“Great innovation only happens when people aren’t afraid to do things differently.”

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.

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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.

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.

The art of concentration is a continual letting go. We let go of what is inessential or distracting. We let go of a thought or a feeling, not because we are afraid of it or because we can’t bear to acknowledge it as a part of our experience; but, because it is UNNECESSARY.

I’m afraid to live any place but in expectation. I’m no life-risk.

Avoid the flourish. Do not be afraid to be weak. Do not be ashamed to be tired. You look good when you’re tired. You look like you could go on forever. Now come into my arms. You are the image of my beauty.

I’m not afraid of anything. That’s just the way I am.

But only he who, himself enlightened, is not afraid of shadows.

You were so afraid of my voice I decided to be afraid of it too.

If you’re afraid – don’t do it, – if you’re doing it – don’t be afraid!

The change you’re afraid of could be the start of better days.