Often people who are critical of whether AI can lead to research breakthroughs are experts in the respective area, who nevertheless are afraid of their future career prospects in academia (getting a permanent position in academia is hard and it is deeply political who gets such a position).
This people are thus not scared by AI per se (it's basically their daily job to devise innovations that advance their field), but their fears are that
- because of the hype around AI the research into which they invested years, often decades, will be considered "unimportant",
- incompotent people in decision-making positions will think researchers can be replaced by AI.
This is a certainty, not a fear =[.
No, it did not. Do not trust the AI propaganda, a match researcher USED AI as a tool to solve unsolved math problems, the AI by itself didn't do anything. They are two entirely different things. If the match researcher didn't give the AI the prompts he gave the AI wouldn't have find any solution.
Yes, we could say that AI is an useful tool to use in math research (the same as calculators, and then computer, are) but no, AI did not solve any problem.