“The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.”

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 than twenty years; every year, and almost every day brings me further in this science.

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

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

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

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

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

Use Campaign link tagging labels all for specifying slight differences in content for split testing.

My beautiful proof lies all in ruins.

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 actual infinite can be demonstrated.

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!

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

Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!

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 essence of mathematics lies precisely in its freedom.

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 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 like the rough impersonality of New York … Human relations are oiled by jokes, complaints, and confessions-all made with the assumption of never seeing the other person again.

Sometimes I’m just as prejudiced as people I point fingers at. And that’s not right. How can I look at white skin and make assumptions but not want assumptions made about me? That’s not right.

Our assumptions are the edges of our worlds.

He had lived and acted on the assumption that he was alone, and now he saw that he had not been. What he had done made others suffer.

You are not naked when you take off your clothes. You still wear your religious assumptions, your prejudices, your fears, your illusions, your delusions.

You don’t even want to play that game. You want to reclaim your mind and get it out of the hands of the cultural engineers who want to turn you into a half-baked moron consuming all this trash that’s being manufactured out of the bones of a dying world.

We define religion as the assumption that life has meaning. Religion, or lack of it, is shown not in some intellectual or verbal formulations but in one’s total orientation to life.

The first and most imperative necessity in war is money, for money means everything else — men, guns, ammunition.