I find it very easy to write with mathematica. There are a lot of templates to choose from, and the formula visualization is cool. Also it's very convenient to manage chapters and sections. With EndNote, citation is not a problem. So isn't it a good idea to write academic papers in mathematics?
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In my experience, journals only accept $\TeX$ (or $\LaTeX$) for publication.
It appears that Mathematica is able to export its notebooks as $\TeX$. You may need to do a fair amount of tweaking to the output to make it acceptable to the journal, though. They will typically have their own style file which must be used, and often other requirements which Mathematica's output may or may not satisfy.
There are a few books written in Mathematica and dealing with mathematical research (to some extent), they are really interesting, e.g. :
Most research journals require $\TeX$, and one can export Mathematica notebooks to $\TeX$, but they'll still need some work to refine and bring them to a required format. On the other hand one can publish in The Mathematica Journal using a specific template, although it doesn't have to be always the best choice.
There is no general definitve answer to this question, since it depends on many factors and skills in programming. I don't think so it is very convenient to manage chapters and sections, e.g. changing stylesheets, screen environments etc. is not in general reversable, at least as one would like it. It is much easier to write good-looking articles in $\TeX$. Perhaps in future it will be much easier to publish research papers with Mathematica, though it is already a great programming environment and really rewarding even nowadays.
I have written the majority of my papers in LATEX. I use Mathematica to create many diagrams, graphs, dynamic models etc. Mathematica, however, imports LATEX. So if it allows you to organize the paper in an easier fashion, I don't see why not. Journals, take note, might have their own required formats though, so make certain Mathematica can meet those requirements.