My beautiful proof lies all in ruins.

This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!

Don't always blindly follow guidance and step-by-step instructions; you might run into something interesting.

To ask the right question is harder than to answer it.

The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.

Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.

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.