The essence of mathematics lies precisely in its freedom.
Georg CantorRead
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.
Interpretation
What this quote means
Fear of the infinite limits our understanding of the vast possibilities of existence.
In this quote, Georg Cantor highlights how fear and limited perception hinder our ability to grasp the concept of infinity. He suggests that while infinity in its purest form is essential to our existence, fear can blind us to its presence in various forms in our lives and thoughts, preventing us from appreciating the true depth and breadth of reality.
Themes
InfinityFearPerceptionMyopiaExistence
In practice
Example use cases
In a philosophical discussion about the nature of existence, this quote can highlight the dangers of limiting oneself to finite thinking.
More from Georg Cantor
All quotes →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 CantorRead
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 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
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