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Top 15 Georg Cantor Quotes (2025 Update)

Georg Cantor Quote: “To ask the right question is harder than to answer it.”

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

— Georg Cantor

Featured in: Math Quotes

Georg Cantor Quote: “Great innovation only happens when people aren’t afraid to do things differently.”

2. “Great innovation only happens when people aren’t afraid to do things differently.”

— Georg Cantor

Featured in: Innovation Quotes

Georg Cantor Quote: “In mathematics, the art of asking questions is more valuable than solving problems.”

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

— Georg Cantor

Georg Cantor Quote: “The essence of mathematics lies precisely in its freedom.”

4. “The essence of mathematics lies precisely in its freedom.”

— Georg Cantor

Georg Cantor Quote: “Don’t always blindly follow guidance and step-by-step instructions; you might run into something interesting.”

5. “Don’t always blindly follow guidance and step-by-step instructions; you might run into something interesting.”

— Georg Cantor

Georg Cantor Quote: “A set is a Many that allows itself to be thought of as a One.”

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

— Georg Cantor

Georg Cantor Quote: “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.”

7. “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

Georg Cantor Quote: “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.”

8. “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

Georg Cantor Quote: “My beautiful proof lies all in ruins.”

9. “My beautiful proof lies all in ruins.”

— Georg Cantor

Georg Cantor Quote: “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.”

10. “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

Georg Cantor Quote: “Use Campaign link tagging labels all for specifying slight differences in content for split testing.”

11. “Use Campaign link tagging labels all for specifying slight differences in content for split testing.”

— Georg Cantor

Georg Cantor Quote: “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.”

12. “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

Georg Cantor Quote: “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.”

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

Georg Cantor Quote: “Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.”

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

— Georg Cantor

Georg Cantor Quote: “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.”

15. “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

Georg Cantor Quote: “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.”

16. “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

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

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

— Georg Cantor

Georg Cantor Quote: “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.”

18. “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.”

— Georg Cantor

Georg Cantor Quote: “I realize 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.”

19. “I realize 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

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