It's amazing how much attention this issue has gotten. What is lost in the hype is no AI can tell you if a proof is correct. An AI can produce a convincing looking proof, but it can have a subtle but critical error or make an assumption that is unfounded. Thus, it ultimately comes down to humans. A mathematician has to craft the prompt, and mathematician to interpret/check the results. Also, these programs are very expensive and propitiatory. They are not like the commercial AI that regular people use. It takes considerable prompting and trial an error to solve even Olympiad/Putnam problems, and tons of work by humans pouring over the results to see if it's correct. For every Erdos problem that captures the headlines, there are many where it failed or untold hours of prompting and token burn to get that result, and manhours verify it.

Please read the article. You've ignored proof checkers.

I don't think you understand the workflow. Terrence Tao has done a lot of work using them in conjunction with LEAN.

You aren't having the AI check the proof, you interactively work on the same LEAN proof, handing off between the AI assistant and having LEAN check it and provide feedback for both of you when there's a mistake.

But just imagine...

(edit: lol didn't realize the sibling comment below is essentially my comment)

AI can't yet come up with any new ideas to make the inductive leap to solve a math problem. New ideas are what get the accolades and using an old idea just means the original author missed something. We are still at the author missed something stage that AI is doing today.

It can definitely be a good research assistant though