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The Feynman Problem-Solving Algorithm:
  (1) write down the problem;
  (2) think very hard;
  (3) write down the answer.
--
A remark about Richard Feynman's genius, often attributed to Gell-Man, but no specific citations have yet been found.

 

Murray Gell-Mann

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Feynman's IQ was measured at 124 when he was young — well above average, but far from genius level. So how'd he become fluent in differential equations by the age of 15? Feynman's fascination with the inner workings of the mechanical objects around him couldn't have hurt his left-brain power. As a kid living in Queens, he took apart everything from radios to wagon wheels. This wide-eyed fascination stuck with him; for his entire life, Feynman's colleagues cited his "childlike" approach to physics problems, which bore great results. In fact, a fellow physicist once said that the “Feynman Problem Solving Algorithm” contained three steps: 1. Write down the problem. 2. Think very hard. 3. Write down the answer.

 

Richard Feynman

 

The answer is in the problem, not away from the problem. I go through the searching, analysing, dissecting process, in order to escape from the problem. But, if I do not escape from the problem and try to look at the problem without any fear or anxiety, if I merely look at the problem — mathematical, political, religious, or any other — and not look to an answer, then the problem will begin to tell me. Surely, this is what happens. We go through this process and eventually throw it aside because there is no way out of it. So, why can’t we start right from the beginning, that is, not seek an answer to a problem? — which is extremely arduous, isn’t it? Because, the more I understand the problem, the more significance there is in it. To understand, I must approach it quietly, not impose on the problem my ideas, my feelings of like and dislike. Then the problem will reveal its significance. Why is it not possible to have tranquillity of the mind right from the beginning?

 

Jiddu Krishnamurti

 

For mathematics education and the world of problem solving it marked a line of demarcation between two eras, problem solving before and after Polya.

 

George Polya

 

From childhood we are trained to have problems. When we are sent to school, we have to learn how to write, how to read, and all the rest of it. How to write becomes a problem to the child. Please follow this carefully. Mathematics becomes a problem, history becomes a problem, as does chemistry. So the child is educated, from childhood, to live with problems — the problem of God, problem of a dozen things. So our brains are conditioned, trained, educated to live with problems. From childhood we have done this. What happens when a brain is educated in problems? It can never solve problems; it can only create more problems. When a brain that is trained to have problems, and to live with problems, solves one problem, in the very solution of that problem, it creates more problems. From childhood we are trained, educated to live with problems and, therefore, being centred in problems, we can never solve any problem completely. It is only the free brain that is not conditioned to problems that can solve problems. It is one of our constant burdens to have problems all the time. Therefore our brains are never quiet, free to observe, to look. So we are asking: Is it possible not to have a single problem but to face problems? But to understand those problems, and to totally resolve them, the brain must be free.

 

Jiddu Krishnamurti

 

I honestly don't believe we will be solving the greater human conflict with our efforts. The problem is not a certain type of legislation or even a certain politician; the problem is the same that it has always been. I am the problem.

 

Don Miller