I was talking to Eduardo the other day, and he told me how he has been trying for years to get people to put a math encyclopedia together online, but he has had no success so far. The idea is very appealing (and has been probably around for a while): a search engine whose search items are mathematical theorems, displayed in a standard format, and containing basic results building up to theories like calculus or group theory, appropiately crossreferenced, as well as recent research results. In other words, an ultimate mathematical reference, one that researchers can use to find the right theorems on subjects in which they are not necessarily specialized, and implemented using current search engine technology. This project, in its most comprehensive form, would be the work of a very large number of mathematicians over an indefinitely long period of time, especially for complementation and reevaluation of the existing database with more recent results, but could dramatically simplify the search of everyday math results for the working mathematician.
One of the main problems on the way are probably copyright laws: all but the oldest results must be published with permission of authors and publishers, and a truly universal reference would make increasingly obsolete many textbooks, resulting on a negative pressure on the part of math publishers like Springer and Elsevier. In any case, all but the most standard results would come with due credit to their authors, and possibly including authors of previous relevant results. Still, copyrights remain a very tricky issue, and the way the theorems are presented will likely benefit some authors to the expense of others. A number of copyright lawyers would be needed for counsel and ideas around these problems. Also, one could bring publishers on one's side by trying to work with them from the beginning.
More towards the mathematical side, the success of such a project will largely depend on the way the information is organized and displayed. There doesn't need to be any real intention of teaching mathematicians a theory by showing one theorem after another. Rather, the reader would be referred to standard textbooks that include the result. I imagine one being able to search for single words appearing in the statement of the theorem, with enphasis on whether they appear in the hypotheses or in the conclusions. Results would be associated with a theory, a branch of that theory and so forth, for searching and browsing purposes. But often a result could be in the intersection of several theories (or subtheories, etc.), and would have to be included in both, which makes the organization tree not really a tree - but then this is how it is organized in our heads. The organization would need to borrow on much mathematical intuition, but CS theories like expert systems (?) could be useful, and one would need the help of guys in the search engine business, like Google.
As a starting point for this rather vast project, one could imagine a proof of principle by constructing a small such search engine with standard basic results from a restricted field, say textbook group theory or number theory (maybe this is on its way already?). I would welcome any feedback on the subject!
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