272 ;;Quote: mathematicians' errors are corrected by other mathematicians, not by formal logic

273 ;;Quote: when a mathematician grasps a proof, he tries it out on his colleagues; it is not absolute

273 ;;Quote: if a mathematical proof is believed, it is internalized, paraphrased

274 ;;Quote: a believable theorem gets used

274 ;;Quote: the truth of a theorem is established through transformations, generalizations, use, and connections

275 ;;Quote: a verification of a program must be accepted blindly without the social processes of mathematical proofs

277 ;;Quote: if we feel that something is provably right then redundancies are removed

277+;;Quote: failure of a system without redundancies is massive and uncontrolled; like the Titanic

277 ;;Quote: a verified program is provably corrected but not reliable and trustworthy; no information about limits

277 ;;Quote: since a program is a human artifact it will contain imperfections and can never be verified

278 ;;Quote: a trivial, minute change can wreak havoc in a massive system; like the time traveler who damages a butterfly

278 ;;Quote: a verification may not be transferable to any other program; prevents social processes

278 ;;Quote: a program is the only complete description of the program's behavior

278 ;;Quote: the construction of symbolic structures uses resources; can be impossibly long if care is not taken

279 ;;Quote: how do engineers create reliable structures from imperfect mechanisms

279+;;Quote: people must act without sufficient knowledge