[onetimeusename]

I'm not arguing that people should do things as hard of a way as possible, I think that's kind of a straw man. I am not saying we should tie stones around us, write things in Latin, and not use computers or something like that.

Math is not really about just piling up results in my opinion. Most people's day to day lives were not directly changed by the recent Erdős problem that was solved by AI. I think most people believe the result would have been more impressive if a human had found the counterexample. People do not list those problems because they need to be urgently solved but because they are hard and interesting and it impresses us when a human solves it.

But not only that, the person gains insight along the journey. I am not sure what insight AI can give us really. It basically maximizes text output over a massive dataset that includes mathematical research. So again, the journey itself is valuable not just because it's hard but because it gives us information.

There's also the problem that credibility for so many things is based on attribution of doing something difficult. A PhD has been a way we measure credibility in a field. It's a fence you hop to get in. If AI can write up a thesis in a tiny fraction of time and cost, it could break attribution if people print theirs with AI but also it breaks the credibility link. Is that important? For math, using PhDs as a measure of credibility in some ways is a bad way to do things, but it's effective and probably the best we have. (For other fields it could be catastrophic). So it destroys a signal about the author which may not be catastrophic here. Where this goes wrong is if getting a PhD is now obsolete. People who have experience and who can review AI output proofs exist right now but how will we ensure anyone is trained in proofs in the future? If we're going to outsource math to AI I think the reason people are right now getting PhDs could be completely obsolete unless we agree it's worth it for people to work through it on their own and gain that experience for themselves.

[briandw]

I'll do my best to restate the problem. If AI does all the work, then we won't have people who can understand the math that AI's are creating.

This is the real problem as I see it and it extends to most technical work. I didn't see that as the main argument of the article.

I was objecting to the old guard defending their turf.

Academia needs to contend with this problem, and start addressing it right now. People are not going to be able to beat AIs at math. So whats the solution? PhDs will have to be able to show competence in new ways. Publishing and review of mathematical work will have to change. The genie is out of the bottle and there is no putting it back.