My own personal understanding of the implications of some of my discoveries is of course important to me, but also have begun to address more my global responsibility. And that global responsibility pushes more care and certainty, which can explain years in working through to be sure of the foundations. Which also worked out great for me, in making more discoveries.

Now though can explain things rather simply, and is my duty to explain simply implications of one of my most important results, which only requires considering a general factorization in the complex plane:

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.

It is trivial to be able to find the g's as algebraic integers, and then step beyond them to other numbers, which are also possible solutions for the g's, which cannot be fractions or like fractions in any way. Which are themselves integer-like, but not previously catalogued.

However, mathematical arguments not recognizing this reality, can appear to prove things NOT true, while looking correct if this reality is ignored.

That in mathematics, as most math students are usually taught, is a ticket to just about anything.

You can with such a problem, potentially appear to prove whatever you want, and my suspicion, since this problem arrived in the late 1800's is that it lead to a shift in the mathematical field towards dominance by people who increasingly exploited it, whether they realized it or not.

Human beings have a knack for finding easier success. Applied mathematicians of course would not be able to exploit it.

If there were not some awareness then my publication of a contradiction back in 2004 would NOT have lead to a math journal imploding, but to a hue and cry, as mathematicians recognized the problem. Instead I've faced what I consider astute use of social things. But for instance,

my post giving first a functional definition of mathematical proof, and later updated with a formalized one, was a reaction to mathematicians in the press, diminishing mathematical proof.

There IS a lot of naive I think especially in academic circles with mathematicians who grew up before the web about how well these stories travel. And have been curious about some of the things I suspect or think I notice that are being tried. With a relentless look to the press from certain people with relief as if that is all that matters.

But I do not need the press. Wouldn't mind their help, but don't have to have it.

My duty is to the discipline. Am stepping carefully as I lock down understanding. And my decisions will follow.

James Harris