Unverified50% confidenceFactExact time
The 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.
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10/11/2026
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UnverifiedConverting natural language or informal mathematical writing into formal proofs currently still requires extensive human intervention, and the time cost may be several times to dozens of times that of the original derivation.73% similarUnverifiedThe process of translating naturally written mathematical proofs into Lean is often more time-consuming and labor-intensive than the original proof.72% 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.72% similarUnverifiedThe 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.72% similarPartially Verified当前自然语言提示的最大问题在于歧义性，同样的需求不同人写出的提示词可能完全不同，AI产出的代码也可能截然不同67% similar
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