### Wednesday, August 27, 2008

## JSH: Simply brutal, algebraic integers undone

What I did was something very clever, unlike anyone before me I constructed bizarre factorizations of a polynomial into non-polynomial factors, and by so doing, I found an error.

It's trivial to show, as consider a simple quadratic:

P(x) = 175x^2 - 15x + 2

I figured out a way to creatively factor it, AFTER you multiply by some constant like 7, so you have

7*P(x) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are the two roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And in so doing blew up over a hundred years of mathematical thought as I leveraged a CONSTANT against functions in each of the factors:

(5a_1(x) + 7) and (5a_2(x)+ 7)

And you can do simple things like use x=0 to see what is happening and find that you have

7*P(0) = (5(-1) + 7)(5(0)+ 7) or 7*P(0) = (5(0) + 7)(5(-1)+ 7) = 14

And if the distributive property works with functions and

a*(f(x) + b) = a*f(x) + a*b

then you know what happens for any x, not just x=0.

So it's trivial.

Arguing against the result is arguing against the distributive property, but in the ring of algebraic integers you CANNOT DIVIDE OFF THE 7 IN GENERAL because that ring has special properties.

I got a paper published. And some sci.math'ers mounted an email campaign against it, the editors of the journal caved and then the journal quietly shut down.

Mathematical proof has so far been limited in effectiveness against social needs for error.

Quite simply, people who are failures at mathematics can use the error to "prove" things that are not true, and find social success.

And kill number theory in the process if allowed.

It's trivial to show, as consider a simple quadratic:

P(x) = 175x^2 - 15x + 2

I figured out a way to creatively factor it, AFTER you multiply by some constant like 7, so you have

7*P(x) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are the two roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And in so doing blew up over a hundred years of mathematical thought as I leveraged a CONSTANT against functions in each of the factors:

(5a_1(x) + 7) and (5a_2(x)+ 7)

And you can do simple things like use x=0 to see what is happening and find that you have

7*P(0) = (5(-1) + 7)(5(0)+ 7) or 7*P(0) = (5(0) + 7)(5(-1)+ 7) = 14

And if the distributive property works with functions and

a*(f(x) + b) = a*f(x) + a*b

then you know what happens for any x, not just x=0.

So it's trivial.

Arguing against the result is arguing against the distributive property, but in the ring of algebraic integers you CANNOT DIVIDE OFF THE 7 IN GENERAL because that ring has special properties.

I got a paper published. And some sci.math'ers mounted an email campaign against it, the editors of the journal caved and then the journal quietly shut down.

Mathematical proof has so far been limited in effectiveness against social needs for error.

Quite simply, people who are failures at mathematics can use the error to "prove" things that are not true, and find social success.

And kill number theory in the process if allowed.