I wonder if professional mathematician uses recreational drugs in their work for muse

Yes: in many cases, caffeine. Voting to close (+1 gilkalai and Noah Snyder)

And, somthing else: there are statements to the extent, I could not produce a reference but I am certain to have read or seen this, that Erdős was not so happy regarding the popularization of this matter, mainly on the grounds that he was worried to set a bad example.

Regarding openness, I think a lot of researchers are pretty open about these types of things. That does not mean this topic is appropriate for MO -- I think perhaps you have the wrong idea of what this forum is about. There's a big difference between relaying a personal anecdote to a friend (or having it in your personal biography) compared with putting it up on an internet forum which Google encourages everyone on the planet to read. Also, this topic strays way too far over the gossip vs. mathematics content line.

The problem here seems to be an absence of a "control" for this thought experiment...

Although I still think it should not be an MO question, I actually find the question interesting. I have strong reason to believe that one of my undergraduate professors took cocaine specifically to enhance his mathematical thinking, although I would not dare name him. Numerous mathematicians have indulged in marijuana and LSD, but again, I wouldn't dare name anyone who had not gone public about that fact.

IMO the question just isn't a good question for MO. All kinds of people abuse drugs, and mathematicians are not special in this regard. You could similarly ask which mathematicians have speeding tickets, or who've gone through multiple divorces, or which mathematicans suffered abnormally from acne as teenagers... These just aren't relevant questions.

p.s. I do not wish to promote smoking. The sole goal is to have correct attributions of opinions.

p.p.s. I agree that this subject is unsuitable for MO.