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Fair enough. But I think you may be conflating an explanation with an excuse. I think your root cause analysis may be fruitful for explaining why they wrote the

by stbede 17d ago

Fair enough. But I think you may be conflating an explanation with an excuse. I think your root cause analysis may be fruitful for explaining why they wrote the letter. But I don't think that it excuses what they actually wrote.

rramadass 15d ago
The letter is just a call to action reminding everyone how Mathematics is done and how Mathematicians operate within their domain with all the Human factors involved. But because of the bad behaviour (plagiarism, going-behind-the-back etc.) and incentives misalignment, AI companies are currently not aligned with that. There is also the structural problem of generating proofs at a rapid pace just because you can but then have no way for "proof digestion" which is the key in the mathematical process. See Terence Tao's writings - https://teorth.github.io/tao-web/ai-views.html https://teorth.github.io/tao-web/ai-views.html
- stbede 15d ago
  I agree. But my frustration is that there is no argument why AI should be aligned with mathematics. Why can't the mathematicians that value their own community remain aloof from what AI companies are doing. Can't they continue to take their time digesting proofs, gaining insights, and attributing credit to mathematicians doing good work. Here's how I perceive the situation: Before: - mathematicians digest current results and develop insights - insights lead to new results - new results give mathematicians an opportunity to credit those insights Now: - AI companies release a bunch of potentially uncredited proofs - mathematicians digest these results and gain insights - mathematicians recapitulate AI proofs in terms of their deeper insights and theory - mathematicians give credit for these new insights and progress in understanding, even though the binary true-false status of theorems were already determined beforehand. If the true-false status itself isn't real mathematics, then mathematicians still can do the real mathematics after the fact and continue to celebrate each others' work. The only thing they lose is the ability to attribute a human to deciding the true-false status, which isn't real math anyways (though maybe valuable for motivation). What they gain is efficiency. Every mathematician working towards proving NS won't blow up can now shift their resources to understanding why it can blowup. Perhaps the letter is implying that the mathematical community itself will become misaligned with how mathematics is currently done. I'm unpersuaded it's entirely the AI companies' fault if that happens. AI may create a lot of temptations for individual mathematicians to become lazy, but that seems like something the mathematical community needs to resolve for itself. Every institution needs to take a lot of self-ownership here. I'm also annoyed about parents complaining about their own children being addicted to their phones as if it isn't in their own power to determine if their children have phones in the first place. I think this letter would be better directed at universities and journals. They should be holding their own institutions to account if they feel like they are adopting the mentalities of the AI companies and no longer faithfully executing the values of mathematics.
- carefree-bob 15d ago
  The real issue is that there is "research" and then there is research. Most publications are simple recapitulations of well known ideas but applied to somewhat unique environments. Imagine if you are a carpenter, you are just using your existing tools to make more stuff, but fundamentally what you are doing is no different from what any other carpenter is doing. It's workmanlike production. The truly valuable stuff is coming up with new ideas, that is, new techniques that allow for breakthroughs. That is rare, is done by only a handful of people in any decade, and is very, very hard. When you study a book on the history of math, you see the names of people that created brand new techniques which allowed them to solve problems no one else could solve. But you still have that 99.9% that needs jobs, and they need to publish, but what they are doing can be mostly replaced by AI. The specific situation with Navier-Stokes really highlights this. Mathematicians came up with the technique, but the AI managed to apply it faster than even the technique inventors. So it appears that AI is now good enough to be doing the workmanlike stuff, which is the bread and butter of a lot of mathematicians that are just trying to get their publications in so they are not fired. I do think this creates real problems for the field and that some changes are necessary.
  - stbede 15d ago
    Exactly. This is what the letter should have focused on. The issue is not alignment, per se. If AI can do the workmanlike stuff at breakneck speeds, academia will decide between two options: 1) Keep the average mathematician employed doing redundant mathematics just to have capable humans around. Every now and then you get one of those mathematicians actually developing new ideas, but most departments will entirely be just for show. It's doable though. College sports is able to keep itself going along these lines (and I mean the track, softball, and polo type sports). 2) You get unemployed mathematicians who were still developing their abilities. And as a result you lose the institutions that generate the mathematicians that contribute new ideas. You get to keep the handful of exceptional mathematicians that are developing new ideas, and that's survivable if you happen to be a Fields medalist. None of this really has to do with the AI companies aligning themselves to giving credit and developing insights. If AI companies became aligned to that, then the AI's would be replacing the Fields medalists, too.

