## JSH: Critical argument, short demonstration

Math people are fighting to defend against accepting they have over one hundred years of error in a "pure" math area of abstract number theory, but I can give you a short proof to cut through their distracting rhetoric:

On the complex plane given the expression

7*(175x^2 - 15x + 2) = 7*(5c_1(x) + 1)(5c_2(x)+ 2)

where the c's are not yet determined function of x, there is NOTHING in algebra that prevents me from choosing:

7*(175x^2 - 15x + 2) = (5*7*c_1(x) + 7)(5c_2(x)+ 2).

If you accept that one point you are 99% of the way to being able to cut through the noise when the math people work desperately to hide their error. Now I introduce new functions:

b_1(x) = 7*c_1(x), and b_2(x) = c_2(x)

and b_1(0) = b_2(0) = 0, and substitute to get

7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2).

and there NOTHING that says I cannot do that on the complex plane.

The b's are still not determined functions of x.

I will introduce a final set of functions:

a_1(x) = b_1(x), and a_2(x) = b_1(x) - 1

Now I'll make those substitutions and get:

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

and now note that a solution—no I'm not saying it's the only solution!!!—for the a's is, as roots of

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

You can now solve for the a's easily using the quadratic formula:

a_1(x) = ((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2

a_2(x) = ((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2

and that is a valid solution as can be verified easily enough by substitution.

Now then, if you believe in mathematical proof, where in that chain of mathematical statements did I do something invalid or blocked by algebra?

But now you have the conclusion that only one of the a's was actually a product of 7, as you know the start:

7*(175x^2 - 15x + 2) = (5*7*c_1(x) + 7)(5c_2(x)+ 2).

The result that only one of the roots of

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

was actually multiplied by 7 becomes a factor result in other rings, but is contradicted by the ring of algebraic integers in specific cases.

THAT brings into question the naive use of that ring, as unfortunately it can be shown that the problem allows you to appear to prove things that are not true, and it also brings into question the usefulness of Galois Theory.

Yes, I know, it can massively hurt huge egos to find out that a ring has been naively used, but that is just reality. Huge egos in the math field may not wish to accept the truth, but they shouldn't be allowed to continue in error.

But they are trying to continue in error.

Which is why posters are so dedicated in arguing with me.

They are working desperately to hide one of the hugest errors in the history of the human species.

If they accept what is mathematically correct, then a house of cards tumbles down.