# Frases de Henri Poincaré

## Henri Poincaré

**Fecha de nacimiento:** 29. Abril 1854**Fecha de muerte:** 17. Julio 1912**Otros nombres:** Анри Пуанкаре

Jules Henri Poincaré ,[1] generalmente conocido como Henri Poincaré, fue un prestigioso polímata: matemático, físico, científico teórico y filósofo de la ciencia, primo del presidente de Francia Raymond Poincaré. Poincaré es descrito a menudo como el último universalista capaz de entender y contribuir en todos los ámbitos de la disciplina matemática. En 1894 estableció el grupo fundamental de un espacio topológico. Wikipedia

### Frases Henri Poincaré

### „El científico no estudia la naturaleza por la utilidad que le pueda reportar; la estudia por el gozo que le proporciona, y este gozo se debe a la belleza que hay en ella. La belleza intelectual se basta a sí misma, y es por ella, más que quizá por el bien futuro de la humanidad, por lo que el científico consagra su vida a un trabajo largo y difícil.“

Fuente: Gerhard Herzberg: an illustrious life in science. Boris P. Stoicheff, National Research Council, Canada. Pág. 389.

### „All that is not thought is pure nothingness“

— Henri Poincaré, libro The Value of Science

Fuente: The Value of Science (1905), Ch. 11: Science and Reality

Contexto: All that is not thought is pure nothingness; since we can think only thought and all the words we use to speak of things can express only thoughts, to say there is something other than thought, is therefore an affirmation which can have no meaning.

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.<!--p.142

### „The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious.“

— Henri Poincaré, libro Science and Method

Part II. Ch. 2 : Mathematical Definitions and Education, p. 128

Variant translation: The chief aim of mathematics teaching is to develop certain faculties of the mind, and among these intuition is by no means the least valuable.

Science and Method (1908)

Contexto: The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality.

### „When we say force is the cause of motion, we talk metaphysics“

— Henri Poincaré, libro Science and Hypothesis

Fuente: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

Contexto: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?

These difficulties are inextricable.

When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.

We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed.

We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74

### „The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful.“

— Henri Poincaré, libro Science and Method

Part I. Ch. 1 : The Selection of Facts, p. 22

Science and Method (1908)

Contexto: The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.

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

— Henri Poincaré, libro Science and Hypothesis

Fuente: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

Contexto: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6

### „A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.“

"Notice sur Halphen," Journal de l'École Polytechnique (Paris, 1890), 60ème cahier, p. 143. See also Tobias Dantzig, Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954) p. 8

Contexto: A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.... we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it.

### „For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.“

— Henri Poincaré, libro Science and Hypothesis

Fuente: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

Contexto: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?

These difficulties are inextricable.

When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.

We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed.

We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74

### „Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us.“

— Henri Poincaré, libro Science and Hypothesis

Fuente: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead

Contexto: But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself.<!--pp.13-14

### „Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.“

— Henri Poincaré, libro Science and Hypothesis

Fuente: Science and Hypothesis (1901), Ch. IX: Hypotheses in Physics, Tr. George Bruce Halsted (1913)

Contexto: The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.