Broken proofs and broken provers
Summary
The post argues that mathematical proofs and machine proofs are not absolutely perfect: proofs can be broken by incorrect assumptions, bugs in proof assistants, or multithreading quirks. It surveys soundness bugs in Isabelle, HOL, Rocq, and PVS, discusses safeguards like locales and explicit premises, and concludes that while machine proofs are not flawless, they advance rigorous verification when used with care.