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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#241

Post by keybored »

piloto_ciego wrote: post #60
kenjackson wrote: post #36

"how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place." That sounds like an "us problem", not an AI or OpenAI/Anthropic problem.

That's how I read it too, Terry Tao, who has been a "pro-AI math guy" is going through the same emotions and confusion that us SWE folks are going through, "oh, wait... this might mean I'm not going to be special anymore!?" I don't mean to be a dick, but I've talked about it previously. These folks are grieving. I get it, I've lived through this sort of life changing thing before, it sucks... but yeah.

It sucks. But yeah. Trillion-dollar industry wants your livelihood. This is but a force of nature.

Re: A misalignment of AI in mathematics

#243

Post by gwd »

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 turns out having an oracle for the "right" answer in chess, even without an explanation, used properly, allows humans to develop broader, more accurate insights.

The argument here sounds similar. The fear, as I understand this statement to be saying, is that by being given the correct answer, in the form of a 100-page Lean proof, humans will be robbed of the chance to from insights about the structure of mathematics itself. I don't see any reason that humans can't continue to develop insights as they try to digest the 100-page Lean proof into something more manageable; but with more certainty and fewer false starts.

Re: A misalignment of AI in mathematics

#244

Post by f311a »

qarl wrote: post #231

Is this really any different than the problem in software engineering - where AI is doing the work of junior programmers and now they aren't getting the development they need? Seems the same to me. And it'll be the same in all industries soon enough. And then it won't just be the junior people. All the same problem: what do people do now?

It’s better to compare this to computer science, especially, theoretical one. LLMs stop people from exploring new languages, architectures and so on.

Re: A misalignment of AI in mathematics

#245

Post by ThalesX »

boron1006 wrote: post #217
Art9681 wrote: post #169

Earlier quoted context omitted.

Nothing is stopping these folks from continuing to study the problems and arriving at their own solutions so they can continue having whatever insights along the way. Well, one thing is stopping them. There will be no more adoration for their genius. If you truly do it for understanding and not the attention, carry on. AI should change nothing about your motivations.

> Nothing is stopping these folks from continuing to study the problems My understanding is they are? And literally everything in this world is based around incentives. If you say “well you can continue to work on understanding, but your kids are going to starve” that’s not nothing.

It boggles my mind. Why cure cancer? The cancer researchers will be out of a job and their kids are going to starve!

Re: A misalignment of AI in mathematics

#246

Post by well_ackshually »

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…

So it wasted everyone's time, thousands of hours of research trying to disprove something said very loudly. What OpenAI is doing is a DoS of the scientific community: wasting your time trying to check if they're not wrong, and claiming glory in the mean time.

Re: A misalignment of AI in mathematics

#247

Post by qarl »

f311a wrote: post #244
qarl wrote: post #231

Is this really any different than the problem in software engineering - where AI is doing the work of junior programmers and now they aren't getting the development they need? Seems the same to me. And it'll be the same in all industries soon enough. And then it won't just be the junior people. All the same problem: what do people do now?

It’s better to compare this to computer science, especially, theoretical one. LLMs stop people from exploring new languages, architectures and so on.

Well... computer science really is math already. :)

Re: A misalignment of AI in mathematics

#248

Post by cubefox »

num42 wrote: post #228
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…

>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.

Re: A misalignment of AI in mathematics

#249

Post by sobellian »

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…

That solution (stop pouring resources in to proofs, stay in your lane) works today. How does it work 5, 10, 20 years from now? The software and hardware advances will continue.

Re: A misalignment of AI in mathematics

#250

Post by jrowen »

This kinda reminds me of the documentary about the top Go master that got beaten by a computer in dramatic fashion and had an existential crisis. Man confronting his own limitations in the realm he previously ruled unchallenged, what a time to be alive.

Nobody is going to care that the math isn't being done in the traditional way. The results speak for themselves, this is now a part of the landscape. No amount of hand-wringing is going to put the cat back in the bag. Adapt or perish.

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