A Quote by George Polya
Beauty in mathematics is seeing the truth without effort.
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[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.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
In the most general terms, the Enlightenment goes back to Plato's belief that truth and beauty and goodness are connected; that truth and beauty, disseminated widely, will sooner or later lead to goodness. (While we're making at effort at truth and goodness, beauty reminds us what we're hold out for.)
I don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers.
It is not expensive to be beautiful. It takes only a little effort to be presentable and beautiful. But it takes some effort. And unfortunately people think of beauty as luxury, beauty as frivolity, ... or extravagance. Beauty is a discipline, beauty is art, is harmony, in the ideological sense and in the theological sense, beauty is God and love made real. And the ultimate reach in this world is beauty.
The teleology of the Universe is directed to the production of Beauty... The type of Truth required for the final stretch of Beauty is a discovery and not a recapitulation... Apart from Beauty, Truth is neither good, nor bad... Truth matters because of beauty.
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.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.
A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school.
Mathematics rightly viewed possesses not only truth but supreme beauty.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
The most natural beauty in the world is honesty and moral truth. For all beauty is truth. True features make the beauty of the face; true proportions, the beauty of architecture; true measures, the beauty of harmony and music.
The economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.
Meditation means removing all your prejudices, putting all your conclusions aside, seeing without any hindrance, seeing without any curtains, seeing clearly without any mediation of any thought, seeing without Buddha standing between you and reality, or Krishna, or Christ.
Suppose you stand on a high place to enjoy the beauty of the sparkling sea below. You need do nothing to create that beauty; you need only BE IN THE SAME PLACE WHERE IT IS, and let nature do the rest. So it is with the inner life. There is nothing we can DO to gain psychic beauty. It already exists without our effort. We need only be where we belong, that is, in self-union. Then, beauty IS.
[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.
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