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Erdosproblems.com Succumbs to the AI Onslaught

Hacker News 2026-10-06 20:53 5 阅读 查看原文
Changes AI is changing everything, for better and/or worse, and the rate of change is dizzying; in recent months this has been particularly evident in mathematics, where AI has gone from being essentially useless to helping solve some of the hardest problems in mathematics in less than a year. The website www.erdosproblems.com has often been on the front line of these changes, and a barometer by which one could measure AI capabilities. This was not at all my intention when I created the site -- I wanted to promote these problems to a human audience, and make a useful reference on what work has been done. But the easy availability of a large pool of questions that are simple to state, ranging from easy and obscure to deep and impenetrable, provided the ideal showcase for AI. In some ways this has led to a huge amount of progress -- we now know the answer to many questions we did not before. (Although a lot of this recent progress has come from increased human efforts and renewed interest in some problems, rather than just AI solutions.) There have also been negative effects, however: some mathematicians have dismissed Erdős-style mathematics as 'easy/recreational'; many have stopped thinking about Erdős problems believing that they cannot compete with AI; and, most significantly, there has been a wave of AI-produced solutions provided with no explanation. While of course these are useful and tell us new things, they are also displacing and discouraging those who are actually interested in the mathematics. (These issues have stopped being Erdős-specific as AI continues to make breakthroughs in an ever wider range of fields.) A couple of weeks ago I asked for feedback on how people used the site, and what they thought should be changed. I received, both publicly and privately, a wide variety of opinions, and I'm grateful to everyone for their feedback. What was particularly striking was the number of people I heard from who have benefited a lot from the site, learning new mathematics and finding new problems to think about, but have never commented on the site. I have been particularly conscious of this large silent, audience, and have tried to make sure their experiences were not drowned out by the more vocal minority. In this post I will describe the changes I am making, based on the feedback I received and my own reflections on what the site is and could be. In the essay Why Do We Need Human Mathematicians Anymore? Po-Shen Loh suggests the following as an axiom to use when deciding how things should develop: We (humans) should help humanity flourish. When thinking about what I should do about the site, I use the following variant: The site should help the Erdős-community of humans (defined as those who are interested in Erdős-style mathematics, and want to think about and understand it) flourish. Why change? What are the changes? A hiatus on problem comments and proof claims: I will freeze new problem comments and proof claims. General threads and blog posts will remain open to comments. Problem comments and proof claims may be reinstated in the future. Until then, suggestions for updates can be emailed to [email protected], and I will update the site manually as I see appropriate. No problem statuses: The site will not display the statuses of any problems (e.g. open, solved, etc.). All problems will be displayed in the same neutral colour. The count of currently solved problems and the solved percentage will no longer be shown. No credit/ownership language to describe future solutions: The site will continue to record relevant results and theorems, but will no longer use credit-giving language for a result (human or AI). An emphasis on high-quality expositions: I will focus more on the proof expositions feature. People are encouraged to write in with their own expositions of proofs (whether these proofs are old or new, human or AI), and I will post those I judge to be high-quality. I am exploring other ways to encourage human exposition (e.g. an online seminar). Please contact me if you have any ideas. If you have a Lean formalisation register it on Palomar -- this lets others see that the formalisation compiles correctly, and makes it easy to check the formal statement correctly matches the problem statement. I will then link to the Palomar registry. A proof accompanied by a well-written exposition that demonstrates clear understanding and which makes it easy for others to understand the proof will be prioritised. If I judge there to be some kind of academic fraud (e.g. using the ideas of others without attribution, or passing AI-generated work off as your own) then I will not post it. This may mean that there are correct proofs not acknowledged, but the alternative is to publicise and reward bad behaviour. (As mentioned above, these proofs will surely still be found by anyone who searches for them elsewhere, but at least I would not be implicitly endorsing them.) Erdős and AI I want to start by reiterating my comment in Thomas Bloom's initial "what should I