by stbede 17d ago

rramadass 15d ago

The letter is just a call to action reminding everyone how Mathematics is done and how Mathematicians operate within their domain with all the Human factors involved. But because of the bad behaviour (plagiarism, going-behind-the-back etc.) and incentives misalignment, AI companies are currently not aligned with that. There is also the structural problem of generating proofs at a rapid pace just because you can but then have no way for "proof digestion" which is the key in the mathematical process. See Terence Tao's writings - https://teorth.github.io/tao-web/ai-views.html https://teorth.github.io/tao-web/ai-views.html

stbede 15d ago
I agree. But my frustration is that there is no argument why AI should be aligned with mathematics. Why can't the mathematicians that value their own community remain aloof from what AI companies are doing. Can't they continue to take their time digesting proofs, gaining insights, and attributing credit to mathematicians doing good work. Here's how I perceive the situation: Before: - mathematicians digest current results and develop insights - insights lead to new results - new results give mathematicians an opportunity to credit those insights Now: - AI companies release a bunch of potentially uncredited proofs - mathematicians digest these results and gain insights - mathematicians recapitulate AI proofs in terms of their deeper insights and theory - mathematicians give credit for these new insights and progress in understanding, even though the binary true-false status of theorems were already determined beforehand. If the true-false status itself isn't real mathematics, then mathematicians still can do the real mathematics after the fact and continue to celebrate each others' work. The only thing they lose is the ability to attribute a human to deciding the true-false status, which isn't real math anyways (though maybe valuable for motivation). What they gain is efficiency. Every mathematician working towards proving NS won't blow up can now shift their resources to understanding why it can blowup. Perhaps the letter is implying that the mathematical community itself will become misaligned with how mathematics is currently done. I'm unpersuaded it's entirely the AI companies' fault if that happens. AI may create a lot of temptations for individual mathematicians to become lazy, but that seems like something the mathematical community needs to resolve for itself. Every institution needs to take a lot of self-ownership here. I'm also annoyed about parents complaining about their own children being addicted to their phones as if it isn't in their own power to determine if their children have phones in the first place. I think this letter would be better directed at universities and journals. They should be holding their own institutions to account if they feel like they are adopting the mentalities of the AI companies and no longer faithfully executing the values of mathematics.
carefree-bob 15d ago
The real issue is that there is "research" and then there is research. Most publications are simple recapitulations of well known ideas but applied to somewhat unique environments. Imagine if you are a carpenter, you are just using your existing tools to make more stuff, but fundamentally what you are doing is no different from what any other carpenter is doing. It's workmanlike production. The truly valuable stuff is coming up with new ideas, that is, new techniques that allow for breakthroughs. That is rare, is done by only a handful of people in any decade, and is very, very hard. When you study a book on the history of math, you see the names of people that created brand new techniques which allowed them to solve problems no one else could solve. But you still have that 99.9% that needs jobs, and they need to publish, but what they are doing can be mostly replaced by AI. The specific situation with Navier-Stokes really highlights this. Mathematicians came up with the technique, but the AI managed to apply it faster than even the technique inventors. So it appears that AI is now good enough to be doing the workmanlike stuff, which is the bread and butter of a lot of mathematicians that are just trying to get their publications in so they are not fired. I do think this creates real problems for the field and that some changes are necessary.
- stbede 15d ago
  Exactly. This is what the letter should have focused on. The issue is not alignment, per se. If AI can do the workmanlike stuff at breakneck speeds, academia will decide between two options: 1) Keep the average mathematician employed doing redundant mathematics just to have capable humans around. Every now and then you get one of those mathematicians actually developing new ideas, but most departments will entirely be just for show. It's doable though. College sports is able to keep itself going along these lines (and I mean the track, softball, and polo type sports). 2) You get unemployed mathematicians who were still developing their abilities. And as a result you lose the institutions that generate the mathematicians that contribute new ideas. You get to keep the handful of exceptional mathematicians that are developing new ideas, and that's survivable if you happen to be a Fields medalist. None of this really has to do with the AI companies aligning themselves to giving credit and developing insights. If AI companies became aligned to that, then the AI's would be replacing the Fields medalists, too.