Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A misalignment of AI in mathematics

mathandai.org

Post reply on HN
Print view View original

221–230 of 617 posts

Re: A misalignment of AI in mathematics

#221

Post by 9question1 »

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.

That's precisely the problem though. You cannot still read and understand an AI written proof at the current skill level of the AI being applied, because they're orders of magnitude longer than human written proofs even when they don't need to be, and spend most of that length on the parts that aren't important. This has been really thoroughly documented by expert mathematicians who are engaging with AI in public like Terence Tao and showing in detail how much work it takes working alongside AI to figure out how to understand AI generated proofs. With human generated proofs that process is forced to happen before publishing the proof because the new style of AI generated proofs validated only by formal verification is supplanting the old human peer review process that forced the burden of understanding onto the publisher and not the reader.

Re: A misalignment of AI in mathematics

#222

Post by willmeyers »

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…

Genuine Art versus Mechanism, from 1901, (https://www.jstor.org/stable/25505621) is another article that I read a few years ago that other people might find interesting.

Re: A misalignment of AI in mathematics

#224

Post by fooker »

Maybe mathematicians should be aligned better, rather than AI?

The current measure of a successful mathematician is the problems they have solved or worked on. At some point in history, the measure of a successful scholar was how well one could copy manuscripts.

Once we have a tool that starts to work well for this task, it's time to define success differently. It's a classic alignment problem! ;)

But seriously, these people should start focusing on finding and proposing more important problems. And the credit of discovery should go to the person who defined a new category of important problems.

It appears to me this is an incredible inflection point in mathematics, a neat forcing function like cryptography was for the development for modern number theory and algebraic geometry.

Fundamental problems with great implications for other fields will be solved by AI because some entity would throw tokens at it. And these would be further built upon.

Re: A misalignment of AI in mathematics

#225

Post by Forgeties79 »

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…

It’s not a parallel. No one ever claimed photography to be the same as painting or some other medium - it was a new medium that wasn’t respected.

AI is being treated and pushed as a replacement for every medium.

Re: A misalignment of AI in mathematics

#226

Post by deaton »

sim04ful wrote: post #164

"We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose" Suppose we eventually have GPT-7-class models running practically on $100 devices, with their activity transparent, inspectable, and reproducible. At that point, what exactly is left for us to fear from this threat?

The fact that those models are encroaching on things only human minds could do. Personally, as a human, I want there to be things humans are the best at, and intellectual things were the final thing that machines hadn't beaten us at.

Re: A misalignment of AI in mathematics

#227

Post by mosura »

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…

> What the mathematicians are saying is stop pouring resources that most mathematicians can only dream of accessing into projects that are actively damaging to their field. They face a massive challenge of figuring out how maths can evolve in the face of this new technology, and this is not helping.

Is it reasonable for any field to make such demands? If this were doctors objecting to AI becoming good at medical practice would you have the same concerns?

While any idea of OpenAI spying on people to pursue their goals is disgusting, the rest of this is par for the course, as Kasparov experienced with IBM in the 90s. Humans still play chess after all.

Re: A misalignment of AI in mathematics

#228

Post by num42 »

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 Future of Experimental Mathematics

https://www.youtube.com/watch?v=rB9YOi3lb7w

and this:

Daniel Litt - Working with LLMs to do high quality math

https://www.youtube.com/watch?v=0wL8NlhxXcU

Re: A misalignment of AI in mathematics

#229

Post by piloto_ciego »

throwaway1921 wrote: post #206
piloto_ciego wrote: post #60

Earlier quoted context omitted.

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.

I think this is ridiculously flippant. If software engineering and the hardest math is solved, that means that eventually a majority of professions and knowledge work is solved. This is hugely problematic because of the way our society currently functions. People need jobs to eat, pay for housing, etc. Dismissing it as "innovations have happened before" is disingenuous. Yes, innovations have happened, but none of tho…

Our current society will certainly not survive. Read Mark Fisher’s capitalist realism. You’re right that all most works are “cooked.”

Re: A misalignment of AI in mathematics

#230

Post by ksoped »

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.

Not "a" human's understanding; Humanity's understanding. Understanding the research problem, and the solution especially, is a lot more involved than simply "read their methods". That's the whole point being made.

It matters if a human came up with it because of everything mentioned in the article... A mathematician's solution is necessarily built on other's ideas that have been disseminated, internalized, pressure tested etc. Methodologies differ too. AI can abuse its compute resources and generate a true/false or counterexample statements, without laying the foundation that a decade of globalized research would have.

Post reply on HN