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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#381

Post by criddell »

bpodgursky wrote: post #186
grufkork wrote: post #47

Earlier quoted context omitted.

Going to the gym and using a forklift

There is an implicit agreement that mathematics is funded, for the most part by the public, as a way to advance the state of knowledge and propagate (even if very indirectly) what has learned for the public good. It was never about helping individual mathematicians demonstrate that they are individually good at math. It happened to work out that way, but it wasn't the goal.

I've been wondering if mathematics is going to go the way of particle physics in that it will start to take a lot of money to make advancements.

Re: A misalignment of AI in mathematics

#382

Post by yunwal »

pred_ wrote: post #77

Seeing how /r/singularity and /r/accelerate are leaking into maths forums, I foresee a wave of comments that fail to understand Tao's message, whether on purpose or not, so let's try to be clear here: Tao is not someone who is anti-AI for the sake of being anti-AI. He has been advocating for the usefulness of AI in maths for a long time, to the point that people have started calling him a shill for the commercial com…

I think most people here get that this is the point?

The point beyond this one is that an AI proof doesn’t prevent humans from working on the problem, it destroys the current economic incentive to work on the problem. Perhaps we should rethink the current incentives. In order to make money as a chess player, you don’t need to beat AI, or ban AI from playing chess.

If mathematics took a similar approach (we don’t get paid for solving net-new problems, we get paid for enriching human understanding), then there’s no issue.

Re: A misalignment of AI in mathematics

#383

Post by demibabs »

tmhn2 wrote: post #280
ksoped wrote: post #252

Earlier quoted context omitted.

It's not just the isolated dumping, it's the fast, isolated, possibly untraceable dumping, without long term support. It'll basically become slop fatigue if OpenAI starts dumping out proofs faster than the community can keep up, and some turn out to be wrong, never formalize it, don't stay to support it, etc.

I wonder if they will continue to dump proofs, though? Their point has been made, the novelty will wear off, and it maybe won't be a priority use of their resources to spend however many millions on another big proof--they will move on to the next thing to show off I'm sure. At that point, the ones generating proofs will be, I hope, mathematicians (professional and otherwise) that are more interested in the results a…

They already told the NYT that they’ve made “substantial progress” on another one of the MP Problems (most likely the Hodge Conjecture).

That said, that’s probably just because of the drama miring their most recent one. After 2 I don’t see why they’d bother anymore.

Re: A misalignment of AI in mathematics

#384

Post by johnsmith1840 »

nancyminusone wrote: post #320
johnsmith1840 wrote: post #298

They can get with the program or be the equivalent of a genius SWE writing assembly on punchcards in 2026. The only thing I read from this is their ego being bruised by a machine. If these people cared more about discovery and advancement of human knowledge the only thing they should be doing is celebrating. There's no proof of plagarism but that's an independent issue. How are they not realizing that in the future c…

for the same reason why you do not get full credit for only writing down an answer without showing work in an exam.

lol what a bad analogy. Why should anyone care how much effort a result takes to achieve? If anything our entire world functions because we reduce that effort as much as possible.

I don't judge you for not growing your own food when you hand me a burger.

Re: A misalignment of AI in mathematics

#385

Post by lbrito »

pllbnk wrote: post #275
david-gpu wrote: post #141

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…

I have listened quite a few interviews with Tao and I see him being very careful about criticizing AI. He very often emphasizes the usefulness of it. Where he is critical has a lot of merit. One of the points I clearly remember him saying that having AI be able to solve many of the open problems, regardless of how important there are (there are many open problems that are not that important) greatly reduces the probl…

>I have listened quite a few interviews with Tao and I see him being very careful about criticizing AI. He very often emphasizes the usefulness of it.

This is tiresome. People should be able to flat-out criticize AI without the implied need to justify themselves all the time or "be careful". Its almost like AI has a trillion-dollar agenda backing it, to the point that you have to add a careful "its really great! But there's this little issue..." for any criticism.

Even those who are very pro AI should have the intellectual honesty of admitting that there are very valid reasons to criticize AI.

Re: A misalignment of AI in mathematics

#386

Post by pfdietz »

ameliaquining wrote: post #83
jonahx wrote: post #37

The concerns seem valid. I'm unclear what the ask is, though. What, even in theory, is a practical and realistic fix?

Well, they could ask frontier labs to stop publishing math results. I find it telling that they stop short of explicitly doing this.

It would be too transparently ridiculous.

Re: A misalignment of AI in mathematics

#387

Post by SpicyLemonZest »

cubefox wrote: post #319
ksoped wrote: post #254

Earlier quoted context omitted.

Did he say so somewhere? I don't think these ideas are contradictory. It's just an pro AI tooling but anti-slop stance.

Where is the difference?

He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things.

He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's understanding of them is like prompting Claude to go through a Jira board, write code for all the open tickets, and then close them without merging or deploying the code.

Re: A misalignment of AI in mathematics

#389

Post by pfdietz »

pred_ wrote: post #232
ameliaquining wrote: post #83

Earlier quoted context omitted.

Well, they could ask frontier labs to stop publishing math results. I find it telling that they stop short of explicitly doing this.

If frontier labs had chosen to go the path of offering to assist in existing endeavors, helping to build knowledge alongside researchers in ongoing projects and following ethical and professional research standards, we wouldn't be having this discussion at all; everyone would be stoked. Instead we have companies that disgracefully try to scoop researchers and fail to properly attribute earlier work and instead rebran…

This sort of nonsense makes me root for the AI companies to set the edifice of organized math on fire.

Re: A misalignment of AI in mathematics

#390

Post by soerxpso »

omnicognate wrote: post #201
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

Are they claiming that the only value in solving these problems was for their field's personal development process? I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology. It would be insane to demand that people avoid making progress on technology that can save lives or improve general quality of life, just to protect the sanctity of your karate belt system. Perhaps in lieu of open problems left to solve, mathematicians should be welcome to take up chess or sudoku to keep their minds spry.
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