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David Hilbert

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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.

 
David Hilbert

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The inequities in human relationships are many, but the lot of the Negro is one of the worst. Here in the south this fact is tragically evident. The poor colored people are kicked from pillar to post, condemned, cussed, ridiculed, accorded no respect, permitted no sense of human dignity. What can be done I don't know. Nearly everyone, particularly the southerners, seem to think the only problem involved is seeing to it that they keep their place, whatever that may be. We supposedly are fighting this war to obliterate the malignant idea of racial supremacy and master-slave relationships. When this war is over the colored problem is apt to be more difficult than ever. May wisdom, justice, brotherly love guide our steps to the right solution.

 
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If "freedom" means, first of all, the responsibility of every individual for the rational determination of his own personal, professional and social existence, then there is no greater fear than that of the establishment of general freedom. Without a thoroughgoing solution of this problem there never will be a peace lasting longer than one or two generations. To solve this problem on a social scale, it will take more thinking, more honesty and decency, more conscientiousness, more economic, social and educational changes in social mass living than all the efforts made in previous and future wars and post-war reconstruction programs taken together.

 
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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
 

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?

 
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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
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