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> LLMs have no issue making definitions (interfaces/traits/abstract classes) in programming, which is formally the same activity. I ask them to form a core "spine" of a program (basically an intelligible theory), and they do it really well.

Is it a "standard" software? Something where the patterns exists in several other software? Try with something that is novel, or is in a limited set. You will find that it will copy heavily from what exists already, going so far as lifting whole functions from another project.



Maybe, but math also has reusable techniques and patterns. c.f. https://www.tricki.org/

The goalpost moving is really getting absurd, to the point where now the machine needs to be a world-class once-a-century genius that invents entire new fields out of thin air (which are of course still relevant to humans) for it to be "intelligent". Meanwhile a well above average human struggles to even apply trivial definitions to particular problems (c.f. programmers that don't understand monoids).




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