In mathematics the art of proposing a question must be held of higher value than solving it.
GEORG CANTORIn mathematics the art of proposing a question must be held of higher value than solving it.
More Georg Cantor Quotes
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My beautiful proof lies all in ruins.
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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.
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A set is a Many that allows itself to be thought of as a One.
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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.
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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.
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In mathematics, the art of asking questions is more valuable than solving problems.
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The essence of mathematics lies precisely in its freedom.
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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.
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The transfinite numbers are in a sense the new irrationalities they stand or fall with the finite irrational numbers.
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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.
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Great innovation only happens when people aren’t afraid to do things differently.
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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!
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Don’t always blindly follow guidance and step-by-step instructions; you might run into something interesting.
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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