Putting hallucination aside, LLM "theory of mind" has gotten worse over time. I feel it peaked in Opus 3 and Sonnet 3.5, GPT 4 and then GPT 4.5 for OpenAI. Since then, even with Opus 5.5, phrasing has needed careful crafting, in order that it not be taken too literally. OpenAI models suffer from this much more than Anthropic models but Claudes have backslid over time too.

This means when writing documentation, tutorials or commit messages, their output is often a garbled jumble. Assuming shared context, using invented terminology without explaining, leaking conversational states due to improper epistemic boundaries and failing to model the reader. This all usually leads to their freely generated explanations being terrible. Getting good explanations requires chaining questions that force them to line things up properly, which is not easy the less you know. These failures as something LLMs naturally struggle with make sense, given the nature of attention and RL with weak signals from human data.

Math is not merely a collection of proofs, it's a way of understanding. A proof presented in a manner that cannot be incorporated remains useless. It does not make it's way to physics like Riemannian geometry and matrix math did. This is no less true when done by humans too.

Your hallucination conclusion, checking if a proof is one, is exactly the counterproductive cost.

Most of us cannot verify that the claims in the OpenAI lore dump are in fact all correct. It will take tons of work from experts to do this. It took subject expert mathematicians to identify the discrepancy and disconnect in the Navier Stokes proofs, for example. LLMs will struggle to make use of their own proofs or turn them into knowledge that accumulates over time.

The act of proving is often more valuable than the proof itself. Human constraints and limitations force us to invent tools and abstractions that a 100,000 x 1M context swarm can bypass. The tradeoff from that AI swarm advantage is work that doesn't usually lend itself to being built upon. It's like doing all the side quests and reading all the books of an RPG versus min maxing a straight path with a guide. We might try to identify new abstractions, but the fact that we don't get access to CoT and that much of it will be illegible means mining LLM traces for what human mathematicians produce naturally will be a tedious chore.