Unverified50% confidenceFactExact time
The verification of semantic equivalence when translating natural-language mathematical definitions into formal languages can, in certain cases, be reduced to an undecidable problem of higher complexity than the halting problem, belonging to higher levels of the arithmetic hierarchy.
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10/11/2026
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UnverifiedThe ambiguity, implicit premises, and context-dependency of natural language cannot always be cleanly mapped to first-order logic, which is a translation boundary challenge for this architecture.78% similarUnverifiedMathematical arguments generated by large language models are highly prone to appearing correct while actually being erroneous, and finding the errors requires word-by-word review by professional mathematicians.73% similarUnverifiedThe process of translating naturally written mathematical proofs into Lean is often more time-consuming and labor-intensive than the original proof.73% similarUnverifiedThe paper mathematically rigorously proves that faithfully translating word-for-word proofs written by humans or AI into the Lean language is extremely difficult, and can in theory reach arbitrary levels of complexity.72% similar
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