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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#251

Post by stabbles »

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…

The maths community is now in the antithesis phase, synthesis will take a while ;)

Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available.

But on the other hand, people learned a lot from chess engines. After decades of chess computers beating humans, there was still a renewed interest in watching Leela beat Stockfish, with many people trying to understand the strategy Leela used.

If your happiness comes from grinding on a problem and making progress, the prospect of having to dig through a corpus of AI-generated proofs might be hard to swallow. But if you're willing to do that, you will still find beautiful things that only so many people can truly appreciate.

Re: A misalignment of AI in mathematics

#252

Post by ksoped »

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 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.

Re: A misalignment of AI in mathematics

#253

Post by well_ackshually »

jrflo wrote: post #173
tmhn2 wrote: post #130

Earlier quoted context omitted.

The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system…

I don't think it really attacks human understanding though. You can still read and understand an AI written proof. If another person comes up with a solution to a problem, you can read their methods and understand it. It doesn't matter if a human came up with that or not. It's really only attacking the "generating new ideas" part.

>You can still read and understand an AI written proof.

No you can't lol, they're multi million lines of Lean, which is already an obscure language to understand. It's an assault on your senses.

Re: A misalignment of AI in mathematics

#254

Post by ksoped »

cubefox wrote: post #248
num42 wrote: post #228

Earlier quoted context omitted.

>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI. Title: Terence Tao - SAIR Competitions and the…

> Dr. Tao said the same thing. Apparently he has since changed his mind.

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

Re: A misalignment of AI in mathematics

#256

Post by nonsensical_ »

azan_ wrote: post #238
nonsensical_ wrote: post #158

I’m trying to determine now if Terence Tao was a plant or a useful idiot. Maybe both.

Care to elaborate?

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 little too late.

Re: A misalignment of AI in mathematics

#257

Post by cubefox »

wbl wrote: post #67
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…

Open problems are not that yardstick. Fermat's Last Theorem is the result of Wiles and Wiles-Taylor, but without key results from Serre, Ribet, Ihara, Langlands-Tunnels, and Frey's program none of what Wiles did would work. But Wiles did get the prize. Nowadays I think the inputs have shrunk a bit by doing more in the R=T theorem so less other cleverness needed.

Doing the last step of solving an open problem is the yard stick. But not for much longer: https://davidbessis.substack.com/p/the-fall-of-the-theorem-e...

Re: A misalignment of AI in mathematics

#258

Post by cevi »

pred_ wrote: post #157
XTXinverseXTY wrote: post #3

Puts the onus on the AI companies to provide a specific replacement mechanism, no? Unless I'm unfamiliar with something else he's written that proposes something more specific and constructive To Tao’s credit he obviously identified the problem very clearly and admits understandably "we did not have the time to have a more consultative process, as with Leiden; but we decided that the urgency of the situation was such…

How specific and constructive it is might be debatable, but he has tried to make concrete recommendations earlier; see e.g. slides 46-51 from the ICM talk: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p... – obviously there's some way to go still.

Nothing makes me respect Terry Tao more than the line "I hate Jean Bourgain" handwritten into the margin of one of Bourgain's papers. IYKYK

Re: A misalignment of AI in mathematics

#259

Post by tossandthrow »

gwd wrote: post #243

This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It…

I like this approach.

A but like whenever the first sprinter hits a new world record other runners follow along.

Knowing that something is possible tends to strengthen our ability to work with it.

We will potentially see the same with math.

Re: A misalignment of AI in mathematics

#260

Post by sim04ful »

Playing a devil's advocate. Why do we need understanding ? To take an example i would say ~99% of the population do not understand how combustion engines or how semiconductors work, what say another 1% ? Is the fear post-apocalyptic in nature ? We need some human priesthood to carry on tradition ? why ?

Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, reasonably un-constrained by any institutional interests.

What say the 1% ?

Lifted up my comment for addition visibility

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