Harristotelian Logic

It is hard to hear that you have been taught wrong, and harder still to confront dogma, because "mathematical proof" is just a phrase for most of you as you've never been put in a situation where you really did not wish to accept a result, so you avoid the mathematical proof but by rationalizing continue to believe yourselves to be mathematicians or real students of mathematics, when you no longer
are.

I defined mathematical proof. Don't believe me? Google it. Google: define mathematical proof

I come up #2 now in most venues.

Physics students should do better. Physicists know about resistance to results and hard to understand results which challenge accepted views, but the field has softened because of the dominance of mathematical techniques, so people who are really mathematicians get to pretend to be physicists, when they are not, and there is a worship as well of authority, so that when the math people say false physics students follow along because, what else can they do? Resist authority? But, but, but…how can they?

All of that is a preamble for one of the simplest most powerful mathematical arguments in the history of human civilization which mathematicians have resisted for over 6 years now despite how easy it is to prove.

It only requires you accept the distributive property and believe that proof is, well, proof.

The distributive property is: a*(b + c) = a*b + a*c

In the complex plane with

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

where the a's are roots of

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

you normalize:

a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have

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

where b_1(0) = 0, b_2(0) = 0.

And you have one factorization out of infinity and in THAT factorization the 7 has distributed in one way, which is easily verifiable at x=0, as then you it distributed through

5b_1(0) + 7,

as that equals 7(0 + 1), so with the distributive property you have a=7, b=0, c=1.

EASY. But remember 6 years of mathematicians arguing against this result!!!

Now if we consider that a*(b+c) = a*b + a*c, is true if one of the elements is a function then I have

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

and the TYPE of the function does NOT MATTER; however, that challenges current mathematical intuition, so while with something like

7(x^2 + 3x + 2) = (7x + 7)(x + 2)

math people found it hard to dispute the distributive property, hide the 7 away with:

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

and they disputed the result as they don't want to believe that with

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

only one root should have 7 as a factor as that's what the distribution shows.

(Remember the factorization is normalized and

a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1.)

Now in case you forgot your algebra classes, it is NOT taught in them that only one of the roots of

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

in general should have 7 as a factor. You can verify one case easily enough, x=0:

a^2 + a = 0

as one root is 0, and 0, of course has 7 as a factor. But use x=1, and you get

a^2 - 6a + 35 = 0

and only one of its roots actually has 7 as a factor, but you can prove in the ring of algebraic integers that NEITHER root has 7 as a factor as neither root does—IN THAT RING.

The ring gives bad results. Techniques based on it give wrong results.

So you have an advancement of human knowledge: it's now possible in this case to determine 7 is a factor of a root without being able to see it directly, where it's also not determined which root.

There is an ambiguity which cannot be removed which means the solutions are paired or entangled in a way that cannot be beaten. You must take them by two's. With quarks you must take them by three's.

Which may indicate some cubic function which controls some aspect of quark behavior, which cannot be probed without advanced analytical tools meaning some aspect of quark behavior may be beyond the vision of humanity with currently accepted mathematical tools, but possible to analytically study with the ones I've introduced.

For perspective I used some of those tools to also generally solve binary quadratic Diophantine equations.

Don't know what those are? Google it. I think I come up #1.

So there may be a ceiling on what humanity can do in physics at this point because it is not using the full mathematical knowledge available, where mathematicians have been resisting this result as it overturns past beliefs, and they wrongly believe their field is immune from revolutionary upheavals.

Their belief is holding back the scientific progress of our species.

And THAT is how you go from a very simple quadratic argument which requires that you only believe the distributive property to understanding how math people could fight for belief for over 6 years against mathematical proof, and hurt the physics community and the progress of the entire human species in the process.