I used to write papers in math on LaTex. I wounder if there exists some program which makes semantic check. I want that there will check for example that it will warn on grammar mistakes, and will know to handle latex. Warn for example if I open ( but not close it. Check for math common mistakes like +\ldots+ ussually should be +\cdots+.
There are ChkTeX and lacheck which are both included in TeX Live. IMHO ChkTeX is superior, but I recently became it's maintainer, so I'm biased. There may be others as well that I don't know about. If there is something that it doesn't check that you would like, feel free to leave a feature request on the bug tracker.
ChkTeX is certainly not a full grammar checker since such a thing is quite hard, and extremely language dependent. But it catches common LaTeX mistakes, but I think that's what you want.