Henri Poincaré - Alone Quotes

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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
Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

Henri Poincaré
Scientists believe there is a hierarchy of facts and that among them may be made a judicious choice. They are right, since otherwise there would be no science... One need only open the eyes to see that the conquests of industry which have enriched so many practical men would never have seen the light, if these practical men alone had existed and if they had not been preceded by unselfish devotees who died poor, who never thought of utility, and yet had a guide far other than caprice.
As Mach says, these devotees have spared their successors the trouble of thinking.

Henri Poincaré
Now what is science?... it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations.... it is in relations alone that objectivity must be sought.... it is relations alone which can be regarded as objective.
External objects... are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation.

Henri Poincaré
It is the intuition of pure number, that of pure logical forms, which illumines and directs those we have called analysts. This it is which enables them not alone to demonstrate, but also to invent.

Henri Poincaré
Logic and intuition have each their necessary role. Each is, indispensable. Logic, which alone can give certainty, is the instrument of demonstration; intuition is the instrument of invention.

Henri Poincaré
The ultimate aim of celestial mechanics is to solve the great question whether Newton 'a law alone will explain all astronomical phenomena.

Henri Poincaré
An isolated fact can be observed by all eyes; by those of the ordinary person as well as of the wise. But it is the true physicist alone who may see the bond which unites several facts among which the relationship is important though obscure.

Henri Poincaré
Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Henri Poincaré
To obtain a result of real value, it is not enough to grind out calculations or to have a machine to put things in order; it is not order alone, it is unexpected order, which is worth while. The machine may gnaw on the crude fact; the soul of the fact will always escape it.

Henri Poincaré