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Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
Engineer
Mathematician
Philosopher
Philosopher Of Science
Physicist
Researcher
Topologist
University Teacher
Le Cateau
Jules Henri Poincaré
Poincaré
Henri Poincare
Jules Henri Poincare
Poincare
Must
Philosophical
Instruments
Mathematics
Study
Purpose
Threefold
Natural
Aesthetic
Science
Instrument
Nature
Provide

More quotes by Henri Poincare

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All of mathematics is a tale about groups.
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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
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Mathematicians do not study objects, but relations among objects they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
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It is far better to foresee even without certainty than not to foresee at all.
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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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The mind uses its faculty for creativity only when experience forces it to do so.
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Les faits ne parlent pas. Facts do not speak.
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Mathematicians do not study objects, but the relations between objects.
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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.
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The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
Henri Poincare
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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them it is that which satisfies the rules of logic. But in education it is not that it is one that can be understood by the pupils.
Henri Poincare
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
Henri Poincare
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A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist his pleasure is as great and of the same nature.
Henri Poincare
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How is error possible in mathematics?
Henri Poincare
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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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Point set topology is a disease from which the human race will soon recover.
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare