Infinities, impossibilities, and the man in the white linen suit

Iain Harper argues that the AI industry's promise of safety guarantees is mathematically unsupported, tracing the limits of rule-based systems from Kurt Gödel's 1931 incompleteness theorems through Alan Turing to contemporary machine learning, where learning tasks are formally undecidable and networks harbor provably unfixable instabilities.

Iain Harper opens with Kurt Gödel's strange, tragic end and works backward to what he actually proved in 1931: that rule-based systems cannot fully account for themselves, an insight that flowed through Turing into the foundations of computing itself. He then traces how those same limits surface in contemporary machine learning — learning tasks that are formally undecidable, networks that look accurate while harboring provably unfixable instabilities, and the impossibility of one system certifying another as unconditionally safe. The sharp edge of the essay is aimed at the AI industry's implicit promise: safety guarantees, Harper argues, that 'the mathematics has never supported.' A literate, historically grounded reminder that better guardrails are achievable and worth building, while certainty is not on the menu.