Experiment is the sole source of truth.
How is error possible in mathematics?
Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
Geometry is the art of correct reasoning from incorrectly drawn figures.
In the old days when people invented a new function they had something useful in mind.
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.