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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#421

Post by nonsensical_ »

kzrdude wrote: post #379
nonsensical_ wrote: post #256

Earlier quoted context omitted.

Mostly that he really should have seen this coming. These people absolutely do not care what happens to mathematics (or any other field). They compulsively lie and steal and they played Tao and others like a fiddle. He danced to their tune and now that the music has stopped, now do they complain. He was the poster boy of the mathematician yielding these tools for his own benefit. But he forgot who the owners are. Too…

You should read his comment from wednesday here: https://terrytao.wordpress.com/2026/09/07/finite-time-blowup... And yes, at one point it gives you right about them taking advantage of him. He sat down for an interview and found later that they just used the "best clips" out of it for an OpenAI ad.

That’s table stakes!

Re: A misalignment of AI in mathematics

#423

Post by dullcrisp »

pfdietz wrote: post #102
dullcrisp wrote: post #25

Earlier quoted context omitted.

They’re not asking them to stop working on AI, but to stop publishing mathematics.

In other news, evangelical christians ask scientists to stop publishing about evolution. We apparently have a moral obligation to protect existing power structures? Tao should maybe consider there are people who are indifferent to, or actively want to tear down, his institutions; why should they cooperate in preserving them? Whatever happens has to be resilient in the face of defection; any scheme where everyone is e…

You have a practical obligation to obey existing power structures. That’s what makes it a power structure. What do you all think is happening here? There have been people who decided what math gets published for centuries.

Re: A misalignment of AI in mathematics

#424

Post by sghiassy »

matco11 wrote: post #401
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…

I get excited at the idea of a world in which advanced mathematical problems (and their solutions) become much more accessible to a much greater number of people. As a result, making mathematics much more loved at a societal level. Imagine a world where these most complex mathematical problems are not accessible to a few hundred people, but a few hundred thousands people. ...Those original few hundred gifted mathemat…

As a laymen, I wish the same. But I also hope it doesn’t disincentivize those that dedicated themselves to the study

Re: A misalignment of AI in mathematics

#425

Post by genxy »

alkyon wrote: post #366
tzumaoli wrote: post #234

Earlier quoted context omitted.

Is this the scenario described in Ted Chiang's short story https://en.wikipedia.org/wiki/The_Evolution_of_Human_Science where scientists are "catching crumbs from the table" trying to decipher the results generated by superhuman intelligence?

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.

Re: A misalignment of AI in mathematics

#426

Post by astrobe_ »

piker wrote: post #191
matherial wrote: post #179

Earlier quoted context omitted.

I'm really tired of these arguments (this and "it's just like calculators"). Photography decimated other forms of visual art, so the concern wasn't wrong. But AI threatens the entirety of human intellectual endeavors . I can make do without oil paintings in my home. I'm not sure I want to live in a future where we make do without brains.

Had me until the last word. Cameras did take away oil paintings, but not eyes.

It did. While you're busy recording an "instagramable" moment, you are not entirely enjoying that moment. Your eyes are on the screen, not on the subject.

In a way, if photography is an ersatz for painting that eventually made imaging available for the masses, then AI could become an ersatz for thinking. But it feels like I'm paraphrasing TFA.

What will happen when AI companies have spent their advertising budget on math problems and whatever else gives the maximum wow effect for the bucks? Probably customers hooked on the vain satisfaction of spending token$ to impress friends.

Re: A misalignment of AI in mathematics

#427

Post by keeda »

I understand this stance and where they are coming from, but I can't help but think this sounds very analogous to engineers' arguments against AI-assisted and vibe-coding, especially with regard to cognitive debt. Yet the software industry is plowing ahead, reportedly pushing mountains of unreviewed code to Prod, and the world hasn't ended.

Of course, nobody's really comfortable with it, so this is also a forcing function for the industry to adapt and figure out new techniques to manage complexity and trust. I think the same will happen with Mathematics.

But it is also possible we will end up with three forms of Mathematics: the one we understand, the one we don't, and the one we don't understand but can prove to work. Kind of like magic -- with all the positive and negative connotations of the word.

It is pretty evident that these models will soon exceed our cognitive capabilities. Is it right to hold them back just because we can't keep up? Many of those discoveries will be so beyond us that we can't do anything with them, but that also means they can't hurt us. On the other hand, there could be many discoveries that we can parlay into practically useful applications, even if we don't understand them.

Just like LLMs.

Re: A misalignment of AI in mathematics

#428

Post by onetimeusename »

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…

But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it.

I don't like nuance here. I think progress is really measured by what humans are able to do and understand, not machines. It is significant if we find problems we struggle to solve. That tells us something. What does it take for humans to solve these problems is related.

The best analogy I can give is if you wanted to climb Mt. Everest you might ask someone for guidance. Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak? This is like the AI versus human gap to me. The helicopter is like using AI to generate a proof. The person who actually climbed Mt. Everest has firsthand knowledge of the experience. Same thing for a difficult proof. The struggle people have is actually valuable here. Likewise, we know people are actually capable of climbing Mt. Everest but if they had only ever rode a helicopter to the top, the knowledge of climbing it would not exist, and surely that is meaningful knowledge given the risks.

So if we rely on AI for proofs I think we lose a sense of what is difficult and why. We lose a sense of what human achievement is. Surely climbing Mt. Everest means more than taking a helicopter up? For students, why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? This would have the affect of destroying knowledge.

(please do not nitpick the analogy because it's the best but perhaps a clumsy way to describe my thoughts)

Re: A misalignment of AI in mathematics

#429

Post by causalmodels »

youoy wrote: post #377
causalmodels wrote: post #269

Earlier quoted context omitted.

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I fee…

It depends. If you are trying to understand better the field, then do a good write up of the proofs so that people can learn from it. If you want to earn the respect of people because you found interesting proofs. Then do a good write up of the proofs so thst people can learn from it. If you want to plant flags and pollute peoples minds. Then please publish it anonimously, no one wants to correct LLM slop for you. Pr…

Maybe I'll end up doing the write ups pseudonymously. I have taken care to make sure the results can meaningfully contribute to field but I don't want to plant flags or really receive credit of any kind. I just think they are interesting.

I like my current life and don't want to get dragged into the current fracas surrounding the use of AI in math.

Re: A misalignment of AI in mathematics

#430

Post by ArcHound »

debatem1 wrote: post #345
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.

Also, you learn to be a better chess player by... playing better players. The widespread availability of chess engines has made flawless opponents available to every player. If your goals are understanding the game, self improvement, building thinking skills-- this is the best chess has ever been. It's only if your goal is to beat every opponent you can find that chess is in a bad place.

It's not that easy. Playing stockfish is like playing tennis against the wall (for untitled players at least).

Even if you don't blunder anything, you'll still find yourself in a worse position without any clue as of what went wrong and why.

Whereas when playing humans, they can usually explain their approach and when they noticed errors in your play.

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