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Four top AI models assigned a 95%+ confidence level to “will halt” for a five-line program based on Goldbach’s conjecture, yet all switched their answers to “I don’t know” when given that option—the article uses this to illustrate that the halting problem and Rice’s theorem mean no AI can determine the answer to such questions without a proof.
A discussion post exploring whether AI-generated content detection could eventually face a fundamental mathematical limit—akin to the halting problem—making AI and human content theoretically indistinguishable rather than just technologically hard to tell apart.
An accessible explanation of Gödel's incompleteness theorems, describing how Gödel numbering maps statements about a system onto statements within the system to prove that any consistent axiomatic system is incomplete.