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by magimas
9 days ago
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I don't know, I don't think this "effort for effort's sake" is a very convincing argument. In particular, I think it's very much affected by recency bias in a way? What we perceive as "effort worth taking" instead of "dull occupational therapy" is very prone to change with technology. If you would argue that modern photographers need to take the time to physically develop their photos and use chemicals to get their effects rather than applying photoshop filters, you'd not be taken very seriously - in the 80s and 90s it would have been a very different discussion where people saw photoshop as "taking the helicopter to the summit of Mt Everest". Same even with paper writing. I still had old school teachers in the 90s and early 2000s who insisted that writing anything on a computer was a "shortcut" that would encourage worse writing because you could undo stuff etc. They did all their handouts and worksheets on their old typewriters. There is a discussion to be had on AI in maths, but I don't think it's this one. I think mathematicians should be talking about what the future of their field is supposed to look like in a time where AI will be able to find the proofs. Maybe maths will turn into a more "experimental" science, where you already know the proof of a theorem, but you want to find a particularly elegant way that helps humans understand it or find other ways to apply the knowledge. Or rewrite old theories from different angles based on all the new proofs generated by AI. I don't know, but I think there's a lot of mathematics to do out there for humans even in a time with AI. |
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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.