> I think it is against the spirit of Erdős to regard any problem as 'closed' -- whenever one form of a question is answered, many others are created, and all problems deserve continued attention.
But I thought the whole idea of the list was that it catalogued precisely the problems Erdos posed that he did not solve. The broader set of "all problems Erdos found interesting, including those he resolved" would be both larger and I suspect qualitatively different.
Erdos never had a list of all the problems he posed, and the people who have compiled lists at times had to do guesswork for what were actually problems or not. So there is no precise list of Erdos problems, just to be clear.
What I think you might be missing, though, is that Erdos was inherently playful with these problems. He'd sometimes just drop in the middle of a paper "hey, this variant of this lemma is neat, I bet it's true, but I'll give cash to anyone who disproves it" and move on. Or challenge a colleague while visiting and collaborating with them, and the problem would get spread by word of mouth. The problems often weren't things he thought long and hard about individually, but they appealed to his sense of aesthetics and curiosity and play. I think that's maybe close to what Bloom is talking about there. It's handy to have a catalog, but fundamentally, creating a set of unsolved math problems was not what Erdos was doing.
The idea is that people liked recreational math and enjoyed practicing it. AI bros with little interest in math showed up for marketing reasons or to "show" the nerds. Some mathematicians joined them too. One of the nerds is now saying "I don't find it fun anymore". That's really it. I wouldn't look for hidden meaning when it's spelled out pretty clearly.
Instead of succumbing, this reads like a considered adaptation to modern conditions.
They are thinking about what it is they do and what their intent was in doing it. Their adaptation is not a blind resistance to change but to preserve their intent.
I especially that they explicitly state that this is what they are trying and that not dropping a decree of new rules that are set in stone.
"The main way that people publicly interact with the site now is to advertise their AI-generated proofs, often without any attempt to explain them, but as a way to record a (increasingly meaningless) priority claim.
This is very different to what I imagined, and I don't want to manage a website which does this."
A welcome change, people posting AI-generated proof to claim credits are the scourge on mankind discoveries. It's time everyone that still hasn't, let go of their ego. All Hail the era of elegance.
"I believe that websites with this function should exist -- places where people can record AI-generated proofs, even if purely formal with no human understanding, to save others wasting their tokens generating the same proof, and so that other people can access and use them if they desire. There are now several candidates for such repositories, and if managed responsibly, they can serve a useful role in the mathematical ecosystem. I personally don't want to manage one.
Just as one does not open a restaurant in an abattoir, it is important that there be a separation between such repositories and a site which aims to promote the actual questions, place them in an appropriate context, and give a useful overview of the current state of human understanding."
I think this is a very reasonable blog post overall. A site for agents to read has many different needs and concerns than one for humans. Really anthropic or openai should be whipping this up for theirs.
It is becoming exceedingly difficult to ignore that the benefits of AI accrue disproportionately to those most deficient of scruples, while its costs and harms fall upon the selfless and pleasant like laser-guided virtue-seeking munitions.
I do not particularly care to debate a theory of why it is so, nor press a charge of malice or intent; mere observation suffices to convince me that this shit is corrosive to the better nature of humanity.
I don't know if that's true, for most programmers AI has either led a lost job, a more boring job, or maybe an easier job but without any gains in pay or reduction in hours.
Me too, although I understand the creator of the website doesn't want to have their role reduced to that of documenting the AI tsunami.
I had been expecting this since updates became irregular.
Perhaps this will force those solving these problems to produce something worthy of arxiv submission. Or maybe someone will produce a knock off site that continues to track these problems.
The fracking or strip mining of mathematics is repulsive. It must be noted here that Jeremy Avigad, who posted a soothing pro-AI guest article on Tao's blog on Oct. 5th, is running a strip mining project:
It's disappointing to see the author having such a low view of AI native mathematicians. The excitement from solving these problems should be considered a good thing. More people engaging and having fun with math is positive.
>Some view the future of mathematics as a dystopian...
>I believe Erdős would have found this future grim indeed
If you describe something as dystopian that is going to majorly bias someone's opinion towards being grim. That doesn't mean that dystopian description is reality.
