The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.
a problem well put is half solved.
The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.
How you define a problem shapes how you address it.
You are right in demanding that an artist approach his work consciously, but you are confusing two concepts: the solution of a problem and the correct formulation of a problem. Only the second is required of the artist.
In the life of a nation, few ideas are more dangerous than good solutions to the wrong problems.
A philosophy is characterized more by the formulation of its problem than by its solution of them.
The task is not so much to solve problems as to propose questions.
If decisions were a choice between alternatives, decisions would come easy. Decision is the selection and formulation of alternatives.
How do we attack important problems? Pose the right question.
In mathematics the art of proposing a question must be held of higher value than solving it.
An almost indispensable skill for any creative person is the ability to pose the right questions. Creative people identify promising, exciting, and, most important, accessible routes to progress - and eventually formulate the questions correctly.
The most successful scientists in the history of the world are those who posed the right questions
You are right in demanding that an artist should take an intelligent attitude to his work, but you confuse two things: solving a problem and stating a problem correctly.
Design is a solution to a problem. Art is a question to a problem.
It is a familiar and significant saying that a problem well put is half-solved.
The incorrectness and weaknesses of a theory cause other minds to formulate the problems more exactly and in this way scientific progress is made.
Any reductionist program has to be based on an analysis of what is to be reduced. If the analysis leaves something out, the problem will be falsely posed.
