Nope, introspecting motivation is useful. There have been similar posts made about people using bots in PvP competitive online gaming: some people play to enjoy the game, and hopefully get better until they reach their skill ceiling. Others play (just)to win, and are open to buying aimbot hardware and software
Not if the essence boils down to moving goalpoasts to the next best thing that will likely be flown past as well within months rather than years. Sure mathematicians who do this stuff purely for the love of it will continue to exist. Just like human chess or the retro-programming scene exist for similar reasons. But if you are a professional who expects to earn a living salary on these things, your intellect will suddenly be outcompeted by orders of magnitude. Ignoring this today by saying LLM's can't do this or that will undoubtedly set you up for a rude awakening. For all we know is that there is still no fundamental limit to what they can do in theory and compute may well be the only true limit.
Which organizations do the most math research? What are their budgets, droves and culture? You may be falling victim to the pre-IPO PR razzle-dazzle by AI companies expending unreasonable resources on problems they know will get them good press and make their models appear superhuman.
A university math department will not spend $20M in one summer to solve 1 problem when it can hire 10 human mathematicians for 10 years.