Speaking of uncountability, here's a similar one for why the set of functions N->{0,1} is not countable. If f:(N->{0,1})->N were a bijection, let g(t)=1-f^(-1)

Speaking of uncountability, here's a similar one for why the set of functions N->{0,1} is not countable. If f:(N->{0,1})->N were a bijection, let g(t)=1-f^(-1)(t)(t), and compute g(f(g)). Anyway, whether something counts as a proof is a matter of whether you (logically) accept it as irrefutable evidence. As with any genre, you have to consider your audience. I hear gauge theorists are content to have as a proof a couple of references to a couple papers which have techniques which apply, with minor alteration, to the current problem. That said, I wouldn't have minded if Zagier actually demonstrated it was an involution with exactly one fixed point!