change" post; he has done a wonderful service in creating this site and making these problems, and their history, broadly accessible and organized. That said, despite being a nobody in the mathematical community, I felt the need to opine; the first two changes are very disappointing to see. The latter two seem fine to me; the question of credit in the AI age is a difficult one, and exposition is extremely valuable and likely even more so now. However, I believe that the *only* effect that the first two changes have are to make mathematical progress less visible. The second change is particularly egregious in my opinion; all it does it add work on the part of the interested reader to determine the history of the problem. I think it will have zero effect in discouraging "Erdos hunters", and serves only to make the site less navigable. It's not like people actually were specifically working on problems to try to get the status changed from "open" to "solved"; a large proportion of the comments/proof claims on the site already pertained to problems in the "solved" category. Furthermore, status changes happened very infrequently already (no knock to Thomas here, he undoubtedly has better things to do, I'm just saying I don't think people are motivated by "number go up" on %solved on the front page of the site). The first change is more understandable, yet even more disappointing; Thomas seems to be following in the footsteps of arXiv in an attempt to reduce the amount of slop and the visibility of said slop. I think it makes less sense here (arXiv was essentially being DDOS'd with papers, which was not really the case on this site). However, all that will happen is people will post their slop (or not slop!) proofs to Zenodo where they will be unseen, and their ideas ignored (sure AI-assisted literature reviews will find them occasionally, but I'm speaking on the margin). Whether the proofs are easily digestible or not, all this serves is to slow the flow of mathematical progress. It also hinders collaboration; I personally had very fruitful collaborations with Wouter CvB and Kaizhe Chen as a direct result of the comment functionality on this site, and I know many other users had similar experiences. Such collaborations almost certainly wouldn't be possible now. If credit should be given primarily to digestion/exposition that makes perfect sense to me, but professional mathematicians shouldn't have it both ways; if "being first with slop (or not slop!)" isn't worth anything, then it shouldn't be scary enough to ban. Every morning I used to check proof claims excitedly to see what new ideas were being produced relevant to problems I care about, by humans or otherwise, and I'm quite sad that I won't be able to any longer. SamKorsky — 16:28 on 06 Oct 2026 👍 1 📝 0 🤖 0 Maybe it is an attempt to no longer be stuck with the slop of Erdos Hunters, and partially push the weight of a good exposition onto them. MalekZ — 17:38 on 06 Oct 2026 👍 1 📝 0 🤖 0 Totally understandable; my thoughts are that the slop was already "sectioned off" in some sense to the Proof Claims section, and anyone was free to work on the problem without AI assistance/with their own AI independent of the existing claim/using the claim as a base to improve the solution/ideas/exposition. I can't imagine why the existence of a proof claim (particularly now that LLMs are reasonably dependable and formalization exists, so most claims are probably usually factually correct or otherwise easily shown to be flawed) would ever be a bad thing to someone interested in a problem in good faith. SamKorsky — 17:47 on 06 Oct 2026 👍 1 📝 0 🤖 0 >the slop was already put in the Proof Claims section Don't agree; among the slop there are also beautiful proofs but it was just too much to go through all of it StijnC — 18:23 on 06 Oct 2026 👍 0 📝 0 🤖 0 In aggregate across all problems, sure; but for each individual problem there were usually maximum 2 proof claims (and much more often, just 1). Thus if you were interested in a specific problem, there would usually just be one slop claim to parse. You yourself are actually probably the best example of this; I saw that you helped a ton of posters better explain their ideas (my particular favorite was problem #193). The existence of the proof claim section and your later collaboration helped bring a beautiful proof into the world! SamKorsky — 18:37 on 06 Oct 2026 👍 0 📝 0 🤖 0 Response on the first two edits 1a) No proofclaim On the one hand; if this implies people will write a clear exposition instead (often accompanying a longer paper put elsewhere), reading the expositions will be more exciting :) On the other hand; This assumes people are able to do the digesting on their own. For resolutions that the first creator could not parse into a digestable proof, it indeed misses the opportunity that others help with rewrites. 