Zitat des Tages von Henri Poincare:
Need we add that mathematicians themselves are not infallible?
In the old days when people invented a new function they had something useful in mind.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
It is far better to foresee even without certainty than not to foresee at all.
The mind uses its faculty for creativity only when experience forces it to do so.
Hypotheses are what we lack the least.
To invent is to discern, to choose.
Mathematicians do not study objects, but relations between objects.
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
Mathematicians are born, not made.
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
Just as houses are made of stones, so is science made of facts.
Science is facts.
No more than these machines need the mathematician know what he does.
A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.
Geometry is not true, it is advantageous.
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
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.
Thought is only a flash between two long nights, but this flash is everything.
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.
A small error in the former will produce an enormous error in the latter.
Facts do not speak.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.
If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Mathematics is the art of giving the same name to different things.
Point set topology is a disease from which the human race will soon recover.
How is an error possible in mathematics?
Mathematical discoveries, small or great are never born of spontaneous generation.
It is through science that we prove, but through intuition that we discover.
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
Science is built up of 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.
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 has adopted the geometry most advantageous to the species or, in other words, the most convenient.