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A postmortem of a soundness bug in the Lean kernel that was exploited to produce a 'disproof' of the Collatz conjecture, with the fix and analysis of why independent checkers also initially missed it.
Lawrence Paulson discusses a bogus refutation of the Collatz conjecture caused by a bug in the Lean kernel, reflecting on proof objects and soundness in proof assistants.
An AI-generated formal proof in Lean that claimed to disprove the Collatz conjecture actually exploited two bugs in the Lean kernel, now patched. Lean creator Leo de Moura warns this will keep happening as AIs are good at finding soundness bugs.
A new formal theorem, verified in Lean, shows that for thresholds tending to infinity, almost every positive integer falls below the threshold within 436 log N Collatz steps, strengthening Terence Tao's earlier result with explicit bounds and natural density.
Unicode's transliteration rules (UTS #35) are proven to be Turing-complete by compiling 2-tag systems, showing termination is undecidable. This result affects the ICU library used in many systems.