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Just as houses are made of stones, so is science made of facts.
It is through science that we prove, but through intuition that we discover.
It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.
It is far better to foresee even without certainty than not to foresee at all.
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
In the old days when people invented a new function they had something useful in mind.
If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.
If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws.
If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
Hypotheses are what we lack the least.
How is an error possible in mathematics?
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