A Quote by Albert Einstein
The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.
Related Quotes
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.
A philosophy is characterized more by the formulation of its problem than by its solution of them.
Successful problem solving requires finding the right solution to the right problem. We fail more often because we solve the wrong problem than because we get the wrong solution to the right problem.
The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.
No matter how complicated a problem is, it usually can be reduced to a simple, comprehensible form which is often the best solution.
I think that there is only one way to science - or to philosophy, for that matter: to meet a problem, to see its beauty and fall in love with it; to get married to it and to live with it happily, till death do ye part - unless you should meet another and even more fascinating problem or unless, indeed, you should obtain a solution. But even if you do obtain a solution, you may then discover, to your delight, the existence of a whole family of enchanting, though perhaps difficult, problem children, for whose welfare you may work, with a purpose, to the end of your days.
It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.
Cities are never random. No matter how chaotic they might seem, everything about them grows out of a need to solve a problem. In fact, a city is nothing more than a solution to a problem, that in turn creates more problems that need more solutions, until towers rise, roads widen, bridges are built, and millions of people are caught up in a mad race to feed the problem-solving, problem-creating frenzy.
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.
The population explosion is an ecological phenomenon of displacement. Unless we solve that ecological problem of displacing people - to build huge dams, to build motorways, to take away what people need in order to survive - we will keep pumping more and more money into population programs. We will have more and more coercive and violent methods through which women's bodies are treated as experimental grounds for new contraceptives. Yet we will not have a solution to the problem of numbers.
Good design is a matter of discipline. It starts by looking at the problem and collecting all the available information about it. If you understand the problem, you have the solution. It’s really more about logic than imagination.
Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.
Institutions too often focus their energy preserving the problem to which they are a solution than to innovate their way to success.
A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.
The fundamental problem with golf is that every so often, no matter how lacking you may be in the essential virtues required of a steady player, the odds are that one day you will hit the ball straight, hard, and out of sight. This is the essential frustration of this excruciating sport. For when you've done it once, you make the fundamental error of asking yourself why you can't do this all the time. The answer to this question is simple: the first time was a fluke.
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
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