“According to this view, the mind is always capable of this direct contact. But only a little may come through at a time. Mathematical discovery consists of broadening the area of contact. Because of the fact that mathematical truths are necessary truths, no actual 'information', in the technical sense, passes to the discoverer. All the information was there all the time. It was just a matter of putting things together and 'seeing' the answer! This is very much in accordance with Plato's own idea that (say mathematical) discovery is just a form of remembering! Indeed, I have often been struck by the similarity between just not being able to remember someone's name, and just not being able to find the right mathematical concept. In each case, the sought-for concept is in a sense already present in the mind, though this is a less usual form of words in the case of an undiscovered mathematical idea.”
“There are two other words I do not understand — awareness and intelligence. Well, why am I talking about things when I do not know what they really mean? It is probably because I am a mathematician an...”
Roger Penrose
“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 calcu...”
Roger Penrose
“Moreover, the complete details of the complication of the structure of Mandelbrot's set cannot really be fully comprehended by anyone of us, nor can it be fully revealed by any computer. It would seem...”
Roger Penrose
“I have been arguing that such 'God-given' mathematical ideas should have some kind of timeless existence, independent of our earthly selves.”
Roger Penrose
“Gödel's theorem shows that this point of view is not really a tenable one in a fundamental philosophy of mathematics. The notion of mathematical truth goes beyond the whole concept of formalism. There...”
Roger Penrose