Georg Cantor Quotes & Sayings

#1. The essence of mathematics lies in its freedom.

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

#3. 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.

Georg Cantor

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

Georg Cantor

#5. 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.

Georg Cantor

#6. 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!

Georg Cantor

#7. The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.

Georg Cantor

#8. 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.

Georg Cantor

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

Georg Cantor

#10. 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.

Georg Cantor

#11. I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

Georg Cantor

#12. 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.

Georg Cantor

#13. Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

Georg Cantor

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

Georg Cantor

#15. Use Campaign link tagging labels all for specifying slight differences in content for split testing.

Georg Cantor

#16. 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.

Georg Cantor