A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

You know, for any problem, no matter how big or complex it may be, there is a solution. All you have to do is find it. And, you can find it by organizing your approach, by attacking the problem emphatically with determination, by working long and hard, by applying your full brain power and by using wisely all the help you can get. You CAN solve it!

If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems.

By all accounts mathematics is mankind’s most successful intellectual undertaking. Every problem of mathematics gets solved, sooner or later. Once solved, a mathematical problem is forever finished: no later event will disprove a correct solution. As mathematics progresses, problems that were difficult become easy and can be assigned to schoolchildren.Thus Euclidean geometry is taught in the second year of high school. Similarly, the mathematics learned by my generation in graduate school is now taught at the undergraduate level, and perhaps in the not too distant future, in the high schools. Not only is every mathematical problem solved, but eventually every mathematical problem is proved trivial. The quest for ultimate triviality is characteristic of the mathematical enterprise.

Who would stand before a blackboard, and pray the principle of mathematics to solve the problem? The rule is already established, and it is our task to work out the solution. Shall we ask the divine Principle of all goodness to do His own work? His work is done, and we have only to avail ourselves of God's rule in order to receive His blessing, which enables us to work out our own salvation.

It’s the same kind of pleasure as with hiking: You hike uphill and it’s tough and you sweat, and at the end of the day the reward is the beautiful view. Solving a math problem is a bit like that, but you don’t always know where the path is and how far you are from the top. You have to be able to accept frustration, failure, your own limitations.

All problems are unsolvable. The essence of the existence of a problem is that there is no solution. Looking for a fact means there is no fact. To think is not to know how to be.

Mathematics can help to solve some of the major problems of our times.

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.

When the mathematician would solve a difficult problem, he first frees the equation of all incumbrances, and reduces it to its simplest terms. So simplify the problem of life, distinguish the necessary and the real. Probe the earth to see where your main roots run.

How you think about a problem is more important than the problem itself – so always think positively. Believe it is possible to solve your problem. Tremendous things happen to the believer. So believe the answer will come. It will.

The answer is in the problem, not away from the problem. I go through the searching, analysing, dissecting process, in order to escape from the problem. But, if I do not escape from the problem and try to look at the problem without any fear or anxiety, if I merely look at the problem — mathematical, political, religious, or any other — and not look to an answer, then the problem will begin to tell me. Surely, this is what happens. We go through this process and eventually throw it aside because there is no way out of it. So, why can’t we start right from the beginning, that is, not seek an answer to a problem? — which is extremely arduous, isn’t it? Because, the more I understand the problem, the more significance there is in it. To understand, I must approach it quietly, not impose on the problem my ideas, my feelings of like and dislike. Then the problem will reveal its significance. Why is it not possible to have tranquillity of the mind right from the beginning?

A mathematical argument, once understood, is in its capacity to compel belief a miracle of enlightened life.

What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very important idea of solving a problem within limits of error is an element of rational culture, coming from the same source. The art of totalizing fluctuations by curves is capable of being carried, in conception, far beyond the mathematical domain, 65 where it is first learned. The distinction between laws and coefficients applies in every department of causation. The theory of Probable Evidence is the mathematical contribution to Logic, and is of paramount importance.