1b) No comments Exactly for discussions, start of collaborations and helping to digest, or add interesting insights and other references, this was a very helpful feature preventing people all working alone. Related to both 1a and 1b #710 is interesting to indcate that even with AI help, people may end up with different simplifications, for which the intersection even helps with further simplifications. So the additional $collaborative possibilities$ created here $should be kept$ ! (preview shows the bold text correctly, but the actual text creates issues) 2) No open/ solved setting When Thomas mentioned this idea first, it felt weird to me as well. But since it is often subjective to say if the story is done or not, and it is a weird responsibility for Thomas to say when something is solved or not (read the text for problem #459 e.g.), this is not necessarily a bad thing. Interested mathematicians indeed may want and be able to proceed further than the result at the moment it was marked as solved. Maybe this is a temporary/transition state and in a year, one can just mark problems that are 100% solved and have a clear exposition / proof from the book. StijnC — 19:02 on 06 Oct 2026 👍 1 📝 0 🤖 0 I want to start by reiterating my comment in Thomas Bloom's initial "what should I change" post; he has done a wonderful service in creating this site and making these problems, and their history, broadly accessible and organized. That said, despite being a nobody in the mathematical community, I felt the need to opine; the first two changes are very disappointing to see. The latter two seem fine to me; the question of credit in the AI age is a difficult one, and exposition is extremely valuable and likely even more so now. However, I believe that the *only* effect that the first two changes have are to make mathematical progress less visible. The second change is particularly egregious in my opinion; all it does it add work on the part of the interested reader to determine the history of the problem. I think it will have zero effect in discouraging "Erdos hunters", and serves only to make the site less navigable. It's not like people actually were specifically working on problems to try to get the status changed from "open" to "solved"; a large proportion of the comments/proof claims on the site already pertained to problems in the "solved" category. Furthermore, status changes happened very infrequently already (no knock to Thomas here, he undoubtedly has better things to do, I'm just saying I don't think people are motivated by "number go up" on %solved on the front page of the site). The first change is more understandable, yet even more disappointing; Thomas seems to be following in the footsteps of arXiv in an attempt to reduce the amount of slop and the visibility of said slop. I think it makes less sense here (arXiv was essentially being DDOS'd with papers, which was not really the case on this site). However, all that will happen is people will post their slop (or not slop!) proofs to Zenodo where they will be unseen, and their ideas ignored (sure AI-assisted literature reviews will find them occasionally, but I'm speaking on the margin). Whether the proofs are easily digestible or not, all this serves is to slow the flow of mathematical progress. It also hinders collaboration; I personally had very fruitful collaborations with Wouter CvB and Kaizhe Chen as a direct result of the comment functionality on this site, and I know many other users had similar experiences. Such collaborations almost certainly wouldn't be possible now. If credit should be given primarily to digestion/exposition that makes perfect sense to me, but professional mathematicians shouldn't have it both ways; if "being first with slop (or not slop!)" isn't worth anything, then it shouldn't be scary enough to ban. Every morning I used to check proof claims excitedly to see what new ideas were being produced relevant to problems I care about, by humans or otherwise, and I'm quite sad that I won't be able to any longer. Maybe it is an attempt to no longer be stuck with the slop of Erdos Hunters, and partially push the weight of a good exposition onto them. MalekZ — 17:38 on 06 Oct 2026 👍 1 📝 0 🤖 0 Totally understandable; my thoughts are that the slop was already "sectioned off" in some sense to the Proof Claims section, and anyone was free to work on the problem without AI assistance/with their own AI independent of the existing claim/using the claim as a base to improve the solution/ideas/exposition. I can't imagine why the existence of a proof claim (particularly now that LLMs are reasonably dependable and formalization exists, so most claims are probably usually factually correct or otherwise easily shown to be flawed) would ever be a bad thing to someone interested in a problem in good faith. SamKorsky — 17:47 on 06 Oct 2026 👍 1 📝 0 🤖 0 >the slop was already put in the Proof Claims section Don't agree; among the slop there are also beautiful proofs but it was just too much to go through all of it StijnC — 18:23 on 06 Oct 2026 👍 0 📝 0 🤖 0 In aggregate across all problems, sure; but for each individual problem there were usually maximum 2 proof claims (and much more often, just 1). Thus if you were interested in a specific problem, there would usually just be one slop claim to parse. You yourself are actually probably the best example of this; I saw that you helped a ton of posters better explain their ideas (my particular favorite was