A Quote by Andrew Wiles
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.
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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.
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.
It is problems that we faced for 30 years and we had to solve them in a couple of years only and the solution really pushed us and the economy couldn't handle it. We had the greatest depression. It wasn't easy and I think we expected the results. But the other thing is we have to try to create the plan B and get us out of this crisis as soon as possible.
We [with husband] try and spend time alone, which is really hard to do. Of course, when you have kids they're like: "Why are you going out? You went out last night... you can't go out tonight!" so, you try to do that, and you try and ask somebody to please turn off the football game because you can't stand it any longer and you'd rather talk to them.You try to make time for each other where you can. You try to plan a trip away somewhere.
Problems will always torment us because all important problems are insoluble: that is why they are important. The good comes from the continuing struggle to try and solve them, not from the vain hope of their solution.
The natural tendency of children is to solve problems, but we try to indoctrinate them with facts, which they are supposed to feed back, and then we fail them. And that's child abuse. And you should never raise children that way. You should cultivate and encourage their natural tendencies to create solutions to the problems around them.
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.
Teaching and writing, really, they support and nourish each other, and they foster good thinking. Because when you show up in the classroom, you may have on the mantle of authority, but in fact, you're just a writer helping other writers think through their problems. Your experience with the problems you've tried to solve comes into play in how you try to teach them to solve their problems.
There is no good reason why we should fear the future, but there is every reason why we should face it seriously, neither hiding from ourselves the gravity of the problems before us nor fearing to approach these problems with the unbending, unflinching purpose to solve them aright.
In mathematics and science we solve our problems as well as create them. But in art and philosophy things are not so simple.
How hard is it to build an intelligent machine? I don't think it's so hard, but that's my opinion, and I've written two books on how I think one should do it. The basic idea I promote is that you mustn't look for a magic bullet. You mustn't look for one wonderful way to solve all problems. Instead you want to look for 20 or 30 ways to solve different kinds of problems. And to build some kind of higher administrative device that figures out what kind of problem you have and what method to use.
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.
Thought is constantly creating problems that way and then trying to solve them. But as it tries to solve them it makes it worse because it doesn't notice that it's creating them, and the more it thinks, the more problems it creates.
I think that education today is a form of child abuse. The natural tendency of children is to solve problems, but we try to indoctrinate them with facts, which they are supposed to feed back, and then we fail them. And that's child abuse. And you should never raise children that way. You should cultivate and encourage their natural tendencies to create solutions to the problems around them.
Kids can't see us bombing, and then listen to us
talking about getting guns out of the schools.
How can we tell them to solve problems without violence,
if, in fact, we can't show an ability to solve problems
without violence?
Most people will solve the problems they know how to solve. Roughly speaking they will solve B+ problems instead of A+ problems. A+ problems are high impact problems for your company but they're difficult problems.
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