But I don't think you understand the role of proof and conjecture. When a proof is found to be wrong, it's wrong forever and it's definitive. When a biology experiment interpretation is "believed" to be "wrong" it takes a good century to get the bad interpretation out of the zeitgeist. Until it makes a comeback.
I see. You know it can't be wrong, but you can't verify it. Very amusing.
No, you don't know it can't be wrong. There was a great deal of argument about whether it was a proper proof. And fear that others would try to prove things in a similar way. If I remember, it didn't get published in a regular journal. But that was a long time ago and Appel and Haken's ideas lead to the verifiable Robertson and Seymour proof. And other proofs of that type did not emerge.
Tell ya what, here's a simple set of arithmetic identities, all valid in finite math,
Uh, what is "finite math"? I assume you're using some sort of Abelian group structure.
Careful about Gödel. That only has to do with a closed system. You just move to a more complete system. For example, x2+x+1 cannot be factored over the reals, so you just pass to complex. Voilá.
Since you know FLT existed for many years unproved, you acknowledge that math exists that hasn't got a proof associated with it.
Well, you've got to have conjecture before proof.
Godel only has to do with DISCRETE systems, such as integer arithmetic, or tabular systems of proof relying on symbols in a row, or quantum orbit calculations. Some continuous systems, like the Calculus, or classic geometry, are known to be theoretically complete, or closed, and do not suffer from the Godel limit. However, much of the universe, and the universe of mathematical discourse in particular is, in fact, discrete, with no obvious escape clause. Are you proposing that any mathematics can escape from the Godelian limit through some form of mathematics as yet undreamed of?
But I don't think you understand the role of proof and conjecture. When a proof is found to be wrong, it's wrong forever and it's definitive.
Really? So the proof of a thing can be wrong. But the disproof is incapable of being wrong? Don't you detect a small assymetry in this argument?
When a biology experiment interpretation is "believed" to be "wrong" it takes a good century to get the bad interpretation out of the zeitgeist. Until it makes a comeback.
Which would be about on par with astro-physics, where the either reigned for at least 100 years, Ptolomaic astronomy reigned for 1000, and the Newtonian time-space invariant framework of the universe reigned for 400.
Should we dismiss astrophysics as beneath consideration as a scientific endeavor as well?