This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.
David Hilbert
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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?
Jiddu Krishnamurti
The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future. There are only two ways of approaching this problem on the assumption that it is a genuine problem, and it is easy to see that neither of them can lead to its solution.
Alfred Jules Ayer
The Catholic solution of our problem, of our unique vital problem, the problem of the immortality and eternal salvation of the soul, satisfies the will, and therefore satisfies life; but the attempt to rationalize it by means of a dogmatic theology fails to satisfy the reason. And reason has its exigencies as imperious as those of life. It is no use seeking to force ourselves to consider as super-rational what clearly appears to us to be contra-rational... Infallibility, a notion of Hellenic origin, is in its essence a rationalistic category.
Miguel de Unamuno
It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.
David Hilbert
The problem of establishing a perfect civic constitution is dependent upon the problem of a lawful external relation among states and cannot be solved without a solution of the latter problem.
Immanuel Kant
Hilbert, David
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