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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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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 do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bathhouse. Objecting to sex discrimination being the reason for rejection of Emmy Noether's application to join the faculty at the University of Gottingen.
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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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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.
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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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The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
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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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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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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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The infinite! No other question has ever moved so profoundly the spirit of man.
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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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Physics is becoming too difficult for the physicists.
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Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
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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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Some people have got a mental horizon of radius zero and call it their point of view.
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Geometry is the most complete science.
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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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Mathematics is a game played according to certain simple rules with meaningless marks on paper.
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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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