100+ reactions to 100+ solutions
proofsandprompts.com
proofsandprompts.com
I think it’s very reasonable to expect the people that are dropping this on other people for review to have reviewed it first, closely, made adjustments, etc, the same way I do before dumping my Claude/ChatGPT assisted PRs onto other people.
The reviewers shouldn’t be exerting more effort than the person that set the prompt.
>The advent of AI was always going to be a seismic shock, but this huge dump of papers is a tsunami that we have no time to prepare for. It’s clear that OpenAI will happily wash away our community’s structures to further their financial interests.
1. Don't do the research internally (except someone else will do it once the model is public)?
2. Do the research internally but wait longer before telling anyone (this is what OpenAI did before, and mathematicians explicitly told them don't do it)?
3. Don't develop better models at all (except that Chinese models are only a few months behind)?
None of the options available to OpenAI would seem to solve the above concerns.
People would be more sympathetic if this was an alien race sharing their math results in not-quite-intelligible-to-us papers, because there at least we could assume that the aliens cared about the math and did their best to transmit their understanding to us.
They need to state it was entirely autonomous.
The stunned responses indicate a set of some of humanity's brightest struggling to comprehend the emergence of such an incomprehensibly creative and powerful intelligence.
AI has come for coding.
AI has come for mathematics.
AI will come for everything else if we don't do something NOW.
Today, g is one of the most robust findings in differential psychology. The tendency for different cognitive abilities to correlate positively has been replicated across numerous studies. g typically accounts for around 40 to 60% of the variance in cognitive test performance and is predictive of numerous life outcomes, including educational achievement and occupational performance. [2]
Evidence of g isn't confined to humans either. Studies of mice have identified a general cognitive factor explaining roughly 30 to 40% of the variation in performance across different learning tasks [3]. We have similar results for primates and birds.
To put it simply, intelligence tends to generalize. Humans who tend to have higher verbal skills also tend to have higher spatial skills, better memories, and faster processing speed. Someone with the cognitive ability to become an exceptional chemist might just as easily have become an exceptional mathematician or software engineer. The knowledge and skills required are obviously different, but the underlying cognitive abilities that make someone successful in one intellectually demanding field often transfer to others.
And yes, there is also evidence of g in LLMs [4].
[1] https://www.jstor.org/stable/1412107
[2] https://pmc.ncbi.nlm.nih.gov/articles/PMC8293439/
[3] https://pmc.ncbi.nlm.nih.gov/articles/PMC2614349/
[4] https://www.sciencedirect.com/science/article/pii/S016028962...
We are doing something now. We're making it so the AI does it all better, so we don't have to do it anymore. Gotta break a few eggs to make an omelet, but it's going to be a delicious fucking omelet when it's ready. I don't understand why people are pushing back so hard on making the world a better place. I personally can't wait until it's clankers all the way down.
i'd think that instead of just giving in and reacting with a cheap insult, highlighting the unreasonable leap in rhetoric might be a bit more persuasive. to be specific:
> I don't understand why people are pushing back so hard on making the world a better place.
"making the world a better place" is not what's receiving the pushback. on the contrary, kind of the whole argument is that the current developments are short sighted, and that they will leave leave the world in a worse place on the long term.
and then one can agree or disagree about that, but at least then we'd not be arguing strawmans anymore, nor approaching increasingly childish insults
So, it's like the story, "We'll see."
There has been a shocking but not altogether surprising development, and all reactions are valid.
Those are activities where repeating the same experience yourself is still enjoyable, kind of like you might eat today even though you already ate yesterday.
Finding mathematical proofs is probably more like seeing the ending to a mystery novel. Once the ending has been spoiled for you, it's really hard for you to enjoy it the same way, and it might be more fun to move on to a different mystery.
> People still play chess and go and StarCraft
Because most people still find them enjoyable. You can't say those are less enjoyable than math. There is no universal scale for enjoyment.
> kind of like you might eat today even though you already ate yesterday
You'd die if you stop eating after yesterday's meals. That's survival.
So math should switch to a Columbo methodology?
lots of people enjoy knowing the end of the story as they start a book, and it does not prevent them from enjoying the book in the slightest.
Something that always comes as a great surprise to those who don't.
There is this idea of advancing human knowledge and adding to the record of what people know in mathematical research that breaks the analogy down, somewhat. But most people aren't Perelman. They would happily take the million dollar prize. And it is out of the question to do anything other than put your name on the published paper.
https://www.youtube.com/watch?v=ouCVJIpSmEE
(This isn't to say I disagree with you.)
I think what people actually want when they say this is to be the hero. They want the admiration. Which is fine, but at least he honest.
Mathematics can be enjoyed recreationally as a puzzle like any other, but it isn’t just an arbitrary puzzle. It’s a science where one discovers truth and seeks an understanding of, and dreams up, new phenomena. It’s not chess, or go, or StarCraft. There’s no fixed rule set and the goal isn’t to ‘win’ or beat your opponents.
Let’s stop repeating this nonsense as if it’s a profound observation.
Poor analogy. Because math is one of those job-hobby type hybrids where the job may be enjoyable but you still need the academic infrastructure to do it on a modern level, both because you need funding and you need others to motivate you to keep to a certain standard.
