A Quote by Hermann Weyl
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.
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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.
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
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.
So there’s a kind of resurgence of the sense of freedom and spontaneity in nature. From nature being bound into a rigid, deterministic model, freedom, spontaneity and openness are emerging once again. It’s now recognized the future is open, not determined by the past. And this is true in many realms, the astronomical realm, the human realm, the meteorological realm in many ways.
Let us simmer over our incalculable cauldron, our enthralling confusion, our hotchpotch of impulses, our perpetual miracle - for the soul throws up wonders every second. Movement and change are the essence of our being; rigidity is death; conformity is death; let us say what comes into our heads, repeat ourselves, contradict ourselves, fling out the wildest nonsense, and follow the most fantastic fancies without caring what the world does or thinks or says. For nothing matters except life.
The essence of mathematics lies in its freedom.
Mathematics is not something that you find lying around in your back yard. It's produced by the human mind. Yet if we ask where mathematics works best, it is in areas like particle physics and astrophysics, areas of fundamental science that are very, very far removed from everyday affairs.
There are very specific demands, though, in television, and you notice the budget constrictions. It's the time constraint and a purse constraint more than anything else that you notice. But the ambition of the writing and, hopefully, the delivery of it gets better and better because we want to outdo ourselves to keep ahead of a very expectant and hungry public.
The spiritual life is part of the human essence. It is a defining characteristic of human nature, without which human nature is not fully human.
The essence of mathematics lies precisely in its freedom.
What freedom and hope is found in Christ! We don’t need to feel beautiful about ourselves to find happiness! In fact, we’re better off not even thinking about ourselves. Rather, God has offered us in Jesus Christ forgiveness, hope, freedom from sin and a joy that never ends.
The conservative "thinks of political policies as intended to preserve order, justice, and freedom. The ideologue, on the contrary, thinks of politics as a revolutionary instrument for transforming society and even transforming human nature. In his march toward Utopia, the ideologue is merciless.
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.
The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics.
It is Deism which depicts God as the passive onlooker rather than the active governor of His world, and which assures us that the guarantee of human freedom lies in the fact that men's actions are not under God's control. But the Bible teaches rather that the freedom of God, who works in and through His creatures, leading them to act according to their nature, is itself the foundation and guarantee of the freedom of their action.
The guarantees of civil liberty are but guarantees of freedom of the human mind and spirit and of reasonable freedom and opportunity to express them...The very essence of the liberty which they guarantee is the freedom of the individual from compulsion as to what he shall think and what he shall say...
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