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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
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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
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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?
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11
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21
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