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

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.

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.

Weak men are afraid of a woman’s strength.

Real leaders aren’t afraid to get their hands dirty.

If You are not afraid of losing, nobody can ever beat You!

Authentic men aren’t afraid to show affection, release their feelings, hug their children, cry when they’re sad, admit it when they’re wrong, and ask for help when they need it.

Remember that everyone you meet is afraid of something, loves something and has lost something.

I need to remind myself all the time that being afraid of things going wrong, is not the way to make things right. All fear has ever done is try destroy any existing hope I have.

I’ve spent a lot of time holding onto things and people that brought me misery because I was afraid of the void that may be there once I let go. I know now my voids were just as illusionary as the fear and insecurities that created them.

The violence and injustice of the rulers of mankind is an ancient evil, for which, I am afraid, the nature of human affairs can scarce admit a remedy.