In mathematics our role is more that of servant than master.

I believe that numbers and functions of Analysis are not the arbitrary result of our minds I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists.

I shall risk nothing on an attempt to prove the transcendence of p. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort.

There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.