I don't know if your hypothesis will be valid in the future. Mathematicians and computer scientists are now working on computer-assisted proof systems (e.g. automated proof verification or proof construction), so in the future, it would be theoretically possible to work in isolation. (For references, see Computer-assisted proof - Wikipedia, the free encyclopedia and Mizar system - Wikipedia, the free encyclopedia.)
There are some other issues, as well. I think that there are some areas where releasing a paper to the community does not help either. For example, I've been told by a few professors that the massive proof of Fermat's Last Theorem is understood by a very small handful of people in the world. In some sense, it isn't all that reliable or satisfactory that almost nobody can understand it. (And this may be some motivation to get computers to do the checking.)
These things aside, I don't think that your claim is specific to mathematics, so I can't really see a point to your book. You can probably name any field in the arts or sciences where people exchange ideas in order to advance the field. It seems more fruitful to look for an activity that is done in complete isolation (which looks like a very hard-press). What specific ideas did you have in mind?