Roger Penrose Quotes

There are sometimes problems for which there is no immediate solution, and there are sometimes problems for which there is no solution.

The problems for which I could find no solution in fact had no solution.

I return to problems i can't solve, not because i am an idiot, but because the real problems can't be solved. The universe is expanding. The more we see, the more we discover there is to see. Always a new beginning, a different end.

We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions.

Some issues have no solutions. If no solution comes, then you should leave it as it is. If you hit a road where you have no solution, it is best you don't touch it.

One of the most important tools in critical thinking about numbers is to grant yourself permission to generate wrong answers to mathematical problems you encounter. Deliberately wrong answers!

A real scientist solves problems, not wails that they are unsolvable.

Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.

Sometimes if you have financial restraints, it's a benefit. It forces you to come up with a more creative way.

Intelligence is like four-wheel drive. It only allows you to get stuck in more remote places.

I had always been - everybody kind of likes comedy. I was very interested in comedy, beyond just liking it. I had friends that took apart radios; I wanted to take apart jokes.

One of the most highly developed skills in contemporary Western civilization is dissection: the split -up of problems into their smallest possible components. We are good at it. So good, we often forget to put the pieces back together again.

I wish people would quit telling me to think. I think. Thinking's easy. It's not thinking that's hard.

Critical thinking does seem a superior sort of thinking because it seems as though the critic is actually going beyond the scope of what is being criticized in order to criticize it. That is only rarely a true assumption because, most often, the critic will seize on some little aspect that he or she understands and tackle only that.

The task is not so much to solve problems as to propose questions.

We can't avoid reasoning; we can only avoid doing it well.

Neither you nor I nor Einstein nor the Supreme Court of the United States is brilliant enough to reach an intelligent decision on any problem without first getting the facts

To solve a problem, you have to be able to state what the problem is or at least say the name.

Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

To develop thinking as a skill, it should be deliberate, focused, confident, and enjoyable.

I get the facts, I study them patiently, I apply imagination.

There are fifty who can reason synthetically for one who can reason analytically.

The key to good decision making is not knowledge. It is understanding. We are swimming in the former. We are desperately lacking in the latter.

The more constraints I have, the more opportunities I have to be creative to fix those constraints.

To investigate a problem is, indeed, to solve it.