Not to argue off of authority or anecdote, but the vision of mathematics described is disparaging to anyone who already is or is on the path of being a mathematician. In particular, I think your view is only amenable to armchair/recreational mathematicians, and I really do not see the world being described as being one that is mathematically elegant or “better”.
I found that this article was supportive of recreational mathematicians. See the closing passage.
>Find a question that is meaningful to you, find other humans who are interested in it, and talk about it. Be confused, be stuck, be inspired. Find a messy proof, then find a better one. Get tired, get hungry, get into a flow state. Argue, laugh, give up, drink some coffee, and attack it again.
You clipped a lot of incredibly relevant context to make his point sound far more inflammatory than it is.
> Some view the future of mathematics as a dystopian arcade of button-pressing, staring at a screen waiting for AI to do the thinking for us, with the main human involvement limited to asking the initial question and offering sporadic words of encouragement. Each new proof is then thrown into a repository, to only ever be read by other AIs, and the human presses the next button.
Is that your view of all AI native mathematicians? It's not mine, but it seems apparent to me that many people think that this is our future, or even should be our future. Same with building software (which is my field, unlike math).
I would find that personally, to use his word, grim.
It doesn't matter what he wrote there. If he had wrote
>Some view the future of mathematics as a dystopian where the terminator hunts down any person who tries to publish a new math proof so he can maintain a monopoly on proofs
People would find that as grim. Even if the chance of that future being realized was 0%.
> I think it is against the spirit of Erdős to regard any problem as 'closed' -- whenever one form of a question is answered, many others are created, and all problems deserve continued attention.
But I thought the whole idea of the list was that it catalogued precisely the problems Erdos posed that he did not solve. The broader set of "all problems Erdos found interesting, including those he resolved" would be both larger and I suspect qualitatively different.
Erdos never had a list of all the problems he posed, and the people who have compiled lists at times had to do guesswork for what were actually problems or not. So there is no precise list of Erdos problems, just to be clear.
What I think you might be missing, though, is that Erdos was inherently playful with these problems. He'd sometimes just drop in the middle of a paper "hey, this variant of this lemma is neat, I bet it's true, but I'll give cash to anyone who disproves it" and move on. Or challenge a colleague while visiting and collaborating with them, and the problem would get spread by word of mouth. The problems often weren't things he thought long and hard about individually, but they appealed to his sense of aesthetics and curiosity and play. I think that's maybe close to what Bloom is talking about there. It's handy to have a catalog, but fundamentally, creating a set of unsolved math problems was not what Erdos was doing.
The idea is that people liked recreational math and enjoyed practicing it. AI bros with little interest in math showed up for marketing reasons or to "show" the nerds. Some mathematicians joined them too. One of the nerds is now saying "I don't find it fun anymore". That's really it. I wouldn't look for hidden meaning when it's spelled out pretty clearly.
Instead of succumbing, this reads like a considered adaptation to modern conditions.
They are thinking about what it is they do and what their intent was in doing it. Their adaptation is not a blind resistance to change but to preserve their intent.
I especially that they explicitly state that this is what they are trying and that not dropping a decree of new rules that are set in stone.
More platforms should take this approach.
(Title is my clickbaiting)
From the link:
"The main way that people publicly interact with the site now is to advertise their AI-generated proofs, often without any attempt to explain them, but as a way to record a (increasingly meaningless) priority claim.
This is very different to what I imagined, and I don't want to manage a website which does this."
A welcome change, people posting AI-generated proof to claim credits are the scourge on mankind discoveries. It's time everyone that still hasn't, let go of their ego. All Hail the era of elegance.
A lack of elegance in AI-generated proofs is just because we haven't developed the right loops, graphs, and evals yet.
"I believe that websites with this function should exist -- places where people can record AI-generated proofs, even if purely formal with no human understanding, to save others wasting their tokens generating the same proof, and so that other people can access and use them if they desire. There are now several candidates for such repositories, and if managed responsibly, they can serve a useful role in the mathematical ecosystem. I personally don't want to manage one.
