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The art of doing mathematics consists in finding that special case which contains all the germs of generality.
David Hilbert
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Interpretation

What this quote means

Mathematics is about identifying specific cases that reveal broader principles.

David Hilbert's quote emphasizes the significance of pinpointing unique cases in mathematics that embody foundational concepts applicable to more general situations. It suggests that true understanding in mathematical exploration arises from these particular instances, which serve as a microcosm of broader principles and theories.

Themes

MathematicsGeneralitySpecial CaseUnderstandingPrinciples

In practice

Example use cases

In a mathematics class, you might use this quote to illustrate the importance of studying specific examples to understand general concepts.

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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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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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Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.
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Mathematics is a game played according to certain simple rules with meaningless marks on paper.
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No one shall expel us from the paradise that Cantor has created for us.
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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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