But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they...

Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert’s program. Here one regards mathematics as a formal game...