Henri Poincaré

1854–1912 · French mathematician, physicist and engineer

Topics: mathematics, physics, scientific method, learning

• 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.

  — Henri Poincaré

• 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

• When we say force is the cause of motion, we talk metaphysics

  — Henri Poincaré

• 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

• [T]he velocity of light... is adopted, such that the astronomic laws compatible with this value may be as simple as possible.

  — Henri Poincaré

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

  — Henri Poincaré

• 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.

  — Henri Poincaré

• 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

• We have not a direct intuition of the equality of two intervals of time.

  — Henri Poincaré

• We do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of translation.

  — Henri Poincaré

• We must, for example, use language, and our language is necessarily steeped in preconceived ideas.

  — Henri Poincaré

• [W]hat postulate do we implicitly admit? It is that the duration of two identical phenomena is the same; or... that the same causes take the same time to produce the same effects. ...Is it impossible that experiment may some day contradict our postulate?

  — Henri Poincaré

• Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.

  — Henri Poincaré

• C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.

  — Henri Poincaré

• What has taught us to know the true profound analogies, those the eyes do not see but reason divines? It is the mathematical spirit, which disdains matter to cling only to pure form.

  — Henri Poincaré

• 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