This post follows on (loosely) from a previous discussion on maths and computing and asks what it really means to ‘prove’ something in each discipline.
An apocryphal story has an Oxbridge maths don lecturing to a group of undergraduates … After some time completely filling a huge blackboard with heavy calculus – with accompanying commentary, he turns to the class and casually notes, “So then, it’s clear that …” (the exact claim isn’t important). As he turns to resume his chalk-work, a particularly bold student enquires, “Excuse me, Professor; but is that really ‘clear’?” The don steps back and surveys his work; studying the entire board from top-left to bottom-right, with numerous head and eye movements to-and-fro – even some pointing – to cross-check various parts with each other. After a full five minutes of silent contemplation, he turns back to the students, smiles, announces, “Yes!”, and carries on as before.
So who’s defining ‘clear’ here?
Turing's Radiator 