemistry in early high school and the proverbial home chemistry set.

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

Mathematics allows for no hypocrisy and no vagueness.

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.