A Quote by Andrew Wiles
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
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String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself.
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.
It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.
It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.
The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.
The definition of the problem, rather than its solution, will be the scarce resource in the future.
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.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
Design is a response to a specific problem. You are given a problem to solve, and then you let the problem itself tell you what your solution is.
Emotions are far harder things to understand than algebra and geometry, yet we spend hours in elucidating mathematics and expect such a problem as that of human relationships to solve itself.
That was the biggest compliment that I can receive - making somebody wonder whether they have the problem, rather than what my problem is.
The trick is to fix the problem you have, rather than the problem you want.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
The problem facing humanity today is not a political problem; it's not a financial problem; it's not a military problem. It's obviously a spiritual problem. That is, it has to do with what we believe to be true about who we are, where we are, why we are where we are, and what are we doing on the Earth. What is the purpose of life itself? What we need right now are leaders or models, people who will stand up and not only help to write a cultural story, but help to model it in the way that they interact with each other.
So that is the design process or the creative process. Start with a problem, forget the problem, the problem reveals itself or the solution reveals itself and then you reevaulate it. This is what you are doing all the time.
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