And talk much as IS important, and they seized upon roots of monic polynomials with integer coefficients as being a good idea for members of a ring. Where monic just means 1 or -1, so for instance something like: x

^{2}- 4x + 3 = 0

To show a flaw with their reasoning I need a generalized quadratic factorization.

In the complex plane consider:

**P(x) = (g**

_{1}(x) + 1)(g_{2}(x) + 2)where P(x) is a primitive quadratic with integer coefficients, g

_{1}(0) = g

_{2}(0) = 0, but g

_{1}(x) does not equal 0 for all x.

Simplest example is: P(x) = (x+1)(x+2)

Where I throw a wrinkle into the mix by doing something no respectable mathematician would do--I add an extra factor I call k.

**g**and

_{1}(x) = f_{1}(x)/k

**g**

_{2}(x) = f_{2}(x) + k-2Multiply both sides by k, and substitute for the g's, which gives me the now symmetrical form:

**k*P(x) = (f**

_{1}(x) + k)(f_{2}(x) + k)**That extra factor is JUST to force one of the f's to have k as a factor, while I can force the f's to be roots of monic polynomials with integer coefficients. And if all seems very distant, consider means can show that 3-sqrt(-26) has 7 as a factor.**

Have talked in detail with this post:

Easily explaining historical miss

Have given a more dry and purely mathematical explanation with:

Non-polynomial factorization short argument

Which is useful for well-trained math people, and it IS all very easy though. Was simply lucky that something this HUGE could be handled with a quadratic and a trivial leap that I force an extra factor which is something math people are trained NOT to do, and in so doing can blow up a hundred years of mathematical thinking.

So they did NOT solidify the mathematical discipline, but instead weakened it, but our species was ok, because most math we use was developed long ago, as I recently explained.

There I note that certain folks are simply not needed for valid mathematics. And yeah, when realized that years ago knew had a bit of a slog to getting these things properly recognized.

Of course have plenty of the demonstrated ability NOW for being the kind of person to figure such a thing out. Actually first came across problem with an entirely different approach using tools I developed, as created my own math discipline. Those same tools also let me do lots of remarkable things. And I found my own way to count prime numbers with a clever tweak on old ideas. Get tired quickly trotting out a list of things, so will stop there. Wow, yeah I have a lot can trot out there for being the person would discover such a thing, I guess.

But also has been lots of luck am sure in it all, though also, fundamental results often DO come from simple, is a good thing. Simple is so cool.

But we humans are clever by much I guess, while also can fall into odd traps, like NOT adding extra factors! While I'm NOT a mathematician, I proudly note, so to me? Why not? So I did.

When will situation resolve? Did you read that part about certain folks NOT being needed?

I'm just the discoverer. I do not make the knowledge. I simply found it, and often wonder.

When humanity feels like it, I guess. Meanwhile, I enjoy the knowledge.

There is such a thrill with discovery. Do appreciate knowledge gained.

Mathematics is endlessly fascinating to me.

James Harris