Do you think that a proof of a theorem can always be made more rigurous? Or there is a limit on how rigurous a proof can be? I mean, what is today considered a rigurous proof of an established theorem, may not be a rigurous proof of tomorrow with more advanced techniques? Or do you (anyone who reads this) think that a proof can be so rigurous that it can not be enhanced in any way? What about alternative proofs? Do you think it is useless to find other proof of an established theorem? Do you think one proof will always be the better/more rigurous? Or that two proofs of a given theorem can have relative advantages in some sense over the other? (rigurous vs simple, etc) What would be the point of finding a proof of an already established theorem? Can it be better in some way? In wich sense? (elemental, simple, rigurous, short, elegant?) (It may be a matter of taste if a proof is more elegant than another, isn't it?) One think that surprised me was to read that Gauss gave 6 different proofs of the fundamental theorem of algebra. Wasn't one good enough? Thanks.