> I can not fathom a LLM could conceive from scratch concepts like the real numbers by Dedekind.

What stops you? I can fathom it alright.

I am always suspicious of these arguments like "a machine won't do thing x which humans can". These always basically pre-suppose that humans aren't machines. If that's what you're arguing for, say it outright.

Just to add that the Dedekind cut example seems to stand beyond any RL policy used in chess or go, AlphaZero or AlphaProof. In the classical RL there is an state-action space. If the solution requires jumping to a totally difference action space (that must be created) the local policy stalls. Dedekind cut is an example of a out-of-distribution state-space generation.

A cynical could say that AI could not interpolate the Dedekind cut but it could extrapolate to create a lot of money but just using an imaginary extra point.

The ironic part is that generating a joke like this requires jumping across three distant fields: real analysis, machine learning limits, and VC market cynicism. For an AI to discover that specific overlap through statistical search, the combinatorial space is absurdly huge. Yet a human brain connects them in a fraction of a second. This tiny joke is a micro-proof of the macro-argument: human conceptual leaps routinely bypass exponential search spaces.