The recent breakthrough of llm’s solving major open problem’s in math is a direct contradiction to the article.

But, there is some truth to the article and perhaps it is more true in chat based interactions. The agentic, hands-off mode might tell a different story.

> The recent breakthrough of llm’s solving major open problem’s in math is a direct contradiction to the article.

I disagree. LLMs are essentially trained on all the math we know, as well as - via RL training - how we apply it to solve given types of problems.

It should be obvious that not every known mathematical technique, or sequence of techniques, have yet been tried by humans to solve every unproven conjecture, so necessarily there is some amount of low hanging fruit where an automaton tasked with throwing the kitchen sink at a problem will be successful. This is not the same as creativity.

If you are familiar with the mathematical notion of a closure, then what LLMs are capable of is generating the generative closure of what they were trained on. They can generate output that is novel in the sense of a sequence of chess moves, or mathematical moves, that was not - as a sequence - in the training set, but yet it WAS in the training set as part of the implicit closure of what an LLM would be capable of generating.