We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.

It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.

You are an extremely valuable, worthwhile, significant person even though your present circumstances may have you feeling otherwise.

The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.