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David Hilbert -
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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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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
.
David Hilbert
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He who seeks for methods without having a definite
problem
in mind seeks for the most part in vain.
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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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. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the
problems
which the science of today sets and whose solution we expect from the future. To such a review of
problems
the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future.
David Hilbert
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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
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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.
David Hilbert
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Living mathematics rests on the fluctuation between the antithesis powers of intuition and logic, the individuality of "grounded"
problems
and the generality of far-reaching abstractions. We ourselves must prevent the development being forced to only one pole of the life-giving antithesis.
David Hilbert
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A
problem
in number theory is as timeless as a true work of art.
David Hilbert
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It is difficult and often impossible to judge the value of a
problem
correctly in advance; for the final award depends upon the gain which science obtains from the
problem
.
David Hilbert
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The infinite, like no other
problem
, has always deeply moved the soul of men. The infinite, like no other idea, has had a stimulating and fertile influence upon the mind. But the infinite is also more than any other concept, in need of clarification.
David Hilbert
Quote of the day
I was not sympathetic to the assumption that criminals had radically different motivations from everyone else.
Gary Becker
David Hilbert
Creative Commons
Born:
January 23, 1862
Died:
February 14, 1943
(aged 81)
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