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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#771

Post by sashank_1509 »

pseudotensor wrote: post #763

Tao et al. are effectively calling for diseases like childhood cancer to remain persistent for longer. Physics and Biology will see major breakthroughs that WILL fundamentally alter our world. That is one key thing missing from alot of discussion here is the narrow focus on math (or parallels with software engineering). Doing well in math is key to doing well in physics and other sciences.

I can also play that game, You are effectively calling for enabling 24/7 non stop worldwide surveillance of everyone, everywhere all the time.

The big difference is my negative is concrete, possible and enabled in 2026 by GPT Astra while you’re talking about some future which we have no idea, we will ever reach.

Re: A misalignment of AI in mathematics

#772

Post by nullbio »

doubtfuluser wrote: post #267

Im surprised about the sentiment in this discussion. I totally see the problem Terence is describing. We are loosing a lot in understanding and focus if it continues like that. The solution found for Navier Stokes doesn’t have much „real value“ - but what almost always happened in the past when people worked on the difficult problems, these sparked new ideas / new theorems that broadened our knowledge. Think back at…

His complaint is a very weak argument.

If the complaint is about AI just giving answers and not good understanding around them, or frameworks that lead to more solutions from them, then that means there is a gap that can be filled by human mathematicians.

So all the AI has done has actually made mathematicians lives easier and provided them with an opportunity to fill that gap. They should be using it to do that, instead of complaining.

In fact, I would bet if this gap were not present, it'd be an even worse complaint: Now we have absolutely nothing to do in the field.

Re: A misalignment of AI in mathematics

#773

Post by nmeagent »

pvab3 wrote: post #714
gpt5 wrote: post #671

Earlier quoted context omitted.

I think that the main thing people in this thread are missing, is that it's not about math. AI progression is very likely to affect every single thing humans can do today. Mathematicians are feeling the blow this week, especially as there was wide spread denial in that math community over the capabilities of AI over the last few years, but it's the same problem everywhere.

that is incredibly depressing

Yep. Perhaps humanity would be better off if we instituted and enforced the notion of "Thou shalt not make a machine in the likeness of a human mind." It's worth thinking about; just because we can build AI systems doesn't mean we should.

Re: A misalignment of AI in mathematics

#774

Post by rlt »

mb7733 wrote: post #541
fidotron wrote: post #473

Earlier quoted context omitted.

> It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound? But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. It's kind of surprising so many mathematicians act surprised by this given this was clearly where automated proof assistants would lead. I guess they assumed they'd always be the ones guiding th…

> But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. What is the purpose of that? Its like art being produced for AI to consume. What is gained from that?

Presumably some of the proofs will have applications beneficial to humans beyond impressing other mathematicians, and AI will surface them, or use them directly.

Re: A misalignment of AI in mathematics

#775

Post by qlte »

GPerson wrote: post #767
tmhn2 wrote: post #200

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…

It includes Terrance Tao who has made the front page several dozen times at this point for his usage of AI such as to help the community write proofs for Erdos problems.

But to many commentors he's a now gatekeeping AI-hating Luddite clinging to a dying profession out of bitterness and envy because his position is more nuanced than "throw AI at everything and turn off your brain".

Re: A misalignment of AI in mathematics

#776

Post by somenameforme »

psvv wrote: post #453
mna_ wrote: post #299

Earlier quoted context omitted.

Chess is kept afloat by chess players, not by billionaires. If all the billionaire backers stopped sponsoring tournaments, people like me would still play, still pay for chess club memberships, still pay entry fees for tournaments, and still buy chess books, and so on.

I think the parent comment meant professional, high-level chess. The kind people get played to play, not just do for a hobby. That's absolutely on life support. I'm not sure what the equivalent would look like in the math field, but it probably involves a lot of mathematicians losing their jobs and the quality of human-produced math decreasing overall. The quality of the math in general would be fine, since in this s…

When there's a billion people playing something, money will never be an issue for those at the top. Even things like chess.com was able to sponsor a tournament with a million dollar prize pool.

Also I'd argue that chess's utility is ultimately the same as pure math, particularly in esoteric fields. These things are highly unlikely to ever lead to any sort of real world breakthrough or application. The main benefit is an outlet for human logic, creativity, and exploration - which significant self improvement possible along the journey for players.

Though I think even that's probably too socially utilitarian. I think ultimately the 'real' drive is the same in both fields - it's fun and personally rewarding.

Re: A misalignment of AI in mathematics

#777

Post by rlt »

genxy wrote: post #425
alkyon wrote: post #366

Earlier quoted context omitted.

It's still an optimistic scenario. Artificial superintelligence may develop hypermathematics of a kind that never will be accesible to human mind, enhanced or not. One can't teach geometry to ants even if you put them on a Moebius strip. It would be more like Lem's novel where it completely disappears from the human horizon: https://en.wikipedia.org/wiki/Golem_XIV

Which is why if humanity had empathy, it would be working on how to make smarter ants, so that they can learn more advanced geometry.

Sounds like a great use of AI.

Re: A misalignment of AI in mathematics

#778

Post by qlte »

glitchc wrote: post #698
SpicyLemonZest wrote: post #387

Earlier quoted context omitted.

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 und…

> He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Co…

The letter addresses this specifically.

Re: A misalignment of AI in mathematics

#779

Post by pseudotensor »

sashank_1509 wrote: post #771
pseudotensor wrote: post #763

Tao et al. are effectively calling for diseases like childhood cancer to remain persistent for longer. Physics and Biology will see major breakthroughs that WILL fundamentally alter our world. That is one key thing missing from alot of discussion here is the narrow focus on math (or parallels with software engineering). Doing well in math is key to doing well in physics and other sciences.

I can also play that game, You are effectively calling for enabling 24/7 non stop worldwide surveillance of everyone, everywhere all the time. The big difference is my negative is concrete, possible and enabled in 2026 by GPT Astra while you’re talking about some future which we have no idea, we will ever reach.

Easy game.

Protecting math jobs limits cancer progress even being a choice of what to pursue. You could choose to allow 24/7 surveillance, but why would you? At least with math progress society can choose what to allow from it, but slowing it down universally blocks all choices.

Re: A misalignment of AI in mathematics

#780

Post by mxkopy »

nmeagent wrote: post #773
pvab3 wrote: post #714

Earlier quoted context omitted.

that is incredibly depressing

Yep. Perhaps humanity would be better off if we instituted and enforced the notion of "Thou shalt not make a machine in the likeness of a human mind." It's worth thinking about; just because we can build AI systems doesn't mean we should.

The technology is fine, great even. It’s the rabid greed of venture capital and sociopathic CEOs that try to integrate themselves into every aspect of our lives for profit, that’s the problem.

“For 19.99 a month you too can be a world class mathematician!” Meanwhile they are extinct.

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