> When you train LLMs on large volumes of text that describe logically consistent facts in a million different ways, the "logic" sort of becomes part of the grammer that the model learns. That is logic becomes a higher kind of "grammer" or a enormous set of grammatical rules that it captures. But that does not mean the model can do actual logic.

This is the kind of stuff people were saying in 2023. But it’s 2026 now and LLMs aren’t just trained by reading lots of text anymore. That’s “pretraining”, and it’s still the first stage, but LLMs also have a huge amount of RLVR training where they actually do solve huge numbers of mathematical and logic puzzles and update their weights in response. They don’t just learn mathematics from reading about it now. They learn it by doing it. That is why they can now solve hard problems and probe theorems.

> that does not mean the model can do actual logic.

But they do, all the time. (Please tell me you’ve at least put a frontier LLM through its paces in the last 6 months?) If you think they can’t do logic and reasoning, can you provide examples of specific math or logic problems that you think a frontier LLM can’t do?