I was thinking it may be useful to have some sort of database of math definitions/theorems for MSE.
At university, we all use the same book. So, it's easy to say something like, by definition 3.2, or by Lemma 4. But as MSE there is no common book. So either I need to write down definitions/theorems of the book, or I must assume people know where I'm talking about.
But sometimes, of course, people don´t know where you´re talking about. And many times it´s very useful for the reader to get reminded of a given theorem/definition.
I wouldn't mind to put all the definitions of my analysis book in a database. Would be a very useful exercise for me. And then I can refer to those definitions every time I (or anybody else) need them. But I don't know how to create such a (mathjax) database.
I'm not talking about a database with the idea to make some universal definitions. I just see it as an easy way to refer to the definitions/theorems in a given book.
I see it like this. You go to the database. You type in the book you're using. And then you can scroll to the definitions/theorems used in that book, select one, and use it as reference at MSE.
If the definitions/theorems of the book you use, doesn't exist yet, it should be very easy to add them. In theory, such a database could become immensely large, but I don't think it would be very complicated to use it. Especially if the user knows which book he wants to refer to.
Edit: This idea doesn't seem very popular, and thinking about, I think if such a database should be made, it would be better to do it independently of stack exchange. Can I close this topic ?
Edit 2: I'm still intrested tough about what would be other (easy/good) ways to refer to definitions/theorems at MSE. Using wikipedia? Wolfram? Proofwiki ? Maybe I can make a discussion from this? Or open a chat room ?
Edit 3: I'm stil fancying this idea, but as I said, maybe it should be done independent of MSE. About making such a thing, copying text literally from online math textbooks, would make the task easier. Of course adding some latex macros takes some time, but for some people this is only a very good exercise. Here are some clear cut benefits I think such a database would give:
- Writing proofs in the same style as usual in a mathbook.
- Easy copy/paste defintions/theorems in mathjax to your post.
- It could be used for interactive math games which train you to memorize those definitions/theorems.
- Could link the reader to a whole set of defintions/theorems the writer is familiar with. Easy way to provide the context the post is written in.
- If such a mathjax database would exist, you could think about writing math proofs using the advantages of the internet. For example, referring to a definition normally makes the reader have to search for it in the book/internet. Giving a little pop-up, would be much more convenient for example.