Henri Poincaré - The Value of Science (1905)

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Tolstoi explains somewhere in his writings why, in his opinion, "Science for Science's sake" is an absurd conception. We cannot know all the facts since they are infinite in number. We must make a selection... guided by utility... Have we not some better occupation than counting the number of lady-birds in existence on this planet?

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

Henri Poincaré
Time and Space … It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.

Henri Poincaré
Astronomy is useful because it raises us above ourselves; it is useful because it is grand;.... It shows us how small is man's body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.

Henri Poincaré
The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile or vain.

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
What is objective must be common to many minds and consequently transmissible from one to the other, and as this transmission can only come about by... discourse... we are even forced to conclude: no discourse no objectivity.

Henri Poincaré
What we call objective reality is, in the last analysis, what is common to many thinking beings, and could be common to all; this common part, we shall see, can only be the harmony expressed by mathematical laws. It is this harmony then which is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.

Henri Poincaré
All laws are deduced from experiment; but to enunciate them, a special language is needful. Ordinary language is too poor... This is one reason why the physicist can not do without mathematics; it furnishes him the only language he can speak. And a well-made language is no indifferent thing.

Henri Poincaré