There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the ….

A set is a Many that allows itself to be thought of as a One..

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

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 ….

In mathematics, the art of asking questions is more valuable than solving problems..

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

Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number..

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 ex….

My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it ….

I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions f….

I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more ….

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with con….

My beautiful proof lies all in ruins..

A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held..

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrati….

The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either b….

The essence of mathematics lies precisely in its freedom..

Great innovation only happens when people aren't afraid to do things differently..

The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of….

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

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 tak….