For a long time, there is a "diagonal method of proof" dominating the mathematics field; with it, Russel finds the paradox of set theory; with it, Cantor proves that "the power set of natural numbers is uncountable" and " the set of real numbers is uncountable"; with it , Gödel proves that " natural number system PA is incomplete"; with it , Turning proves that " halting problem" is undecidable and proves that " there is non-recursive sets on sets of natural numbers" in recursion theory and so on; proofs of these significant propositions all apply the same mathematic method which is praised as " a golden diagonal". On the basis of analyzing paradoxes, the paper finds that paradoxes are unclosed terms on closed calculus (that is extra-field term). Classical logic system cannot handle such extra-field terms, so it is transformed to the logic systems SL, SK that may handle unclosed calculus. It can be found that "diagonal proof method" is to construct paradoxes in nature through further analysis, and it is an unclosed proof method, which can prove that real numbers constructed by Cantor’s "diagonal proof method are extra-field terms which will not affect count-ability of sets of real numbers; The Gödel’s undeterminable proposition is an extra-field term, which will not affect completeness of system PA. The undeterminable Turing machine in the Turing halt problem is also an extra-field term. So, the proof that real number is uncountable is wrong; the proof of Gödel’s incomplete theorem and diagonal method of proof, all of them are wrong, should be completely corrected.