Roger Penrose Quotes

The mere imparting of information is not education. Above all things, the effort must result in making a man think and do for himself.

Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.

The reason the gifted students of the world like Khan Academy is because we don't say, 'Memorize this formula,' but say, 'Let's try to derive it from core principles,' or, 'I forgot my trig identity, so I'm going to just try to prove this to you.'

Give the pupils something to do, not something to learn; and the doing is of such a nature as to demand thinking; learning naturally results.

A book is less important for what it says than for what it makes you think.

This is that which I think great readers are apt to be mistaken in; those who have read of everything, are thought to understand everything too; but it is not always so. Reading furnishes the mind only with materials of knowledge; it is thinking that makes what we read ours. We are of the ruminating kind , and it is not enough to cram ourselves with a great load of collections:;; unless we chew them over again, they will not give us strength and nourishment.

No thought, no idea, can possibly be conveyed as an idea from one person to another. When it is told it is to the one to whom it is told another fact, not an idea. The communication may stimulate the other person to realize the question for himself and to think out a like idea, or it may smother his intellectual interest and suppress his dawning effort at thought. But what he directly gets cannot be an idea. Only by wrestling with the conditions of the problem at first hand, seeking and finding his own way out, does he think.

Synthesize new ideas constantly. Never read passively. Annotate, model, think, and synthesize while you read, even when you're reading what you conceive to be introductory stuff. That way, you will always aim towards understanding things at a resolution fine enough for you to be creative.

All genuine learning is active, not passive. It involves the use of the mind, not just the memory. It is a process of discovery, in which the student is the main agent, not the teacher.

Keep reading books, but remember that a book’s only a book, and you should learn to think for yourself.

One of the few ways I can almost be certain I'll understand something is by sitting down and writing about it. Because by forcing yourself to write about it and putting it down in words, you can't avoid having your say on the subject. You might be wrong, but you have to think about it very intensely to write about it.

Let us use our energy and our initiative to solve our problems without relying on prayers and wishful thinking. When we have faith in ourselves, we will find we do not have to have faith in gods.

The only effective way to help well-intentioned, intelligent persons to do the best they can in raising children is to encourage and guide them always to do their own thinking in their attempts at understanding and dealing with child-rearing situations and problems, and not to rely blindly on the opinions of others.

Brains are no good if you don't use them.

Some people spend their entire lives reading but never get beyond reading the words on the page, they don't understand that the words are merely stepping stones placed across a fast-flowing river, and the reason they're there is so that we can reach the farther shore, it's the other side that matters...

... we must read, not only for what we read but for what it makes us think.

Perception of ideas, rather than the storing of them, should be the aim of education.

One must be an inventor to read well.

Read, every day, something no one else is reading. Think, every day, something no one else is thinking.

There is no need of a teacher for those who know how to think.

If I hold up one corner of a square and the student cannot workout the other three for himself, I won't go any further.

We seem to have trouble with [critical thinking]. And our political system doesn't help.

I think it's important to reason from first principles rather than by analogy. The normal way we conduct our lives is we reason by analogy. [With analogy] we are doing this because it's like something else that was done, or it is like what other people are doing. [With first principles] you boil things down to the most fundamental truths…and then reason up from there.

It is certainly not a matter of indifference whether I learn something without effort or finally arrive at it myself through my system of thought. In the latter case everything has roots, in the former it is merely superficial.

The important thing to remember about mathematics is not to be frightened