Georg Cantor - Mathematics Quotes

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The essence of mathematics lies entirely in its freedom.

Georg Cantor
Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.

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

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

Georg Cantor
Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts.

Georg Cantor