I feel like this kind of "result dump" just cheapens mathematics. How about having a little respect for those whose work this builds on, and current mathematicians some of who may have spent years working on these problems.
Rather than sitting on these results until they had enough for a "shock and awe" 10-result dump, how about releasing these results individually as they were made/verified, as well as the failures (equally valuable to assess the current capabilities of LLMs), and try to make some analysis of HOW these breakthrough results were made. What were the prompts for each of these, how much guidance was there from the mathematicians employed by OpenAI, and most importantly how did the model arrive at these results ... what lines of reasoning resulted it in exploring ideas that humans had previously not explored?
I know it’s tough, but I am not a fan of elitism. Mathematics is no different from all other branches which themselves are just intellectual labor which is again just a special type of labor. There is nothing magical about it and if computers can trivialize it, so be it.
Where were all the mathematicians and academics in general when “regular joe” was automated? Now it’s hitting close to home and their foreheads are starting to get sweaty. I’d say let them. Tough luck. Make mathematics as “cheap” as possible. Nobody owes them any favors.
Let’s commoditize “being smart” and let go of arbitrary divisions between us.
This is what the Ludites were trying to accomplish with an (armed) uprising.
Go back 100 years and 15 percent of the population was "Farmer", and 30 percent were in some sort of "domestic" work.
Most modern jobs are a product of the fact that technology continues to advance. And by all measures it does not look like "ai" is going to change that.
Yes, but in practice that doesn’t happen. Again, I did not hear a loud protest against automation of all types of labor from the intelligentsia in the past.
In practice automation is great, as long as it doesn’t hit “the ones that matter” (a label which they themselves assign). I find it very hard to not imagine the smallest, tiniest violin playing the saddest song for them.
Again, “respect for mathematicians” and “their work”.. please. Just produce results. That’s all that ever mattered and let’s not change the rules of the game just because they don’t suit you anymore.
Protests against automation, or for the restructuring of society to accommodate automation without causing suffering of laborers, etc, is literally one of the largest and most extensively discussed topics in modern history.
It is so incredibly liberating to see the intellectual elite struggling with was already reality for 99% of the rest of us: your understanding is not required, it might in fact be detrimental as it amounts to a handbrake on progress.
Understanding never was the goal, results were. We will be getting boatloads of those. What does your understanding get us? You get a fancy house out of it and you might be intellectually stimulated by it, sure, but I hope you can see how that does not constitute a valid need for the rest of society to labor just to support your class and its lifestyle.
Same thing on coding - business doesn’t care one bit about your clean architecture or clever design, so long as the AI can change the implementation fast enough to ship whatever product comes up with.
People are having a rough time figuring out that good design and fundamentals no longer align with the business side of things.
I shouldn't be surprised how prevalent this viewpoint is, given the entrenched anti-intellectualism these days in the US and across the world, but it's disturbing to see it so widespread on HN of all places.
You are of course free to wield this new technology any way you choose (to the extent its owners and your wallet allow you to, for now at least), and if you can enrich yourself by doing so power to you. I won't attempt to dissuade you from your apparent hatred of those who have spent their lives trying to expand the boundaries of human understanding. I'll just state my equally emotion-driven opposing view: It always was and always will be about the understanding. "Results" and "progress" without sufficient thought are the reason our enormous modern wealth is accompanied by so much human misery.
I don't relish the prospect of living in your predicted world of multiplying technology untempered by human thought, if that's what happens to emerge. I don't think it will be a good place for anyone but a handful of the very richest.
Good luck adding yourself to their number.
Your reply isn't a response to the comment, but rather a general expression of antipathy towards mathematicians, who are apparently fatcats who have fancy lifestyles.
That is the point: Make "X can be done by AI" common discourse and watch industries "being disrupted". At least with open weights we'd be able to verify the claims.
You can actually do all of that meta analysis if you have the conversation that led to the solution. This is as easy as just having people release logs of their conversations, and then you can load it into another LLM as context to ask a bunch of questions about it.
I hope this will be normal practice eventually. “Show your work” is trivial if you use AI to solve a problem.
I’m looking forward to the days where AI would help in tackling the problems in biology. Especially, on creating new drugs, enzymes and understanding the genetic diseases. An absolutely interesting time to live.
