[capstone]

I don't know about this. My father is a scientist, and while he signs his correspondence as Sasha, he publishes under Alexander. As for метмах vs. матмех - it could easily be Perelman having a dyslexic moment, or the journalist misquoting. All these "clues" are so nitpicky... not worth a conspiracy theory IMHO.

You are right about nicknames though. I used it in a colloquial sense but the correct term would be a familiar form.