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It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

— Henri Poincaré Science and Method (1908)

C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.

Original text (French)

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Notes from Wikiquote

Part II. Ch. 2 : Mathematical Definitions and Education, p. 129

Topics

Mind

More quotes by Henri Poincaré

To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.

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The very possibility of the science of mathematics seems an insoluble contradiction.

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The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.

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There is no science apart from the general. It may even be said that the very object of the exact sciences is to spare us these direct verifications.

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In this domain of arithmetic,.. the mathematical infinite already plays a preponderant rôle, and without it there would be no science, because there would be nothing general.

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Attribution

Quote text and notes from Wikiquote: Henri Poincaré (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.