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Mathematics Quotes by Henri Poincare

42 Mathematics quotes by Henri Poincare

All Mathematics quotes Henri Poincare’s page

Henri Poincare sees mathematics as a bridge that links abstract facts to real‑world laws through analogy. He notes that intuition discovers new ideas while logic checks them, and that the field also serves philosophy and deeper meaning. Groups, geometry, and space are tools, not ends.

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All of mathematics is a tale about groups.

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Mathematicians are born, not made.

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Need we add that mathematicians themselves are not infallible?

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Mathematicians do not study objects, but relations between objects.

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Mathematics is the art of giving the same name to different things.

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Geometry is not true, it is advantageous.

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How is error possible in mathematics?

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How is an error possible in mathematics?

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One geometry cannot be more true than another; it can only be more convenient.

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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

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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…

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[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

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Mathematical discoveries, small or great are never born of spontaneous generation.

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It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances…

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No more than these machines need the mathematician know what he does.

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Geometry is the art of correct reasoning from incorrectly drawn figures.

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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…

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The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to…

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Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of…

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Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so…

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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,…

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If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the…

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“The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights…

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One would have to have completely forgotten the history of science so as to not remember that the desire to know nature…

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I entered an omnibus to go to some place or other. At that moment when I put my foot on the step…

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“ Derrière la série de Fourier , d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par…

Henri Poincaré

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A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen…

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Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it…

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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer…

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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ...…

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So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a…

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I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion…

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“... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines.…

Henri Poincaré

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If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the…

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Mathematicians do not study objects, but the relations between objects.

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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…

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. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the…

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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…

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A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

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The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to…

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More by Henri Poincare

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge…

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most…

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation…

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves,…

Science is facts.

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves,…

All of mathematics is a tale about groups.

A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.

In the old days when people invented a new function they had something useful in mind.

Intuition is more important to discovery than logic.

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

Experiment is the sole source of truth.

“ Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se…

Henri Poincaré

If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the…

“ Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de…