A Quote by Andrew Wiles
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.
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You know you can usually solve almost any problem, or you'll realize you can't, but usually you can solve almost any problem through some sort of trickery one way or another and get the shot to work, but you know when to give up.
A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
We cannot solve a problem by saying, "It's not my problem." We cannot solve a problem by hoping that someone else will solve it for us. I can solve a problem only when I say, "This is my problem and it's up to me to solve it."
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.
Solving the population problem is not going to solve the problems of racism, of sexism, of religious intolerance, of war, of gross economic inequality. But if you don't solve the population problem, you're not going to solve any of those problems. Whatever problem you're interested in, you're not going to solve it unless you also solve the population problem. Whatever your cause, it's a lost cause without population control.
It's much more interesting to watch someone who is ill-equipped to solve their problem fight to solve their problem than wallow in the knowledge that they're ill-equipped to solve their problems.
When you're in the day-to-day grind, it just seems like it's another step along the way. But I find joy in the actual process, the journey, the work. It's not the end. It's not the end event.
Every problem is super-interesting and has its own nuances, and you solve it today, but you try to solve it with an architecture. You build a machine to solve the problems that are like it later. And then you move on to the next.
Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.
Investigation may be likened to the long months of pregnancy, and solving a problem to the day of birth. To investigate a problem is, indeed, to solve it.
It's feeling the sense of responsibility, the sense of ownership, to step in, to try to solve any problem - and the humility to step back and embrace the better ideas of others. Your end goal, is what can we do together to problem-solve. I've contributed my piece, and then I step back.
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.
Hundreds of investors ask me questions each year about the dilemmas they confront. Their worst problem? Uncertainty. They are traumatized and become emotional or confused to the state of inaction. Even worse, they try to solve a short-term problem in a way that hurts them financially in the long run.
There is first of all the problem of the opening, namely, how to get us from where we are, which is, as yet, nowhere, to the far bank. It is a simple bridging problem, a problem of knocking together a bridge. People solve such problems every day. They solve them, and having solved them push on.
Solve a real problem. You don't start a company because you want to be an entrepreneur or the fame and glory that comes along with it. You become an entrepreneur to solve a real problem.
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