Is there a modern mathematical canon

Question

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

Answer 1

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.