34 Quotes by Georg Cantor

My beautiful proof lies all in ruins.

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

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

I realise 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.

The essence of mathematics lies in its freedom.

started to tell his friends that he had not been the inventor of the ideas about infinity that he had published. He was merely a mouthpiece, inspired by God to communicate parts of the mind of God to everyone else.

One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

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

Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!