24+ Georg Cantor Quotes On Education, Democracy And Math

Georg Cantor was a German mathematician who is best known for his work in set theory, which has revolutionized mathematics. He is also credited with introducing the concept of cardinality, which is the notion of the size of a set, and the continuum hypothesis, which states that there is no set of numbers between the integers and the real numbers. His work has had a lasting impact on mathematics and set theory in particular. Following is our collection on famous quotes by Georg Cantor on life, education, democracy.

Top 10 Georg Cantor Quotes

1. 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.
2. To ask the right question is harder than to answer it.
3. Don't always blindly follow guidance and step-by-step instructions; you might run into something interesting.
4. In mathematics, the art of asking questions is more valuable than solving problems.
5. Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
6. The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
7. 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.
8. A set is a Many that allows itself to be thought of as a One.
9. Use Campaign link tagging labels all for specifying slight differences in content for split testing.
10. Great innovation only happens when people aren't afraid to do things differently.

Georg Cantor Quotes About Held

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

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

In mathematics the art of proposing a question must be held of higher value than solving it. — Georg Cantor

Georg Cantor Famous Quotes And Sayings

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

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

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

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

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

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

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type. — Georg Cantor

The essence of mathematics lies in its freedom. — Georg Cantor

My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things. — Georg Cantor

What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers. — Georg Cantor

My beautiful proof lies all in ruins. — Georg Cantor

Life Lessons by Georg Cantor

1. Georg Cantor's work showed that mathematics can be used to explore the infinite, demonstrating that infinity is not just an abstract concept but something that can be studied and understood.
2. He also showed that there are different levels of infinity, and that some are larger than others.
3. Finally, his work showed that mathematics can be used to explore the abstract and the unknown, and that it can be used to discover new truths.