The essence of mathematics lies precisely in its freedom.
Georg CantorRead
The essence of mathematics lies in its freedom.
Interpretation
Mathematics embodies freedom in thought and creativity.
In this quote, Georg Cantor emphasizes that the true beauty and power of mathematics stem from the freedom it offers to explore ideas, create new concepts, and think independently. This freedom allows mathematicians to innovate and pursue abstract thought without constraints, leading to profound discoveries and insights.
In practice
In a lecture on the philosophy of mathematics, one might cite this quote to illustrate the creative aspect of mathematical thought.
The essence of mathematics lies precisely in its freedom.
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.
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.
As for solitude, I cannot understand how certain people seek to lay claim to intellectual stature, nobility of soul and strength of character, yet have not the slightest feeling for seclusion; for solitude, I maintain, when joined with a quiet contemplation of nature, a serene and conscious faith in creation and the Creator, and a few vexations from outside is the only school for a mind of lofty endowment.
This world's existence is one night long. There's a great lively gathering that night, but some people sleep through it.
My characters aren't losers. They're rebels. They win by their refusal to play by everyone else's rules.
I realized that Eastern thought had somewhat more compassion for all living things. Man was a form of life that in another reincarnation might possibly be a horsefly or a bird of paradise or a deer. So a man of such a faith, looking at animals, might be looking at old friends or ancestors. In the East the wilderness has no evil connotation; it is thought of as an expression of the unity and harmony of the universe.
You have no doubt guessed long since that the conquest of time and the escape from reality, or however else it may be that you choose to describe your longing, means simply the wish to be relieved of your so-called personality. That is the prison where you lie.
As soon as you look at the world through an ideology you are finished. No reality fits an ideology. Life is beyond that. That is why people are always searching for a meaning to life. But life has no meaning; it cannot have meaning because meaning is a formula; meaning is something that makes sense to the mind. Every time you make sense out of reality, you bump into something that destroys the sense you made . Meaning is only found when you go beyond meaning.
Subscribe for the occasional hand-picked quote. No noise.