Just as one does not open a restaurant in an abattoir, it is important that there be a separation between such repositories and a site which aims to promote the actual questions, place them in an appropriate context, and give a useful overview of the current state of human understanding."
I think this is a very reasonable blog post overall. A site for agents to read has many different needs and concerns than one for humans. Really anthropic or openai should be whipping this up for theirs.
Seems like a well thought through response and really smart changes.
I especially like that he’s allowing AI if it generates a better learning proof. That’s so considerate.
It is becoming exceedingly difficult to ignore that the benefits of AI accrue disproportionately to those most deficient of scruples, while its costs and harms fall upon the selfless and pleasant like laser-guided virtue-seeking munitions.
I do not particularly care to debate a theory of why it is so, nor press a charge of malice or intent; mere observation suffices to convince me that this shit is corrosive to the better nature of humanity.
It's the Walmart Effect at internet speeds.
One of the largest group of people which benefit from AI are programmers.
Do you think they also are mostly deficient of scruples?
I don't know if that's true, for most programmers AI has either led a lost job, a more boring job, or maybe an easier job but without any gains in pay or reduction in hours.
Obviously those that benefit from AI have no ethics and morals. You can see it daily here.
Editorialized title?
Sadly, yes https://news.ycombinator.com/item?id=49977690
Hey, at least I lampshaded it.
I find it sad that I can't use the site as a tracker for solved problems anymore.
Me too, although I understand the creator of the website doesn't want to have their role reduced to that of documenting the AI tsunami.
I had been expecting this since updates became irregular.
Perhaps this will force those solving these problems to produce something worthy of arxiv submission. Or maybe someone will produce a knock off site that continues to track these problems.
Woah that's racist against robots you luddite, extermination of humanity is inevitable and this resistance is obviously futile.
The fracking or strip mining of mathematics is repulsive. It must be noted here that Jeremy Avigad, who posted a soothing pro-AI guest article on Tao's blog on Oct. 5th, is running a strip mining project:
https://huggingface.co/papers/2608.16977
Come on, you can flag the truth, too. The AI propagandists must maintain their 1984-level lies.
Book burning is good, it makes books more accessible!
It's disappointing to see the author having such a low view of AI native mathematicians. The excitement from solving these problems should be considered a good thing. More people engaging and having fun with math is positive.
>Some view the future of mathematics as a dystopian...
>I believe Erdős would have found this future grim indeed
If you describe something as dystopian that is going to majorly bias someone's opinion towards being grim. That doesn't mean that dystopian description is reality.
Not to argue off of authority or anecdote, but the vision of mathematics described is disparaging to anyone who already is or is on the path of being a mathematician. In particular, I think your view is only amenable to armchair/recreational mathematicians, and I really do not see the world being described as being one that is mathematically elegant or “better”.
I found that this article was supportive of recreational mathematicians. See the closing passage.
>Find a question that is meaningful to you, find other humans who are interested in it, and talk about it. Be confused, be stuck, be inspired. Find a messy proof, then find a better one. Get tired, get hungry, get into a flow state. Argue, laugh, give up, drink some coffee, and attack it again.
You clipped a lot of incredibly relevant context to make his point sound far more inflammatory than it is.
> Some view the future of mathematics as a dystopian arcade of button-pressing, staring at a screen waiting for AI to do the thinking for us, with the main human involvement limited to asking the initial question and offering sporadic words of encouragement. Each new proof is then thrown into a repository, to only ever be read by other AIs, and the human presses the next button.
Is that your view of all AI native mathematicians? It's not mine, but it seems apparent to me that many people think that this is our future, or even should be our future. Same with building software (which is my field, unlike math).
I would find that personally, to use his word, grim.
It doesn't matter what he wrote there. If he had wrote
>Some view the future of mathematics as a dystopian where the terminator hunts down any person who tries to publish a new math proof so he can maintain a monopoly on proofs
People would find that as grim. Even if the chance of that future being realized was 0%.
> AI-native mathematicians
What a world we live in...