4
$\begingroup$

Gauss has proven FTA several times. Are any of Gauss's FTA proofs considered rigorous in modern mathematics?

Or is it that, despite many proofs, there is not a single one that can be considered modern mathematically rigorous?

$\endgroup$
1
  • 3
    $\begingroup$ Hi and welcome to HSM SE! Please write the body of your question such that it can be read independently of the title. $\endgroup$ Commented May 19 at 3:11

1 Answer 1

5
$\begingroup$

The second proof and third proofs by Gauss, both of which were publish in 1816, are correct, even by modern standards. The second proof is essentially algebraic (the only fact used taken from Analysis is the theorem that any real polynomial of odd degree always has a real zero), whereas the third one is more topological. The basic idea of this proof is still to be found in the modern Complex Analysis proofs based on Rouché's theorem.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.