David Hilbert quotes - page 2

[O]ur purpose is to give a presentation of geometry... in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems... beyond this, it is possible... to depict the geometric outline of the methods of investigation and proof, without... entering into the details... In this manner, geometry being as many-faceted as it is and being related to the most diverse branches of mathematics, we may even obtain a summarizing survey of mathematics as a whole, and a valid idea of the variety of problems and the wealth of ideas it contains. Thus a presentation of geometry in large brushstrokes... and based on the approach through visual intuition, should contribute to a more just appreciation of mathematics by a wider range of people than just the specialists. (David Hilbert)
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. View quote
David Hilbert
Only an idiot could believe that scientific truth needs martyrdom. View quote
David Hilbert
One of the supreme achievements of purely intellectual human activity. View quote
David Hilbert
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. View quote
David Hilbert
But he (Galileo) was not an idiot,... Only an idiot could believe that scientific truth needs martyrdom - that may be necessary in religion, but scientific results prove themselves in time. View quote
David Hilbert
No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. View quote
David Hilbert
He who seeks for methods without having a definite problem in mind seeks in the most part in vain. View quote
David Hilbert
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. View quote
David Hilbert
The infinite! No other question has ever moved so profoundly the spirit of man. View quote
David Hilbert
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science. (David Hilbert)
History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. View quote
David Hilbert
To new concepts correspond, necessarily, new signs. View quote
David Hilbert
An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us. View quote
David Hilbert
To new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena which were the occasion for the formation of the new concepts. View quote
David Hilbert