Need we add that mathematicians themselves are not infallible?
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.
In the old days when people invented a new function they had something useful in mind.
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.
Geometry is not true, it is advantageous.
Mathematics is the art of giving the same name to different things.
Mathematicians are born, not made.
Thought is only a flash between two long nights, but this flash is everything.
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.
A small error in the former will produce an enormous error in the latter.
If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Mathematicians do not study objects, but relations between objects.
How is an error possible in mathematics?
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
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.
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
It is through science that we prove, but through intuition that we discover.
Point set topology is a disease from which the human race will soon recover.