ABSTRACT
Mathematicians, like the rest of us, cherish clever ideas; in particularthey delight in an ingenious picture. But this appreciation does notoverwhelm a prevailing scepticism. After all, a diagram is – at best – just a special case and so can’t establish a general theorem. Even worse, it can be downright misleading. Though not universal, the prevailing attitude is that pictures are really no more than heuristic devices; they are psychologically suggestive and pedagogically important – but they prove nothing. I want to oppose this view and to make a case for pictures having a legitimate role to play as evidence and justification – a role well beyond the heuristic. In short, pictures can prove theorems.1
