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

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.

To ask the right question is harder than to answer it.

Great innovation only happens when people aren't afraid to do things differently.

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

The essence of mathematics lies precisely in its freedom.

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

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

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

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.

No good deed goes unpunished.

You know how you let yourself think that everything will be alright if you can only go to certain place or do a certain thing. But when you get there you find it's not that simple.

The first thing others see is YOU—not your resume, background, or credentials. A picture is truly worth a thousand words and how you dress is the “picture” you provide for all the world to see.

Our instinct as parents is to order our kids around — it's easier, and frankly, we're usually right. [But] reverse the waterfall as much as possible. Enlist the children in their own upbringing.

Deep in every heart slumbers a dream and the couturier knows it: every woman is a princess

To me, it's a great day every time I receive a letter from somebody who climbed inside one of my books, inhabited it for a while, learned a little something, and emerged grateful.

I eat meat, the rarer the better.

Don't just stand back and play the way you're coached. A great player must rise to the occasion and turn the game around on his own.

One of the simplest things about all facts of life is that to get where you want to go, you must keep on keeping on.

If you change the belief first, changing the action is easier.