To a very, very good approximation no proofs in actual published mathematical papers and books are “proofs” in the sense you describe here.
The intention is that they could be turned into such proofs without substantial creative effort, but it’s almost unknown for anyone to bother doing it and those who do typically find that it’s a lot of work.
To a very, very good approximation no proofs in actual published mathematical papers and books are “proofs” in the sense you describe here.
The intention is that they could be turned into such proofs without substantial creative effort, but it’s almost unknown for anyone to bother doing it and those who do typically find that it’s a lot of work.
https://proofwiki.org/wiki/ProofWiki:Jokes/Physicist_Mathematician_and_Engineer_Jokes/Burning_Hotel
The diffrence between thinking you have a solution and having a solution. And indeed the former admits great degrees of uncertainty.