Quotes of All Topics . Occasions . Authors
Mathematicians are born, not made.
To invent is to discern, to choose.
How is error possible in mathematics?
Hypotheses are what we lack the least.
Experiment is the sole source of truth.
How is an error possible in mathematics?
Geometry is not true, it is advantageous.
All of mathematics is a tale about groups.
Les faits ne parlent pas. Facts do not speak.
Intuition is more important to discovery than logic.
It is by logic we prove. It is by intuition we discover.
It is not order only, but unexpected order, that has value.
Need we add that mathematicians themselves are not infallible?
Just as houses are made of stones, so is science made of facts.
Analyse data just so far as to obtain simplicity and no further.
Mathematics is the art of giving the same name to different things.
Mathematicians do not study objects, but relations between objects.
No more than these machines need the mathematician know what he does.
Mathematicians do not study objects, but the relations between objects.
It is with logic that one proves; it is with intuition that one invents.
Geometry is the art of correct reasoning from incorrectly drawn figures.
Chance ... must be something more than the name we give to our ignorance.
A small error in the former will produce an enormous error in the latter.
Every good mathematician should also be a good chess player and vice versa.
Point set topology is a disease from which the human race will soon recover.
It is through science that we prove, but through intuition that we discover.
It is far better to foresee even without certainty than not to foresee at all.
One geometry cannot be more true than another; it can only be more convenient.
Thought is only a flash between two long nights, but this flash is everything.
But for harmony beautiful to contemplate, science would not be worth following.
The mind uses its faculty for creativity only when experience forces it to do so.
Mathematical discoveries, small or great are never born of spontaneous generation.
There are no solved problems; there are only problems that are more or less solved.
Sociology is the science with the greatest number of methods and the least results.
In the old days when people invented a new function they had something useful in mind.
One does not ask whether a scientific theory is true, but only whether it is convenient.
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.
A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.
We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.