A Quote by Hermann Hankel
In mathematics alone each generations adds a new story to the old structure.
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In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure.
New generations of humans inherit the acquired discoveries of generations past, allowing cosmic insight to accumulate without limit. Each discovery of science therefore adds a rung to a ladder of knowledge whose end is not in sight because we are building the ladder as we go along. As far as I can tell, as we assemble and ascend this ladder, we will forever uncover the secrets of the universe - one by one.
Plot is what happens in your story. Every story needs structure, just as every body needs a skeleton. It is how you 'flesh out and clothe' your structure that makes each story unique.
A good story, a story resonant and remarkable, can be remade endlessly to tell new sides of itself for new generations of readers.
The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
When you're all alone out there, on the end of the typewriter, with each new story a new appraisal by the world of whether you can still get it up or not, arrogance and self-esteem and deep breathing are all you have. It often looks like egomania. I assure you it's the bold coverup of the absolutely terrified.
One of the remarkable qualities of the story is that it creates space. We can dwell in a story, walk around, find our own place. The story confronts but does not oppress; the story inspires but does not manipulate. The story invites us to an encounter, a dialogue, a mutual sharing. As long as we have stories to tell to each other there is hope. As long as we can remind each other of the lives of men and women in whom the love of God becomes manifest, there is reason to move forward to new land in which new stories are hidden.
Each new generation of children grows up in the new environment its parents have created, and each generation of brains becomes wired in a different way. The human mind can change radically in just a few generations.
It's all a question of story. We are in trouble just now because we do not have a good story. We are in between stories. The old story, the account of how we fit into it, is no longer effective. Yet we have not learned the new story.
The life of a thinking man will probably be divided into two parts -- the first in which he desires to exterminate modern thinkers, and the second in which he desires to watch them exterminating each other. ... Suppose, for instance, there is an old story and a new skeptic who is skeptical of the story. We have only to wait a little while for a yet newer skeptic who is skeptical of the skeptic. He will probably find the old notion actually a help in his new notion. This process is an abstract truth applying to anything, apart from agreement or disagreement.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
The EU lacks a story. For previous generations, the peace argument was a sufficient. But what story do I tell my 20-year-old son? How do I explain to him that we need the EU for the future?
Who keeps the old akindle and adds new knowledge is fitted to be a teacher.
For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?
The Greeks used to use the same stories, the same mythology, time after time, different authors. There was no premium placed upon an original story, and indeed, Shakespeare likewise. A lot of people wrote plays about great kings. They didn't expect a brand-new story. It was what that new author made of the old story. It is probably the same now. We disguise it by inventing what seem to be new stories, but they're basically the same story anyway.
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