I think he was looking for "mathematician".

I think Perelman himself wouldn't care too much what you call him. He would say something like: “Everybody understood that if the proof is correct then no other recognition is needed.” (As he said before.)

You don't need a license to be a mathematician. There's this conjecture, undecided for 100 years. Whoever solves it gets the glory. He doesn't have to be a "mathematician" or an "expert". A correct proof is all it takes.

He solved it, and all that's left for us is to discuss whether he's an expert or not:)

Is there some reason to assume that all mathematicians are experts?

At least in the context of the headline, you can assume any mathematician being offered a $1m prize is likely to be an expert.

In wider usage, I guess you could say "Math expert" to distinguish between students and professionals, but it's still as clear as mud because it doesn't state which field of mathematics the person is an expert in.