How to write mail to super senior renowned mathematicians?
"Respected Sir" seems off and pretentious, at least in an international setting. It's not commonly used. 

Use "Dear" to be on the save side, and by the way, there's no need to gesture "greater respect" in your greeting. Your appreciation of the researchers previous work and career should be prevalent in the content of your message, in which you demonstrate knowledge of their achievements and capabilities. Attempts at scoring cheap points with cheesy greetings are not the way.