MacTutor
In mathematics the art of proposing a question must be held of higher value than solving it.
(A thesis defended at Cantor's doctoral examination)
The essence of mathematics lies in its freedom.
Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
Je le vois, mais je ne le crois pas!
I see it but I don't believe it!
My theory stands as firm as a rock; every arrow directed against it will quickly return to the archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.
A set is a Many that allows itself to be thought of as a One.
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
In mathematics the art of proposing a question must be held of higher value than solving it.
The essence of mathematics lies in its freedom.
… the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.