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All that is not thought is pure nothingness...And yet—strange contradiction for those who believe in time—geologic history shows us that life is only a short episode between two eternities of death, and that, even in this episode, conscious thought has lasted and will last only a moment. Thought is only a gleam in the midst of a long night. But it is this gleam which is everything.

— Henri Poincaré The Value of Science (1905)

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Mathematics

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)

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

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)

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Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist.

Kenneth Boulding to Kenneth Boulding in: United States. Congress. House (1973)

If the doors of perception were cleansed, everything would appear to man as it is: infinite.

William Blake The Marriage of Heaven and Hell (1790)

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing.

Bertrand Russell

The land of easy mathematics where he who works adds up and he who retires subtracts.

Núria Añó

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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.