A Quote by Georg Cantor
The essence of mathematics lies in its freedom.
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The essence of mathematics lies precisely in its freedom.
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.
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.
Lies cannot nourish or protect you. Only freedom from fear, freedom from lies, can make us beautiful, and keep us safe.
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.
The most important aspect of freedom of speech is freedom to learn. All education is a continuous dialogue - questions and answers that pursue every problem on the horizon. That is the essence of academic freedom.
The history of humanity is the history of human freedom...Freedom is not, as Engels thought, "the recognition of necessity." Freedom is the opposite of necessity. Freedom is necessity overcome. Progress is, in essence, the progress of human freedom. Yes, and after all, life itself is freedom. The evolution of life is the evolution of freedom.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
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