RecursivelyIronic
Reputation
351
Top tag
Next privilege 500 Rep.
Access review queues
 Feb 15 comment Is it possible to prove a mathematical statement by proving that a proof exists? It's a matter of taste. I guess you could view this as the more fundamental viewpoint that, that any statement true for all sufficiently high characteristic algebraically closed fields must be true of the complex numbers as well. I don't know much about complex analysis or algebraic geometry, so the model theoretic proof is certainly more intuitive to me. However, I think the nondegeneracy of the Jacobian of all injective holomorphic maps is a better geometric explanation, and nonobvious for polynomial maps in the positive-characteristic case. May 27 awarded Nice Answer Feb 9 awarded Nice Answer Jun 21 awarded Yearling Jan 21 revised Is it possible to prove a mathematical statement by proving that a proof exists? Fix incorrect argument related to the characteristic of the field Jan 18 comment Is it possible to prove a mathematical statement by proving that a proof exists? Rudin's proof seems more powerful than the model-theory proof above, and it elucidates better why the theorem is true. Still, this is a standard proof which directly addresses the original question. Jan 18 comment Is it possible to prove a mathematical statement by proving that a proof exists? Not off the top of my head. I'm guessing it goes something like this: Since every function on finite fields is a polynomial function, there should be an upper bound $U(n, d, p)$ on the degree of the inverse for every $n$. If that function can be made independent of $p$, then just use "$\phi_{d,n}$ AND there is a polynomial of degree at most $U(n,d)$ which is an inverse of $f$" instead of just $\phi_{d,n}$. The proof would go the same. I don't know how to make the upper bound on the degree independent of $p$, however. (Is it possible?) Jan 18 revised Is it possible to prove a mathematical statement by proving that a proof exists? Clean up sentence. Jan 18 awarded Editor Jan 18 revised Is it possible to prove a mathematical statement by proving that a proof exists? Improve confusing choice of variable name. Jan 18 answered Is it possible to prove a mathematical statement by proving that a proof exists? Jan 11 awarded Teacher Jan 11 answered How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards? Jan 11 awarded Supporter Jun 21 awarded Autobiographer