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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#261

Post by kzrdude »

fwlr wrote: post #146

In internet culture there’s this phrase “Hydrogen Bomb vs Coughing Baby”, meant to highlight the absurd power difference between two combatants. In almost any scenario even tangentially involving mathematics, twenty-five Fields medallists uniting to denounce something would be a veritable Tsar Bomba. It should give you pause that here they feel like the ailing infant.

Well OpenAI took one step on the back foot at least, withdrawing from sponsoring this math hackathon event https://xcancel.com/danintheory/status/2098125701782372640

Re: A misalignment of AI in mathematics

#262

Post by fantasizr »

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…

=> If chess.com was worth billions and Daniel Rensch was threatening everyone to do what he says.

Re: A misalignment of AI in mathematics

#263

Post by omnicognate »

mosura wrote: post #227
omnicognate wrote: post #201

Earlier quoted context omitted.

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 prac…

It's not a simple matter of "becoming good at", and yes, I could very well have similar concerns, depending on how it impacts the field. The statement itself mentions that such concerns exist in many other fields.

I doubt OpenAI will take such a combative stance and accuse these mathematicians of "demanding" things, as you do. As I said, the purpose of this is marketing and the statement simultaneously undermines the value of that marketing (showing these projects as irresponsible) and gives these companies an even better piece of marketing in its place: "our AI got so good at maths the mathematicians begged us to stop". It's entirely possible they will stop pouring millions into these projects.

Re: A misalignment of AI in mathematics

#264

Post by forshaper »

oytis wrote: post #59

Looks like mathematicians (like people in many other professions) have to redefine what their work means and how to define success. Hard to agree that a tool that can find a proof is detrimental by itself, rather it voids some assumptions people relied on previously

afaict it all started with taxes, farming, administration, astronomy, & construction, perhaps they could return to seeking results there

Re: A misalignment of AI in mathematics

#265

Post by edgyquant »

oytis wrote: post #213
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…

Is it not an option to make academia more like a normal job, where people focus on collectively achieved outcomes rather than credit, priority etc.?

How is that like a normal job?

Re: A misalignment of AI in mathematics

#266

Post by ksoped »

well_ackshually wrote: post #246
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.

Agreed! Although, if done by a mathematician, it's not a ~complete waste. I think the community learns something along the way.

Is there an established term for the idea of "DoS"? I've taken to calling it slop fatigue.

Re: A misalignment of AI in mathematics

#267

Post by doubtfuluser »

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 your grad studies, figuring out a proof as homework was hard, sometimes incredibly hard, but while doing it we gained a lot of understanding how things work. Now asking AI for the solution and „just“ getting it, risks our understanding, our creativity and our ability to connect the dots with other territories. I see it in students nowadays, there is much less understanding, much less creativity in finding solutions. I truly think this „short-path“ solution with the „death of struggle is one of the biggest risks with AI already for human development

Re: A misalignment of AI in mathematics

#268

Post by buellerbueller »

td2 wrote: post #235
trillobyte wrote: post #100

OpenAI: "Our mission is to ensure that artificial general intelligence benefits all of humanity." - Except the mathematicians who we'll scoop and cause existential dread among their entire field. - Except the software developers. They'll need to become plumbers or live on UBI. - Except the people in countries that can't afford the cost of AI tokens to keep up with the rest of the world. Just keep picking off groups o…

But its normal, and good, that technologal progress creates, and destroys some jobs. Imagin a cheap, 100% reliable, self driving car would be released. Death from Traffic incidence fall by orders of magnitude Would you argue it didnt benefit humanity, because taxi/bus drivers are nolonger required

the thing with all this innovation is that it seems to be inextricably linked to rent extraction, so where is this "cheap" you speak of?

Re: A misalignment of AI in mathematics

#269

Post by causalmodels »

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 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 feel like the mathematicians working on these should know about them, but on the other I feel a bit like a barbarian who suddenly finds themselves sacking Rome.

Re: A misalignment of AI in mathematics

#270

Post by avsegal »

againstapples wrote: post #125

At this rate AI will be doing all of the mathematics within 5 years, I don’t see why a mathematician would be worried about anything other than that at this point?

Sure, but who will care?

If no one understands it, it may as well have not happened. There's not much incentive to understand or internalize the results generated by AI. A human operator gives it a prompt and it produces some lean proof no one wants to (maybe can) read.

Without the community of human mathematicians internalizing the proof, simplifying it, and re-communicating it to others we end up losing the main output of mathematics as an institution.

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