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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:

  1. Writing proofs in the same style as usual in a mathbook.
  2. Easy copy/paste defintions/theorems in mathjax to your post.
  3. It could be used for interactive math games which train you to memorize those definitions/theorems.
  4. 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.
  5. 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.
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  • $\begingroup$ Like a massive online math-textbook? $\endgroup$ – Thomas Dec 17 '12 at 14:49
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    $\begingroup$ We'll make our own copy of wikipedia ... $\endgroup$ – GEdgar Dec 17 '12 at 14:52
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    $\begingroup$ While it might be useful for some contexts, the problem in relation to MSE is that the usefulness for this site would be that people did not have to write the definitions they were using but could refer to that database. Unfortunately, there are often a lot of equivalent definitions, and a lot of questions here are basically about proving those equivalences, which would make that usefulness go away. $\endgroup$ – Tobias Kildetoft Dec 17 '12 at 15:08
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    $\begingroup$ @GEdgar: Will it contain the same mistakes, or do we intend to correct them while at it? :-) $\endgroup$ – Asaf Karagila Dec 17 '12 at 15:08
  • $\begingroup$ @Tobias But instead of referring, they could also just copy/paste the mathjax code of the defintion to the question ? Which would be useful right ? $\endgroup$ – Kasper Dec 17 '12 at 15:26
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    $\begingroup$ Only if the definition in the database matches the one they have been given. So this would require the database to contain a lot of possible definition for each thing. $\endgroup$ – Tobias Kildetoft Dec 17 '12 at 15:27
  • $\begingroup$ @Tobias Yes, that is the idea. To order the definitions per book. If the book you're using is not in the database, you can just write down the definition (like you normally do), and maybe add them to the database for other people (or for yourself in the future). $\endgroup$ – Kasper Dec 17 '12 at 15:29
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    $\begingroup$ Have you given any thought to the number of texts that are used in universities around the world? Who do you think will be going through these texts and MathJax-ify everything? And then you also have to think about the number of common texts that usually aren't used in courses. The benefits (if any) hardly compare to the costs of such an undertaking. $\endgroup$ – user642796 Dec 17 '12 at 15:31
  • $\begingroup$ @ArthurFischer I don't see it like starting the mission: "Mathjax-ify everyting". I see it like, I would like to put some definitions/theorems in a database so I can refer to them easily. This doesn't cost anybody anything. If someone else feels like putting some definitions in a database as well, it would be nice if he put in the same database, so the database becomes more and more useful. $\endgroup$ – Kasper Dec 17 '12 at 15:40
  • $\begingroup$ People use different books because their tastes differ. It would be impossible to create a book/database which everyone liked! Thus, such a thing can never be standardised... $\endgroup$ – user1729 Dec 17 '12 at 15:40
  • $\begingroup$ @user1729 I guess my post wasn't so clear.. You're actually in line with what I'm saying. "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." $\endgroup$ – Kasper Dec 17 '12 at 15:43
  • $\begingroup$ @Kasper: Putting anything in a database has a cost, even if it is miniscule. First, the database has to exist, and even if there is no monetary cost for that there must be at least a cost in terms of work to set up the database. Second, databases have a way of growing and never shrinking. Eventually, even the smallest database will become big enough that the storage needed incurs some monetary cost, or significant barter. I can't think of one thing useful in the world that doesn't cost anybody anything. $\endgroup$ – Todd Wilcox Dec 17 '12 at 18:20
  • $\begingroup$ @ToddWilcox Okay, I agree. I don't know anything about databases, so I guess you're right. $\endgroup$ – Kasper Dec 17 '12 at 19:33
  • $\begingroup$ @Kasper "We all use the same book"?? Oh wow.... $\endgroup$ – user38268 Dec 19 '12 at 5:42
  • $\begingroup$ If you really want to begin something like this, perhaps start up a Wiki somewhere (there are some free Wiki-farms that have MathJax support) and begin inputting the definitions and theorems from the texts you want to reference. It won't be a database, per se, but at least you will begin to see the sort of effort that will be involved if you ever want to set it up properly. $\endgroup$ – user642796 Dec 19 '12 at 6:33
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When the definition is not likely to be known, it can always just be typed into the answer. Space is not limited there.

For general online reference purposes, I think the coverage in Wikipedia is decent enough. They have a definition of most mathematical topics, and the definitions are usually right. Trying to recreate that seems like a duplication of effort without any significant benefit. Many people here just link to Wikipedia when they want to give a general reference.

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  • $\begingroup$ Many theorems which will never appear on Wikipedia, only because they have not been given a name. $\endgroup$ – Kasper Dec 17 '12 at 21:38
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    $\begingroup$ @Kasper: Dear Kasper, It would probably be more productive to add material to wikipedia if you think it is lacking in certain areas, rather than try to duplicate it. Also, dozens (hundreds?) of new theorems are being proved in mathematics every day. It's not feasible to imagine cataloguing them all. Regards, $\endgroup$ – Matt E Dec 19 '12 at 6:04
  • $\begingroup$ @Kasper You may be more interested in ProofWiki then, where all theorems (are to) appear. $\endgroup$ – punctured dusk Oct 22 '17 at 9:53
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PlanetMath is a wiki project whose goal is somewhat similar to this; you might want to contribute articles over there. I agree with everyone that this is not a good fit for math.SE's mission.

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In my respectful opinion, I think that your idea is way off the point. The point of Stack Exchange is to create simplistic forums. In the existence of millions of online resources, it is pointless to create one more. I would prefer helping other mathematical portals such as Wikipedia's to duplicating it. It would be a waste of time, as well as money. I would like to echo Carl Mummert and Matt E.

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  • $\begingroup$ The point is not to make anything like Wikipedia anyway. Its about being able to refer to books. To exact duplicates. Not imitatio, not aemulatio, just translatio. $\endgroup$ – Kasper Dec 19 '12 at 12:32

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