Friday, May 18, 2007
JSH: Why proof is not enough
So the latest story is that I wrote an updated paper which specifically takes away all the objections that sci.math'ers tossed at my older paper, and it gives this really cool and amazing result with very deep number theoretic implications.
It tells you more about numbers than you could know before reading it.
But the reaction on your newsgroups has been a lot about posters ignoring the proof.
Maybe it is about all the arguing over the years and some of you may wonder, why all that arguing? Why couldn't I have been nicer? Why couldn't the discussions have been more polite?
And I say, disagreement is not a bad thing, and to the extent that people would give me nothing, and attack my ideas, as it was much better from my perspective as I need proof, and proof is not about social niceties.
And you can see the benefits of that approach, as my latest research is a continuation somewhat forced by the need for me to explain in such a way as to remove the ability of people like the sci.math'ers to credibly object.
So now you know definitely that I have proof, because I can talk about subtracting from identities not changing the ring, and you know that must be true.
Proof taken to the ultimate level of detail means that to doubt it you have to doubt the most basic axioms in mathematics, and if you find yourself wondering now if identities can change the ring then you are there.
Like how can
x=3Dx or x+y =3D x+y or x + 2xy + z =3D x + 2xy + z
change the ring?
So now I have a paper where I show the full picture showing how you can get a handle on the factorization of a quadratic such that you can cover NOT just the polynomial factors—the trivial factorization most mathematicians focus on—but ALL the possible factorizations, over infinity:
175x^2 =E2=88=92 15x + 2 =3D 2(f(x) + 1)* (g(x) + 1)
That is what's factored where I show how f(x) and g(x) can be totally defined and you can actually check through them and find when they can be algebraic integers functions with an algebraic integer x.
That is, you find when given algebraic integer x, f(x) and g(x) can give you an algebraic integer result.
The answer is enough to take away Galois Theory as it is usually taught, and change number theory itself entire as a discipline, which is more than enough for some Usenet posters to work very hard as you can see them doing, to try and hide the result.
What you are facing now is history in the making.
That means massive change.
And massive change is usually massively resisted.
My suggestion is to READ THE PAPER FOR YOURSELF as I have it in pdf format. You can get it and download it and not have to tell anyone you did.
http://groups.google.com/group/extrememathematics/web/non-polynomial-factorization-paper
Understand what all the fighting is about—please read the paper.
It tells you more about numbers than you could know before reading it.
But the reaction on your newsgroups has been a lot about posters ignoring the proof.
Maybe it is about all the arguing over the years and some of you may wonder, why all that arguing? Why couldn't I have been nicer? Why couldn't the discussions have been more polite?
And I say, disagreement is not a bad thing, and to the extent that people would give me nothing, and attack my ideas, as it was much better from my perspective as I need proof, and proof is not about social niceties.
And you can see the benefits of that approach, as my latest research is a continuation somewhat forced by the need for me to explain in such a way as to remove the ability of people like the sci.math'ers to credibly object.
So now you know definitely that I have proof, because I can talk about subtracting from identities not changing the ring, and you know that must be true.
Proof taken to the ultimate level of detail means that to doubt it you have to doubt the most basic axioms in mathematics, and if you find yourself wondering now if identities can change the ring then you are there.
Like how can
x=3Dx or x+y =3D x+y or x + 2xy + z =3D x + 2xy + z
change the ring?
So now I have a paper where I show the full picture showing how you can get a handle on the factorization of a quadratic such that you can cover NOT just the polynomial factors—the trivial factorization most mathematicians focus on—but ALL the possible factorizations, over infinity:
175x^2 =E2=88=92 15x + 2 =3D 2(f(x) + 1)* (g(x) + 1)
That is what's factored where I show how f(x) and g(x) can be totally defined and you can actually check through them and find when they can be algebraic integers functions with an algebraic integer x.
That is, you find when given algebraic integer x, f(x) and g(x) can give you an algebraic integer result.
The answer is enough to take away Galois Theory as it is usually taught, and change number theory itself entire as a discipline, which is more than enough for some Usenet posters to work very hard as you can see them doing, to try and hide the result.
What you are facing now is history in the making.
That means massive change.
And massive change is usually massively resisted.
My suggestion is to READ THE PAPER FOR YOURSELF as I have it in pdf format. You can get it and download it and not have to tell anyone you did.
http://groups.google.com/group/extrememathematics/web/non-polynomial-factorization-paper
Understand what all the fighting is about—please read the paper.
# posted by James Harris @ 20:46 
