A Quote by Roger Scruton
In mathematics and science we solve our problems as well as create them. But in art and philosophy things are not so simple.
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Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve.
Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.
We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions.
We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions
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.
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate.
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. Fermat's Last Theorem is the most beautiful example of this.
What is the central core of the subject [computer science]? What is it that distinguishes it from the separate subjects with which it is related? What is the linking thread which gathers these disparate branches into a single discipline. My answer to these questions is simple -it is the art of programming a computer. It is the art of designing efficient and elegant methods of getting a computer to solve problems, theoretical or practical, small or large, simple or complex. It is the art of translating this design into an effective and accurate computer program.
You can see the meaning of the statement that "Literature is a living art" most easily and clearly, perhaps, by contrasting Science and Art at their two extremes - say Pure Mathematics and Acting. Science as a rule deals with things, Art with man's thought and emotion about things.
Contempt for science could perhaps depend on the fact that, science hasn't been able to solve any of our basic problems, for example the environmental pollution or the problems with HIV and AIDS. This is the worst disease of our time, and scientists are lost. I believe that many people are disappointed with science when the answers we need are not delivered.
Art is a form of understanding like philosophy and science and mathematics are an understanding but the difference is that art has the capacity to hold all these different things. It is the form of understanding that is best suited for the contemporary time.
Maybe philosophical problems are hard not because they are divine or irreducible or meaningless or workaday science, but because the mind of Homo sapiens lacks the cognitive equipment to solve them. We are organisms, not angels, and our minds are organs, not pipelines to the truth. Our minds evolved by natural selection to solve problems that were life-and-death matters to our ancestors, not to commune with correctness ot to answer any question we are capable of asking.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
No scientist is admired for failing in the attempt to solve problems that lie beyond his competence. ... Good scientists study the most important problems they think they can solve. It is, after all, their professional business to solve problems, not merely to grapple with them.
Innovative, bottom-up methods will solve problems that now seem intractable—from energy to poverty to disease. Science and technology, powered by the fuel of entrepreneurial energy, are the largest multipliers of resources we have to solve our many social problems.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
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