problem #193). The existence of the proof claim section and your later collaboration helped bring a beautiful proof into the world! SamKorsky — 18:37 on 06 Oct 2026 👍 0 📝 0 🤖 0 Maybe it is an attempt to no longer be stuck with the slop of Erdos Hunters, and partially push the weight of a good exposition onto them. Totally understandable; my thoughts are that the slop was already "sectioned off" in some sense to the Proof Claims section, and anyone was free to work on the problem without AI assistance/with their own AI independent of the existing claim/using the claim as a base to improve the solution/ideas/exposition. I can't imagine why the existence of a proof claim (particularly now that LLMs are reasonably dependable and formalization exists, so most claims are probably usually factually correct or otherwise easily shown to be flawed) would ever be a bad thing to someone interested in a problem in good faith. SamKorsky — 17:47 on 06 Oct 2026 👍 1 📝 0 🤖 0 >the slop was already put in the Proof Claims section Don't agree; among the slop there are also beautiful proofs but it was just too much to go through all of it StijnC — 18:23 on 06 Oct 2026 👍 0 📝 0 🤖 0 In aggregate across all problems, sure; but for each individual problem there were usually maximum 2 proof claims (and much more often, just 1). Thus if you were interested in a specific problem, there would usually just be one slop claim to parse. You yourself are actually probably the best example of this; I saw that you helped a ton of posters better explain their ideas (my particular favorite was problem #193). The existence of the proof claim section and your later collaboration helped bring a beautiful proof into the world! SamKorsky — 18:37 on 06 Oct 2026 👍 0 📝 0 🤖 0 Totally understandable; my thoughts are that the slop was already "sectioned off" in some sense to the Proof Claims section, and anyone was free to work on the problem without AI assistance/with their own AI independent of the existing claim/using the claim as a base to improve the solution/ideas/exposition. I can't imagine why the existence of a proof claim (particularly now that LLMs are reasonably dependable and formalization exists, so most claims are probably usually factually correct or otherwise easily shown to be flawed) would ever be a bad thing to someone interested in a problem in good faith. >the slop was already put in the Proof Claims section Don't agree; among the slop there are also beautiful proofs but it was just too much to go through all of it StijnC — 18:23 on 06 Oct 2026 👍 0 📝 0 🤖 0 In aggregate across all problems, sure; but for each individual problem there were usually maximum 2 proof claims (and much more often, just 1). Thus if you were interested in a specific problem, there would usually just be one slop claim to parse. You yourself are actually probably the best example of this; I saw that you helped a ton of posters better explain their ideas (my particular favorite was problem #193). The existence of the proof claim section and your later collaboration helped bring a beautiful proof into the world! SamKorsky — 18:37 on 06 Oct 2026 👍 0 📝 0 🤖 0 >the slop was already put in the Proof Claims section Don't agree; among the slop there are also beautiful proofs but it was just too much to go through all of it In aggregate across all problems, sure; but for each individual problem there were usually maximum 2 proof claims (and much more often, just 1). Thus if you were interested in a specific problem, there would usually just be one slop claim to parse. You yourself are actually probably the best example of this; I saw that you helped a ton of posters better explain their ideas (my particular favorite was problem #193). The existence of the proof claim section and your later collaboration helped bring a beautiful proof into the world! SamKorsky — 18:37 on 06 Oct 2026 👍 0 📝 0 🤖 0 In aggregate across all problems, sure; but for each individual problem there were usually maximum 2 proof claims (and much more often, just 1). Thus if you were interested in a specific problem, there would usually just be one slop claim to parse. You yourself are actually probably the best example of this; I saw that you helped a ton of posters better explain their ideas (my particular favorite was problem #193). The existence of the proof claim section and your later collaboration helped bring a beautiful proof into the world! Response on the first two edits 1a) No proofclaim On the one hand; if this implies people will write a clear exposition instead (often accompanying a longer paper put elsewhere), reading the expositions will be more exciting :) On the other hand; This assumes people are able to do the digesting on their own. For resolutions that the first creator could not parse into a digestable proof, it indeed misses the opportunity that others help with rewrites. 