Does anyone else have trouble telling how much of this news (along with the 'AI escaping and hacking' stories) is genuine, vs how much is just AI firms overstating their capabilities due to strong commercial incentives?
We hacked a company and blame the tool! Somehow it is not negligence, but cool!
We hacked 3 companies and tripple blame the tool! We are even cooler!
We hacked companies amd therefore other peoples models need to be restricted! See, us accidentally pointing a hacking tool on others proove we are the only ones that can be trusted with the tool!
Unlike the hacking one, this would be impossible to bullshit as long as the proofs are released. They can be verified independently, and the alternative is that they solved 10 major open mathematical questions without the AI, which seems less likely.
The LLM marketing loop is getting awfully long in the tooth. I saw a meme on Twitter the other day that showed a circular state diagram with something like:
> “GPT solved a math problem” -> “Claude solved a math problem” -> “GPT escaped the sandbox” -> “Claude escaped the sandbox” -> …
I believe this is what we wanted computers to help us solve along with other prior hard problems prior to computers. This should be viewed as a good thing even if Anthropic, OpenAI, etc benefit just like IBM benefitted from mainframes.
Indeed. I specifically recall my logic lecturers in a compsci course expressing the view the one purpose of computers is to work towards enabling automatic proofs, partly because they saw this as the universal problem in compsci (esp compilers) as well as massive potential for scientific progress generally.
I feel like this kind of "result dump" just cheapens mathematics. How about having a little respect for those whose work this builds on, and current mathematicians some of who may have spent years working on these problems.
Rather than sitting on these results until they had enough for a "shock and awe" 10-result dump, how about releasing these results individually as they were made/verified, as well as the failures (equally valuable to assess the current capabilities of LLMs), and try to make some analysis of HOW these breakthrough results were made. What were the prompts for each of these, how much guidance was there from the mathematicians employed by OpenAI, and most importantly how did the model arrive at these results ... what lines of reasoning resulted it in exploring ideas that humans had previously not explored?
I know it’s tough, but I am not a fan of elitism. Mathematics is no different from all other branches which themselves are just intellectual labor which is again just a special type of labor. There is nothing magical about it and if computers can trivialize it, so be it.
Where were all the mathematicians and academics in general when “regular joe” was automated? Now it’s hitting close to home and their foreheads are starting to get sweaty. I’d say let them. Tough luck. Make mathematics as “cheap” as possible. Nobody owes them any favors.
Let’s commoditize “being smart” and let go of arbitrary divisions between us.
I'd prefer the reverse approach. Let's value the "regular Joe" instead of cheapening everyone.
This is what the Ludites were trying to accomplish with an (armed) uprising.
Go back 100 years and 15 percent of the population was "Farmer", and 30 percent were in some sort of "domestic" work.
Most modern jobs are a product of the fact that technology continues to advance. And by all measures it does not look like "ai" is going to change that.
Yes, but in practice that doesn’t happen. Again, I did not hear a loud protest against automation of all types of labor from the intelligentsia in the past.
In practice automation is great, as long as it doesn’t hit “the ones that matter” (a label which they themselves assign). I find it very hard to not imagine the smallest, tiniest violin playing the saddest song for them.
Again, “respect for mathematicians” and “their work”.. please. Just produce results. That’s all that ever mattered and let’s not change the rules of the game just because they don’t suit you anymore.
Protests against automation, or for the restructuring of society to accommodate automation without causing suffering of laborers, etc, is literally one of the largest and most extensively discussed topics in modern history.
that's an incredibly narrow view of what's happening.
It is so incredibly liberating to see the intellectual elite struggling with was already reality for 99% of the rest of us: your understanding is not required, it might in fact be detrimental as it amounts to a handbrake on progress.
Understanding never was the goal, results were. We will be getting boatloads of those. What does your understanding get us? You get a fancy house out of it and you might be intellectually stimulated by it, sure, but I hope you can see how that does not constitute a valid need for the rest of society to labor just to support your class and its lifestyle.
Same thing on coding - business doesn’t care one bit about your clean architecture or clever design, so long as the AI can change the implementation fast enough to ship whatever product comes up with.
