“The essence of mathematics lies precisely in its freedom.”

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.

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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 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.

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.

In mathematics the art of proposing a question must be held of higher value than solving it.

To ask the right question is harder than to answer 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 frequently defended on the nature of numbers.

Especially as an artist, the creative freedom we have makes us who we are. We’re human beings-we’re gonna mess up sometimes. I definitely feel like people should continue being who they are. As long as you’re staying true to who you are, that’s super important.

To call her a seamstress is irrelevant, She was not arrested for sewing. She was a freedom fighter.

The freer I get, the higher I go. The higher I go, the more I see. The more I see, the less I know. The less I know, the more I’m free.

The arts are not just a nice thing to have or to do if there is free time or if one can afford it. Rather, paintings and poetry, music and fashion, design and dialogue, they all define who we are as a people and provide an account of our history for the next generation.

Free yourself from the illusion of good and bad days. Labeling time makes us nostalgic of the past and demanding of the future. There is only here and now. Let it be.

No one should negotiate their dreams. Dreams must be free to fly high. No government, no legislature, has a right to limit your dreams. You should never agree to surrender your dreams.

From this it follows that, the larger the State, the less the liberty.

Freedom is a possession of inestimable value.