1b) No comments Exactly for discussions, start of collaborations and helping to digest, or add interesting insights and other references, this was a very helpful feature preventing people all working alone. Related to both 1a and 1b #710 is interesting to indcate that even with AI help, people may end up with different simplifications, for which the intersection even helps with further simplifications. So the additional $collaborative possibilities$ created here $should be kept$ ! (preview shows the bold text correctly, but the actual text creates issues) 2) No open/ solved setting When Thomas mentioned this idea first, it felt weird to me as well. But since it is often subjective to say if the story is done or not, and it is a weird responsibility for Thomas to say when something is solved or not (read the text for problem #459 e.g.), this is not necessarily a bad thing. Interested mathematicians indeed may want and be able to proceed further than the result at the moment it was marked as solved. Maybe this is a temporary/transition state and in a year, one can just mark problems that are 100% solved and have a clear exposition / proof from the book. StijnC — 19:02 on 06 Oct 2026 👍 1 📝 0 🤖 0 Response on the first two edits 1a) No proofclaim On the one hand; if this implies people will write a clear exposition instead (often accompanying a longer paper put elsewhere), reading the expositions will be more exciting :) On the other hand; This assumes people are able to do the digesting on their own. For resolutions that the first creator could not parse into a digestable proof, it indeed misses the opportunity that others help with rewrites. 1b) No comments Exactly for discussions, start of collaborations and helping to digest, or add interesting insights and other references, this was a very helpful feature preventing people all working alone. Related to both 1a and 1b #710 is interesting to indcate that even with AI help, people may end up with different simplifications, for which the intersection even helps with further simplifications. So the additional $collaborative possibilities$ created here $should be kept$ ! (preview shows the bold text correctly, but the actual text creates issues) 2) No open/ solved setting When Thomas mentioned this idea first, it felt weird to me as well. But since it is often subjective to say if the story is done or not, and it is a weird responsibility for Thomas to say when something is solved or not (read the text for problem #459 e.g.), this is not necessarily a bad thing. Interested mathematicians indeed may want and be able to proceed further than the result at the moment it was marked as solved. Maybe this is a temporary/transition state and in a year, one can just mark problems that are 100% solved and have a clear exposition / proof from the book. I for one second this idea, I've been trying to contact authors and set up a more detailed breakdown of their claims, in attempt to help with the numerous proof claims without recognition. For reference, here is a count of all proof claims today: 291 total proof claims 155 claims with zero comments 14 claims with only the submitter's comments 112 claims with at least 1 comment from another user. Extra findings: 61 problems have multiple proof claims. 77 of the zero-comment claims were submitted before September. Of 14 claims submitted since 1 October, 7 have no comments. Now I cannot comment on why this is happening. Maybe some problems bare no interest to people here, others might have a proof claim so overly-complex that it would be a bigger task to fix it than rewrite it. I myself was once one of the 'Glory Chasers' you describe. Finally, will problems still have tags (e.g. Number Theory, Analysis, etc)? MalekZ — 13:07 on 06 Oct 2026 👍 0 📝 0 🤖 0 Thanks; in general I think no bad thing to pause things and take stock! Yes, the tag system should be working as before - please let me know if there are any problems (either by direct message or in the Site Suggestions thread). Thomas Bloom — 13:11 on 06 Oct 2026 👍 1 📝 0 🤖 0 I for one second this idea, I've been trying to contact authors and set up a more detailed breakdown of their claims, in attempt to help with the numerous proof claims without recognition. For reference, here is a count of all proof claims today: 291 total proof claims 155 claims with zero comments 14 claims with only the submitter's comments 112 claims with at least 1 comment from another user. Extra findings: 61 problems have multiple proof claims. 77 of the zero-comment claims were submitted before September. Of 14 claims submitted since 1 October, 7 have no comments. Now I cannot comment on why this is happening. Maybe some problems bare no interest to people here, others might have a proof claim so overly-complex that it would be a bigger task to fix it than rewrite it. I myself was once one of the 'Glory Chasers' you describe. Finally, will problems still have tags (e.g. Number Theory, Analysis, etc)? Thanks; in general I think no bad thing to pause things and take stock! Yes, the tag system should be working as before - please let me know if there are any problems (either by direct message or in the Site Suggestions thread). Thomas Bloom — 13:11 on 06 Oct 2026 👍 1 📝 0 🤖 0 Thanks; in general I think no bad thing to pause things and take stock! Yes, the tag system should be working as before - please let me know if there are any problems (either by direct message or in the Site Suggestions thread).