I have a long tex document and I would like to perform a search for finding some string inside math environments. Is there a search function already provided by auctex to do this? Other solutions are welcomed.
(I found https://stackoverflow.com/questions/19845598/emacs-regex-replacing-a-string-inside-a-latex-equation on a similar topic for replacing a string inside math environments).
Bundled with AUCTeX there is the texmathp utility (which, however, is independent from the TeX modes provided by AUCTeX and can be used without it), which allows you to test whether point is inside a mathematical mode or not.
The simplest suggestion I can give you is to combine texmathp with search-forward, here is a possible implementation:
(defun mg-search-in-math (string) (interactive "MSearch string: ") (while (null (and (search-forward string) (texmathp))))) 
texmathp(to test whether the string is inside math mode) together with standard Emacs searching facilities, but this possibility is already mentioned in the question on stackoverflow you linked. What's wrong with it?