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
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.
In practice
During a lecture on mathematical philosophy, you might reference this quote to illustrate the importance of challenging accepted notions.
The essence of mathematics lies precisely in its freedom.
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.
A set is a Many that allows itself to be thought of as a One.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
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.
The essence of mathematics lies in its freedom.
St. Paul introduced an entirely novel view of marriage, that it existed primarily to prevent the sin of fornication. It is just as if one were to maintain that the sole reason for baking bread is to prevent people from stealing cake.
A man is not idle because he is absorbed in thought. There is a visible labor and there is an invisible labor.
Grace can neither be bought, earned, or won by the creature. If it could be, it would cease to be grace.
God sent Jesus to join the human experience, which means to make a lot of mistakes. Jesus didn't arrive here knowing how to walk. He had fingers and toes, confusion, sexual feelings, crazy human internal processes. He had the same prejudices as the rest of his tribe: he had to learn that the Canaanite woman was a person. He had to suffer the hardships and tedium and setbacks of being a regular person. If he hadn't the incarnation would mean nothing.
Many a professing Christian is a stumbling-block because his worship is divided. On Sunday he worships God; on weekdays God has little or no place in his thoughts.
Are your convictions so fragile that mine cannot stand in opposition to them? Is your God so illusory that the presence of my Devil reveals his insufficiency?
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