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“Erdos problem #728 was solved more or less autonomously by AI”

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41–50 of 385 posts

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#41

This is great, there is still so much potential in AI once we move beyond LLMs to specialized approaches like this. EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle ( https://arxiv.org/abs/2510.01346 ) is key here folks. EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM…

Every stage of this 3-stage pipeline is an LLM.

1. "The search algorithm is a highly parallel Monte Carlo Graph Search (MCGS) using a large transformer as its policy and value functon." ... "We use a generative policy to take progressively widened [7] samples from the large action space of Lean tactics, conditioning on the Lean proof state, proof history, and, if available, an informal proof. We use the same model and prompt (up to a task token) to compute the value function which guides the search."

See that 'large transformer' phrase? That's where the LLM is involved.

2. "A lemma-based informal reasoning system which generates informal proofs of mathematical state-ments, breaks these proofs down into lemmas, formalizes each lemma into Lean, and iterates this process based on formal feedback" ... "First, the actions it generates consist of informal comments in addition to Lean tactics. Second, it uses a hidden chain of thought with a dynamically set thinking budget before predicting an action."

Unless you're proposing that this team solved AGI, "chain of thought" is a specific term of art in LLMs.

3. "A geometry solver which solves plane geometry problems outside of Lean using an approach based on AlphaGeometry [45]." ... following the reference: "AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. "

AlphaGeometry, like all of Deepmind's Alpha tools, is an LLM.

Instead of accusing people of not reading the paper, perhaps you should put some thought into what the things in the paper actually represent.

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#42

Reconfiguring existing proofs in ways that have been tedious or obscured from humans, or using well framed methods in novel ways, will be done at superhuman speeds, and it'll unlock all sorts of capabilities well before we have to be concerned about AGI. It's going to be awesome to see what mathematicians start to do with AI tools as the tools become capable of truly keeping up with what the mathematicians want from…

If this isn't AGI, what is? It seems unavoidable that an AI which can prove complex mathematical theorems would lead to something like AGI very quickly.

AGI in its standard definition requires matching or surpassing humans on all cognitive tasks, not just in some, especially some where only handful of humans took a stab on.

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#45
post #41

This is great, there is still so much potential in AI once we move beyond LLMs to specialized approaches like this. EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle ( https://arxiv.org/abs/2510.01346 ) is key here folks. EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM…

Every stage of this 3-stage pipeline is an LLM. 1. "The search algorithm is a highly parallel Monte Carlo Graph Search (MCGS) using a large transformer as its policy and value functon." ... "We use a generative policy to take progressively widened [7] samples from the large action space of Lean tactics, conditioning on the Lean proof state, proof history, and, if available, an informal proof. We use the same model an…

If you think "transformer" = LLM, you don't understand the basic terminology of the field. This is like calling AlphaFold an LLM because it uses a transformer.

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#47

Can anyone with specific knowledge in a sophisticated/complex field such as physics or math tell me: do you regularly talk to AI models? Do feel like there's anything to learn? As a programmer, I can come to the AI with a problem and it can come up with a few different solutions, some I may have thought about, some not. Are you getting the same value in your work, in your field?

I work in quantum computing. There is quite a lot of material about quantum computing out there that these LLMs must have been trained on. I have tried a few different ones, but they all start spouting nonsense about anything that is not super basic. But maybe that is just me. I have read some of Terence Tao's transcripts, and the questions he asks LLMs are higher complexity than what I ask. Yet, he often gets reason…

Which models did you try?

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#49

This almost implies mathematicians aren’t some ungodly geniuses if something as absolutely dumb as an LLM can solve these problems via blind pattern matching. Meanwhile I can’t get Claude code to fix its own shit to save my life.

> Meanwhile I can’t get Claude code to fix its own shit to save my life.

Maybe this should give you some hint to that you're trying to use it in a different way than others?

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#50

Reconfiguring existing proofs in ways that have been tedious or obscured from humans, or using well framed methods in novel ways, will be done at superhuman speeds, and it'll unlock all sorts of capabilities well before we have to be concerned about AGI. It's going to be awesome to see what mathematicians start to do with AI tools as the tools become capable of truly keeping up with what the mathematicians want from…

I agree only with the part about reconfiguring existing proofs. That's the value here. It is still likely very tedious to confirm what the LLMs say, but at least it's better than waiting for humans to do this half of the work. For all topics that can be expressed with language, the value of LLMs is shuffling things around to tease out a different perspective from the humans reading the output. This is the only realis…

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