On Friday, 2 May 2014 22:32:14 UTC+2, Dan Christensen wrote:
> No. That is the nature of formal proof. If you have a formal proof, you know exactly what rules, axioms and assumptions were used.
And you can guess, most times, that the result is useless. For example there exists a formal proof that ever set can be well-ordered, but it is impossible to do so. This shows that this formal proof is rubbish.
Another formla proof proves the existence of uncountably many real numbers. Alas, they do not exist in mathematics. This shows that also this formal proof is rubbish.