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I'm currently reading a book on analysis and always refer to specific theorems (e.g. chapter 2, theorem 3) when I need to prove something in the exercises.

Looking at a different analysis book, the same theorems have (of course) different identifiers.

So except the theorems that have widely known names, it is hard to crossreference them. For example if I want to prove a theorem using other theorems, how could I refer to them without explicitly mention them?

Is there an attempt to create a unified index of theorems, so you can refer to them on the internet? Is there even already such an index? (A proof of a theorem then could use references to this index, so a traversable graph of theorems and how they relate to each other could be built and you could have statistics on theorem usage etc.)

itmuckel
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One problem with this program is the fact that different books (and textbooks, especially) use slightly different definitions, so two theorem statements in two different books can be (1) identical in wording but yet (2) asserting different things. More subtly, a text book might make a global assumption throughout, in effect tacitly adding the list of hypotheses in each theorem in the book. That way, apparently different theorems are actually identical.

kimchi lover
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  • I imagined that with the perfect logical axiomatic/deductive method one could build a global work of knowledge where every theorem had a globally unique identifier. Would be interesting to have such a thing on the web, so the whole body of knowledge could be skimmed through. The math articles on wikipedia might be the closest thing we have so far... – itmuckel May 17 '20 at 19:38
  • I would add: the Wikipedia math articles are especially bad with regard to terminological consistency, and any argument relying on 2 or more such articles should be double checked to make sure they are consistent. In general I think your program is pretty close to the original Bourbaki program, which is refreshing in concept but in practice turgid in its handling of details of fine distinctions. – kimchi lover May 17 '20 at 19:50