A Quote by Georg Cantor
The essence of mathematics lies precisely in its freedom.
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The essence of mathematics lies in its freedom.
We can never intimidate and discourage the people who voice their words with courage. The essence of freedom rests precisely here - in the freedom of expression of the people. And we must protect it.
In mathematics, our freedom lies in the questions we ask — and in how we pursue them — but not in the answers awaiting us.
Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
The essence of man is his freedom. Sin is committed in that freedom. Sin can therefore not be attributed to a defect in his essence. It can only be understood as a self-contradiction, made possible by the fact of his freedom but not following necessarily from it.
...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
Freedom. Freedom of religion. Freedom to speak their mind. Freedom to build a life. And yes, freedom to build a business. With their own hands. This is the essence of the American experience.
What is the essence of America? The essence of America is finding and maintaining that perfect, delicate balance between freedom "to" and freedom "from."
Freedom is the very essence of our economy and society. Without freedom the human mind is prevented from unleashing its creative force. But what is also clear is that this freedom does not stand alone. It is freedom in responsibility and freedom to exercise responsibility.
Let me go over this again on the reclaiming the civil rights movement. People of faith that believe that you have an equal right to justice - that is the essence. And if it's not the essence, then we've been sold a pack of lies. The essence is everyone deserves a shot - the content of character, not the color of skin.
A poet’s freedom lies precisely in the impossibility of worldly success. It is the freedom of one who knows he will never be anything but a failure in the world’s estimation, and may do as he pleases. The poet is a man on the sidelines of life, sidelined for life. He belongs to the aristocracy of the outcast, the lowest of the low, below the salt of the earth. A member of the most ancient regime in the world. One that cannot, it seems, be overthrown.
Lies cannot nourish or protect you. Only freedom from fear, freedom from lies, can make us beautiful, and keep us safe.
Know, then, that now, precisely now, these people are more certain than ever before that they are completely free, and at the same time they themselves have brought us their freedom and obediently laid it at our feet. It is our doing, but is it what you wanted? This sort of freedom?' Again I don't understand', Alyosha interrupted, 'Is he being ironic? Is he laughing?' Not in the least. He precisely lays it to his and his colleagues' credit that they have finally overcome freedom, and have done so in order to make people happy.
Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us.
...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
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