Georg Cantor Quotes

25 quotes in 451 categories

• In mathematics the art of proposing a question must be held of higher value than solving it.
• The essence of mathematics lies precisely in its freedom.
• The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
• Great innovation only happens when people aren't afraid to do things differently.
• I like creativity in data collection. Here are a few creative Google Analytics tracking ideas I have seen:
• Use Campaign link tagging labels all for specifying slight differences in content for split testing.
• Don't always blindly follow guidance and step-by-step instructions; you might run into something interesting.
• My beautiful proof lies all in ruins.
• 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…
• 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…
• 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…
• 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…
• In mathematics, the art of asking questions is more valuable than solving problems.
• 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…
• To ask the right question is harder than to answer it.
• The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational…
• 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…
• 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…
• I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature…
• 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…

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