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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.

— Henri Poincaré Science and Hypothesis (1901)

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More quotes by Henri Poincaré

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

Science and Hypothesis (1901)

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

Science and Hypothesis (1901)

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.

Science and Hypothesis (1901)

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.

Science and Method (1908)

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.

Science and Hypothesis (1901)

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