Need we add that mathematicians themselves are not infallible?
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
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.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
Mathematicians are born, not made.
Mathematicians do not study objects, but relations between objects.