The essence of mathematics lies precisely in its freedom.
Georg CantorRead
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.
Interpretation
What this quote means
Cantor challenges conventional views on infinity and numbers in mathematics.
In this quote, Georg Cantor expresses his awareness that his mathematical work, particularly concerning the concept of infinity, opposes widely accepted beliefs about numbers. He acknowledges the contentious nature of his ideas and the resistance he may face from established perspectives in the field of mathematics.
Themes
InfinityMathematicsNumbersPhilosophyOpposition
In practice
Example use cases
During a lecture on mathematical philosophy, you might reference this quote to illustrate the importance of challenging accepted notions.
More from Georg Cantor
All quotes βMathematics, 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 CantorRead
A set is a Many that allows itself to be thought of as a One.
Georg CantorRead
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
Georg CantorRead
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 CantorRead
The essence of mathematics lies in its freedom.
Georg CantorRead
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