A Quote by Gian-Carlo Rota
Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).
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Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!
Geometry existed before the creation. It is co-eternal with the mind of God...Geometry provided God with a model for the Creation.
The present author confesses that, to him, geometry is nothing at all, if not a branch of art ...
A Treatise on Algebraic Plane Curves
Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
I didn't invent satire. I didn't come up with it. And it will continue to be a very powerful tool to disrupt political taboos and social taboos and religious taboos, because those taboos are always used to control and to curb people's way of creativity and thinking, by making them feel guilty because they want to make a change.
American poetry is always about defining oneself individually,claiming one's right to be different and often to break taboos.
Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.
Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.
Music is the only place that I can have no taboos. In real life I have a lot of taboos, and I can't talk about everything easily.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
Remember, taboos are just a map of what a society feels it's acceptable to be neurotic about. Taboos aren't rational.
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
Geometry existed before creation.
I see some recurring themes: things that feel threaded together, some symbolic references, and songs about some of the big questions, like death. There are a lot of references to weather, too!
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