Tuesday, September 25, 2001
Understanding short FLT Proof requires paradigm shift
One thing that's clearly emerged from replies to some of my posts on the newsgroup is a problem created by people looking at the math just one way.
To explain I like to give the simple quadratic
fx^2 + gx + h = (a1 x + b1)(a2 x + b2), where f, g and h are integers.
Apparently, a lot of you immediately want to solve that, and it might take you a little while to realize you can't with the information given.
Now if I give you
x^2 + 4x + 4 = (a1 x + b1)(a2 x + b2),
you may jump to a conclusion based on ONE solution out of infinity.
What also seems clear is that most of you by reflex think I'm talking about
fx^2 + gx + h = 0, and x^2 + 4x + 4 = 0, when there isn't any evidence to support that conclusion.
So, what's the point of my going over the above?
The point is that some of you have made replies claiming flaws in my short proof of Fermat's Last Theorem that depend on your not understanding clearly factorization as an ABSTRACT and NOT just as a way to solve polynomials set to 0.
Why do I say this?
Some on the newsgroup have accepted an argument against the proof that depends on something like saying f cannot equal 0, with fx^2 + gx + h because then they claim everything is undefined.
Sound puzzling? Solve for x, with fx^2 + gx + h = (a1 x + b1)(a2 x + b2), using the quadratic formula and it should be clear to you then.
If you think that f cannot equal 0 because you get a divide by 0 error, watch this:
gx + h = b1(a2 x + b2).
Is that undefined because of a divide by 0 error?
My proof, like the examples above, depends on only the ring operations of multiplication and addition, so it CANNOT have divide by 0 errors.
So why are there people on this newsgroup so confident that the proof is wrong based on an objection that depends on the assertion of a divide by 0 error?
I don't know, but I wish you'd tell me. I find the illogic strange and discomfiting, as well as surprising.
In any event, I won't post the link to the proof here because I have a post today that not only links to it, but explains briefly the idea behind it.
Eventually the proof will be accepted as I push people making mathematical replies to using objectivity instead of emotion, but considering how things look now, it could take a while.
To explain I like to give the simple quadratic
fx^2 + gx + h = (a1 x + b1)(a2 x + b2), where f, g and h are integers.
Apparently, a lot of you immediately want to solve that, and it might take you a little while to realize you can't with the information given.
Now if I give you
x^2 + 4x + 4 = (a1 x + b1)(a2 x + b2),
you may jump to a conclusion based on ONE solution out of infinity.
What also seems clear is that most of you by reflex think I'm talking about
fx^2 + gx + h = 0, and x^2 + 4x + 4 = 0, when there isn't any evidence to support that conclusion.
So, what's the point of my going over the above?
The point is that some of you have made replies claiming flaws in my short proof of Fermat's Last Theorem that depend on your not understanding clearly factorization as an ABSTRACT and NOT just as a way to solve polynomials set to 0.
Why do I say this?
Some on the newsgroup have accepted an argument against the proof that depends on something like saying f cannot equal 0, with fx^2 + gx + h because then they claim everything is undefined.
Sound puzzling? Solve for x, with fx^2 + gx + h = (a1 x + b1)(a2 x + b2), using the quadratic formula and it should be clear to you then.
If you think that f cannot equal 0 because you get a divide by 0 error, watch this:
gx + h = b1(a2 x + b2).
Is that undefined because of a divide by 0 error?
My proof, like the examples above, depends on only the ring operations of multiplication and addition, so it CANNOT have divide by 0 errors.
So why are there people on this newsgroup so confident that the proof is wrong based on an objection that depends on the assertion of a divide by 0 error?
I don't know, but I wish you'd tell me. I find the illogic strange and discomfiting, as well as surprising.
In any event, I won't post the link to the proof here because I have a post today that not only links to it, but explains briefly the idea behind it.
Eventually the proof will be accepted as I push people making mathematical replies to using objectivity instead of emotion, but considering how things look now, it could take a while.
# posted by James Harris @ 19:01 
