formal-math

ing, and no, it does not do tool calling for basic arithmetic any more than humans might. Isolation of individual concepts in intermediate layers can already be demonstrated, or else transfer learning wouldn't possibly work. Nobody is saying that LLMs are humans. But we need labels for some of the things that we observe and dismissing them because "statistical" is laughable. Look at the proof of this: https://github.com/anthropics/formal-math/blob/795efb86f1917... . Forget the Lean, look at the underlying argument construction. At the very least, this is continuing from an argument that was hinted at in the literature in 2024, but these proceedings were difficult enough that humans were not able to do them within two years. Do you attribute this to the harness alone? If so, that's a pretty sophisticated bit of engineering, I would say! Probabilities are far too small to argue infinite monkey theorem. If there was even a shred of a reasonable argument that LLMs were incapable of concept extraction and manipulation, I and my colleagues would be all over it. We would relish in it. It would bring us comfort. It is unbelievable that people think they can spew whatever basic garbage they think of as a gotcha, and think that minds all over the world haven't already considered that. This is like climate denial at this point.