“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 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.

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

You are always your own best guru, your own best teacher, the answers are always inside you.

If you find it complicated to answer someone’s question, do not answer it, for his container is already full and does not have room for the answer.

It’s okay to not have it all figured out. If someone does have all the answers, that’s when I should be worried.

There is nothing more dangerous than a person with only one right answer.

Blessed is the person who sees the need, recognizes the responsibility, and actively becomes the answer.

Meeting you was like finding the answer to a question I had long since forgotten asking.

I have always prided myself that I do my own thinking. I have my own philosophy. I have my own answer to the reasons things have turned out in my life.

So many words to say but silence always seemed to be the answer.