Georg Cantor Short Quotes

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The essence of mathematics lies entirely in its freedom.

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

Georg Cantor
In mathematics the art of asking questions is more valuable than solving problems.

Georg Cantor
The pure mathematician knows that pure mathematics has an end in itself which is more allied with philosophy.

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
Of his father:
However, he was born in Copenhagen, of Jewish parents, of the Portuguese Jewish community there.

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

Georg Cantor
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
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
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