Can somebody explain me how modern mathematic knowledge is "managed".
I mean: Is there an international mathematical "canon", that says what parts a valid sections of mathematics, which says that for instance, the pythagorean theorem is part of that canon, or which says, that
if 2 figures have the same shape and size it is called "congruence" and not another word.
Thanks alot in advance
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Wolfgang Adamec
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1You might want to check out the recommendations in PlanetMath with respect to this topic. – Jose Arnaldo Bebita Dris Jun 15 '17 at 17:05
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For the classification of modern mathematics and definitions of standard terminologies, you can also refer to the Princeton Companion to Mathematics. – Jose Arnaldo Bebita Dris Jun 15 '17 at 17:08
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@Jose Arnaldo Bebita Dris I'm afraid that's not what the OP meant. I think this is about canonical mathematical notations, and things are not well, there. Look at the various notations for Stirling numbers, for example. Periodically, popular textbooks introduce some consense among the students using them, but generally speaking, there's a lot of anarchy. – Jun 15 '17 at 17:12
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Your tag for the question encapsulates a big part of the answer: definition.
It's all but impossible to do any mathematics without defining what you mean. The idea of congruence has different meaning depending on what branch of mathematics you're talking about. In plane geometry, a working definition might be: "Two figures are congruent if and only if one figure can be mapped to the other with a series of size-preserving translations and rotations." Congruence means something different when speaking about modular arithmetic.
But getting to canon, I'd think, would require a body of work that develops a mathematical paradigm using definitions, which through its creation by many mathematicians becomes a de facto standard.
John
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