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David Hilbert

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If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems.

 
David Hilbert

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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
 

Design is really a special case of problem solving. One wants to bring about a desired state of affairs. Occasionally one wants to remedy some fault but more usually one wants to bring about something new. For that reason design is more open ended than problem solving. It requires more creativity. It is not so much a matter of linking up a clearly defined objective with a clearly defined starting position (as in problem solving) but more a matter of starting out from a general position in the direction of a general objective

 
Edward de Bono
 

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
 

Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i.e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. ...A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.

 
Hans Reichenbach
 

The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess. The economic problem of society is thus not merely a problem of how to allocate "given" resources — if "given" is taken to mean given to a single mind which deliberately solves the problem set by these "data." It is rather a problem of how to secure the best use of resources known to any of the members of society, for ends whose relative importance only these individuals know. Or, to put it briefly, it is a problem of the utilization of knowledge which is not given to anyone in its totality.

 
Friedrich Hayek
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