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Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.

David Hilbert

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David Hilbert
Age: 81 †
Born: 1862
Born: January 23
Died: 1943
Died: February 14
Mathematician
Philosopher
Physicist
University Teacher
Königsberg i. Pr.
Discipline
Development
Goes
Three
Naive
Every
Formal
Mathematical
Critical
Periods

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Mathematics is a game played according to certain simple rules with meaningless marks on paper.
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[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
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Some people have got a mental horizon of radius zero and call it their point of view.
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The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics it is mathematics which builds the linking bridges and gives the ever more reliable forms.
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We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.
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Mathematics knows no races or geographic boundaries for mathematics, the cultural world is one country.
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The infinite! No other question has ever moved so profoundly the spirit of man.
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The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
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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.
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One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs
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Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.
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I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later.
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Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific result will establish itself.
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Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.
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Geometry is the most complete science.
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Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.
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Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.
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If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.
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Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.
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Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible whole... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples.
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