Quotes from Georg Cantor

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

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.

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.

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.

My beautiful proof lies all in ruins.

The essence of mathematics is in its freedom.

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

In der Mathematik ist die Kunst Fragen zu stellen wertvoller als Probleme zu lösen.

Je le voie, mais je ne le crois pas.

what wonderful power there is in the real numbers, since one is in a position to determine uniquely, with a single coordinate, the elements of an n-dimensional continuous space.

The idea of considering the infinitely large not only in the form of the unlimitedly increasing magnitude and in the closely related form of convergent infinite series...but to also fix it mathematically by numbers in the definite form of the completed infinite was logically forced upon me, almost against my will since it was contrary to traditions which I had come to cherish in the course of many years of scientific effort and investigations.

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

The essence of mathematics lies precisely in its freedom.