People are having a rough time figuring out that good design and fundamentals no longer align with the business side of things.
what are even "results" in mathematics if not understanding? for instance, what's the utility of the counterexamples built by openAI?
It seems you're fighting an hallucinated enemy.
I shouldn't be surprised how prevalent this viewpoint is, given the entrenched anti-intellectualism these days in the US and across the world, but it's disturbing to see it so widespread on HN of all places.
You are of course free to wield this new technology any way you choose (to the extent its owners and your wallet allow you to, for now at least), and if you can enrich yourself by doing so power to you. I won't attempt to dissuade you from your apparent hatred of those who have spent their lives trying to expand the boundaries of human understanding. I'll just state my equally emotion-driven opposing view: It always was and always will be about the understanding. "Results" and "progress" without sufficient thought are the reason our enormous modern wealth is accompanied by so much human misery.
I don't relish the prospect of living in your predicted world of multiplying technology untempered by human thought, if that's what happens to emerge. I don't think it will be a good place for anyone but a handful of the very richest. Good luck adding yourself to their number.
Your reply isn't a response to the comment, but rather a general expression of antipathy towards mathematicians, who are apparently fatcats who have fancy lifestyles.
OpenAI sat on the results so they could drop 10 at a time. It's rumored that they are sitting more results: https://mathoverflow.net/questions/513818/a-serious-challeng...
So not only are we not going to get boatloads of results, we're only get as many results as necessary for OpenAI to market their models.
That is the point: Make "X can be done by AI" common discourse and watch industries "being disrupted". At least with open weights we'd be able to verify the claims.
Not that I disagree, but I think this is how many people feel about AI output in fields they care about.
It's also a funny historical mirror to an earlier phase of math proof culture: in a previous era, cryptic result dumps were quite common.
You can actually do all of that meta analysis if you have the conversation that led to the solution. This is as easy as just having people release logs of their conversations, and then you can load it into another LLM as context to ask a bunch of questions about it.
I hope this will be normal practice eventually. “Show your work” is trivial if you use AI to solve a problem.
I’m looking forward to the days where AI would help in tackling the problems in biology. Especially, on creating new drugs, enzymes and understanding the genetic diseases. An absolutely interesting time to live.
Henry Yuen's (whose work problem 6 builds on) comments on this are worth reading IMO: https://bsky.app/profile/henryyuen.bsky.social/post/3ms2jpch...
Does anyone else have trouble telling how much of this news (along with the 'AI escaping and hacking' stories) is genuine, vs how much is just AI firms overstating their capabilities due to strong commercial incentives?
We hacked a company and blame the tool! Somehow it is not negligence, but cool!
We hacked 3 companies and tripple blame the tool! We are even cooler!
We hacked companies amd therefore other peoples models need to be restricted! See, us accidentally pointing a hacking tool on others proove we are the only ones that can be trusted with the tool!
Unlike the hacking one, this would be impossible to bullshit as long as the proofs are released. They can be verified independently, and the alternative is that they solved 10 major open mathematical questions without the AI, which seems less likely.
I mean once they release the proof you can check the maths yourself and I’m pretty sure it would be peer verified as well.
Dupe: https://news.ycombinator.com/item?id=49132058
The LLM marketing loop is getting awfully long in the tooth. I saw a meme on Twitter the other day that showed a circular state diagram with something like:
> “GPT solved a math problem” -> “Claude solved a math problem” -> “GPT escaped the sandbox” -> “Claude escaped the sandbox” -> …
I believe this is what we wanted computers to help us solve along with other prior hard problems prior to computers. This should be viewed as a good thing even if Anthropic, OpenAI, etc benefit just like IBM benefitted from mainframes.
Indeed. I specifically recall my logic lecturers in a compsci course expressing the view the one purpose of computers is to work towards enabling automatic proofs, partly because they saw this as the universal problem in compsci (esp compilers) as well as massive potential for scientific progress generally.
Ok nice... I am waiting for the "math is dead" argument
By itself not so interesting announcement. I wish the models were open weights so we could at least do some interesting geometry on the math.
It s like a rich man showing off his car collection.
Next: LLM model made 10 paperclips.
Replace paper clips with data centers and we are already there…