It doesn’t “try” anything… it can’t “try” anything. If prompted to ask a question it can ask a question… indeed if the provided prompt leads to a question being

It doesn’t “try” anything… it can’t “try” anything. If prompted to ask a question it can ask a question… indeed if the provided prompt leads to a question being the statistically most likely response then the response will most likely be a question. At no point and in no way is it attempting to gather novel information. You could specialize it towards asking tougher questions of those who prompted it that it was chatting with a famous mathematician, I suppose, though it wouldn’t know a famous mathematician from anyone adequately mimicking (or really just purporting to be) that mathematician. It could be made to learn their response and give it greater than usual future weight, as well, but woe be unto anyone who tries to use what it learned from such a one-off interaction to do anything important.