Harristotelian Logic

Pure math by not being connected to the real world leaves in the possibility of most people getting basic mathematical ideas wrong and not correcting for it for a long time.

Here's an easy refutation of standard interpretations of Galois Theory using some basic algebra, and once you read through it, consider why real results from the real world are important in keeping people correct—and honest:

This thing is so trivially easy too, as you start with

x^2 - ax + n = 0

and

y^2 - by + n = 0

and easily find

(y + x - a)(y - x) = (b-a)y

by subtracting one from the other and doing some basic algebra.

But with that simple result, I can now just let

a = 5/3, b=14/3, and n=1

as I then have as a solution

y = (14 + sqrt(196 - 36))/6 = (14 + sqrt(16))/6

and

x = (5 + sqrt(25 - 36))/6 = (5 + sqrt(-11))/6

so

((14 + sqrt(16))/6 + (5 + sqrt(-11))/6 - 5/3)((14 + sqrt(16))/6 - (5 + sqrt(-11))/6) = 9((14 + sqrt(16))/6)

which is

(3/2 + (sqrt(16) + sqrt(-11))/6 )((3/2 + (sqrt(16) - sqrt(-11))/6) = 3((14 + sqrt(16))/2)

And pay attention to factors of 3.

So some easy algebra proves that

sqrt(16) + sqrt(-11) or sqrt(16) - sqrt(-11)

must have 3 as a factor, but provably neither can have 3 itself as a factor in the ring of algebraic integers.

Pull the thread and a hundred plus years of math results go up in smoke in number theory.

But this is just another way I found of proving the problem but it's "pure math" so rather than acknowledge it, supposedly ethical, brilliant and honest mathematicians have just continued with the old stuff that doesn't work.

So they are neither ethical, brilliant, nor honest—but who can stop them.

This situation is like if physicists had ignored quantum mechanics because they liked Newtonian too much—and refused to go with what worked.

In "pure math" areas mathematicians clearly can get away with ignoring whatever they want, as my travails in getting my research recognized show.

Pure math is a pure bust because of simple human denial.

In physics that can be fought with experiments from the real world.

In mathematics, mathematicians just keep going, and get away with it, as what can you do?

Post in Usenet? I'm doing that, and don't say get published. I did that too. The journal pulled the paper after some sci.math'ers emailed them claiming it was wrong.

Too easy in a field where "pure" means just believe a bunch of guys who have salaries that depend on what is false.

The field is corrupted. And with a lot of money going to people who need the fake stuff, who can stop them.

So they teach their poor pathetic students crap. And the world lets them. The academic field is corrupted.