No more than these machines need the mathematician know what he does.
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.
Mathematicians do not study objects, but relations between objects.
Mathematicians are born, not made.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
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.
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