Job-hobby hybrids like this are not the same as running and Starcraft where you can do it by yourself and still reap a lot of benefit from it in the same way. Hobbyists might still do math but if it were just up to the hobbyists, we wouldn't have the level of discovery we have today.
but very few get paid to do that
At least starving artists are safe!
Though its funding does move with the number of major projects academia is tasked with that rely on mathematics to advance, it's a fundamental knowledge area that has no operational requirements to exist.
> With these AI-generated papers, I feel that we, as a community, are not applying the same standards of quality and rigour. They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, unclear logical structure, multiple dead ends, and strange or unsettling terminology — in other words, slop. And we are then expected to go through it, check it, clean it up, simplify it, and explain what is actually going on. This comes at a considerable cost to us in terms of time and effort, while they can simply move on and slop-bulldoze the next conjecture. And, of course, the credit remains theirs. In some sense, we are willingly contributing to our own demise.
I'm not a mathematician, so I didn't even try to read it. But if it is unreadable slop -- then why should we (humans) believe it is correct? And why should professional mathematicians labor through reading it?
I like this website though because it collects a lot of the important frustrations from the mathematical community, these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject. The claim that AI proofs will open new frontiers for mathematics research could probably be true but misses the point that the manner OpenAI has gone about their “contribution” does more to cauterize the field than promote anything productive. OpenAI is functionally reducing the communities ability to ask real questions. Math is ultimately a very different field from the rest of the natural sciences, and I suspect a lot of the more simple discussion on this subject misses the objections because of those differences. All this to say, I don’t know that OpenAI is doing these haphazard releases cynically, with the assurance that all that matters is the headline, but it really does feel that way right now.
1. "...these open problems were curated in order to organize a field around, most to all of them only have/had value in so far as they promoted study of the subject" - I don't understand, how were the open problems curated? Do you mean that mathematicians put a lot of work into coming up with the problems and now all that work is somehow worthless now?
2. "OpenAI is functionally reducing the communities ability to ask real questions." How? Let's assume all the remaining proofs are correct (big assumption): how does resolving conjectures reduce the ability to pose new problems? This only makes sense to me if the assumption is that there are a relatively small number of possible problems to solve and so it's like a game that's coming to an end with no more interesting areas to explore. Surely math is bigger than these?
In particular, for Mathematicians worried about the inscrutability of AI-generated proofs and about the fact that Maths is first and foremost about understanding rather than proving for the sake of proving, they're vastly underestimating what AI will be able to deliver in years to come.
IMO, it's very likely that:
- AI will not just be able to prove theorems but more importantly *increase* the speed at which we *intuitively* understand the phenomenon under scrutiny. All these AI companies are busy using AIs to prove stuff, none of them has yet tried to point an AI in the direction of making an existing proof more understandable and intuitive to a human. My bet is there will be AIs trying to find the shortest path (where shorter = easier to understand) from an existing body of knowledge to a theorem proof, thereby iteratively slowly but surely "compressing" the whole universe of Mathematical knowledge over time (and making it easier for humans to digest).
- Same story for "discovering new mathematics", the other many-times-rehashed concern that AI-doing-math will impede that particular endeavor. Who's to say we can't define a bunch of criteria that quantify "interesting", point a bunch of AI's at it and press the button?1. Reacting from the POV of the individual person: disappointment, disillusionment, and/or grief from those who've worked on some problem for years and now don't have something to work on; it's been a part of their identity. As well as those whose career tracks and plans were thrown in disarray.
I wholeheartedly sympathize with the above.
2. Reacting from the POV of the entirety of mathematics as a field of study/research:
"If OpenAI wanted to destroy the mathematical community, this would be a great way to go about it."
"...it will create conflict in the mathematical community;"
"I feel that solving so many problems in such a short time may damage the math community and profession"
"They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with redundant arguments, ... — in other words, slop. And we are then expected to go through it, check it, clean it up, simplify it, and explain what is actually going on. This comes at a considerable cost to us ...And, of course, the credit remains theirs."
"Open problems are a resource that the mathematical community developed over decades or even centuries"
What if a human dropped all of these without AI? I suspect there wouldn't be the same reaction for some reason.
If OpenAI were coming up with interesting problems that everyone could explore as they foreclosed all these existing ones, I don't think the response would be as critical. Obviously, that's much more difficult and doesn't tie into the only telos of these companies (having a huge IPO to make all their investors and equity holding employees rich).
As usual (at least, as of recently), Terry Tao's assessment is measured but trenchant. Mathematical research has been a human process of improving understanding, to an extent that if you go far back enough in time, it was not distinguished from "philosophy". Part of that involves (involved?) ac academic engagement with the pursuit of knowledge, which means that results are discussed, presented, picked apart, etc., in a community of other people in pursuit of knowledge. The end result being the sum knowledge that humanity possesses grows. The way these results were dumped unceremoniously bypasses all of that. And, because we have all seen what regard the tech leadership class have shown for humanity, even in much more concrete and significant ethical questions than "is it ok to destroy the academic community", such as "is it ok to lower the friction to surveilling and/or enacting violence on society to the extent that it's all encompassing", I think it's pretty reasonable that their complicity in the latter will extend to the former.
I should point out that this is not a categorical treatment of AI results. I think about outcomes. Would I be angry if OpenAI dropped full contents of all the Vesuvius Challenge scrolls? Obviously not.