This is not about the mathematical evidence, but the lack of evidence that AI has made mathematical breakthroughs.
The point here is there is rarely any evidence for the claims about AI amazing accomplishments.
The burden of proof is on the one with the claim that AI has made these accomplishments, not on the one being sceptic about it.
Articles with proofs have been published, both by AI companies as well as by mathematicians who disclosed the whole development of the proof was done autonomously by LLMs.
There is no evidence stated in the first article, and it’s paywalled.
The second article doesn’t show independent confirmation that the alleged proofs are real. Which was exactly what the original criticism was about.
Yes we all know the claims, and you have done nothing but parroting those claims without evidence.
I am not a mathematician, thus I don’t really know where to find indipendent confirmation or even how that is generally handled by mathematicians.
However: there are plenty proofs on arxiv that disclose have been found with LLMs.
Some of these proofs relate to famous problems and have been in the news.
Fields medal winners discuss the importance of LLMs and how it may produce too many proofs for humans to handle.
I trust that those proofs published on arxiv have been reviewed by many mathematicians, if they were incorrect that would have rapidly become known.
Doesn’t have to be scientific articles, it can easily be a normal article that state that scientists have confirmed the findings independently.
This is a very common thing for normal media to describe. The second article you linked would most probably have included that if such confirmation existed.
I linked to evidence that mathematicians are using LLMs to find proofs
No you didn’t, the article described a researcher testing the capabilities of AI, nothing in the article was really about math, it was all about the AI, and the whole story reeks of sensationalism.
Scientists don’t often publish when they confirm an article is correct. Knowing a few mathematicians, probably they see no need to do that. They checked the proof, it was ok and that’s it.
Either way, many of those proofs come with a computer program which checks and confirms the proof is correct.
I trust that an expert mathematician talking about such things has reviewed a few of those articles and has checked the proof.
You may not do that; check the proof yourself or pay a mathematician to do it for you.
“you don’t really need evidence” we are talking about mathematics. The evidence is the point.
This is not about the mathematical evidence, but the lack of evidence that AI has made mathematical breakthroughs.
The point here is there is rarely any evidence for the claims about AI amazing accomplishments.
The burden of proof is on the one with the claim that AI has made these accomplishments, not on the one being sceptic about it.
Articles with proofs have been published, both by AI companies as well as by mathematicians who disclosed the whole development of the proof was done autonomously by LLMs.
Which is way more possible to link to. But you chose not to?
https://www.nature.com/articles/d41586-026-01553-1
https://e.vnexpress.net/news/news/education/fields-medalist-terence-tao-warns-ai-could-produce-more-math-proofs-than-humans-can-handle-5102580.html
There is no evidence stated in the first article, and it’s paywalled.
The second article doesn’t show independent confirmation that the alleged proofs are real. Which was exactly what the original criticism was about.
Yes we all know the claims, and you have done nothing but parroting those claims without evidence.
Yes, scientific articles are expensive. I know that, that sucks. That’s why most of this stuff is on arxiv.
I linked to evidence that mathematicians are using LLMs to find proofs and publish those proofs. Which is what I said is happening.
https://academia.stackexchange.com/questions/221183/can-i-publish-a-novel-theorem-which-was-proven-with-ai-assistance
I am not a mathematician, thus I don’t really know where to find indipendent confirmation or even how that is generally handled by mathematicians. However: there are plenty proofs on arxiv that disclose have been found with LLMs. Some of these proofs relate to famous problems and have been in the news. Fields medal winners discuss the importance of LLMs and how it may produce too many proofs for humans to handle.
I trust that those proofs published on arxiv have been reviewed by many mathematicians, if they were incorrect that would have rapidly become known.
Doesn’t have to be scientific articles, it can easily be a normal article that state that scientists have confirmed the findings independently.
This is a very common thing for normal media to describe. The second article you linked would most probably have included that if such confirmation existed.
No you didn’t, the article described a researcher testing the capabilities of AI, nothing in the article was really about math, it was all about the AI, and the whole story reeks of sensationalism.
If you wish, this was indipendently confirmed: the same proof was published by two authors at the same time.
https://www.scientificamerican.com/article/ai-helped-produce-two-proofs-for-the-same-cryptography-problem/
Scientists don’t often publish when they confirm an article is correct. Knowing a few mathematicians, probably they see no need to do that. They checked the proof, it was ok and that’s it.
Either way, many of those proofs come with a computer program which checks and confirms the proof is correct.
I trust that an expert mathematician talking about such things has reviewed a few of those articles and has checked the proof.
You may not do that; check the proof yourself or pay a mathematician to do it for you.