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.
But that’s not really the point, the point is that yes maybe AI can solve long standing mathematical problems, but they need to be confirmed by REAL mathematicians.
Because AI has been shown to hallucinate and lie when presented with problems they can’t solve.
There are many claims about AI solving hard mathematical problems, but very few that are confirmed. These stories seem to at least to some degree to act as advertising for AI services.
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.
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/
But that’s not really the point, the point is that yes maybe AI can solve long standing mathematical problems, but they need to be confirmed by REAL mathematicians.
Because AI has been shown to hallucinate and lie when presented with problems they can’t solve.
There are many claims about AI solving hard mathematical problems, but very few that are confirmed. These stories seem to at least to some degree to act as advertising for AI services.
Two researchers came to the same solution to a problem. In my books that’s better than peer review.
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.
This sounds like something you outright made up.
Classical unsolved math problems have rewards.
Mathematics absolutely have peer review:
https://pubmed.ncbi.nlm.nih.gov/28029799/
Indeed peer reviewed exists in mathematics. Now, whether it is common practice to publish stuff on arxiv and leave it there is another thing.
I don’t know about mathematics, but I know plenty other Fields where it is common practice to just publish on arxiv.