Monday, October 16, 2017

Notice to governments

Have come across a problem in mathematics in an important prestigious field, which is number theory. And was able to demonstrate with publication in a formally peer reviewed mathematical journal. The problem is severe enough that the response from the mathematical community was to avoid, including that the chief editor tried to delete the paper out of the electronic publication.

What I did was show that you can present a mathematical argument, correct under ALL mathematical rules established, which gives an incorrect conclusion.

That was back in 2004. When the mathematical community did not act with the appropriate response realized had a bigger problem and endeavored since then to verify my own argument, and was able to so do with secondary means. I found another way to prove the same thing.

Relevance to national governments: mathematicians working for you who are number theorists may not be actually qualified for their positions. This problem can allow them to have invalid research which appears correct by established measures.

You can check. These people are NOT actually effective, of course. But with a problem that has been in the field since the late 1800's they have built a support structure around themselves.

They should not hold security clearances. They should not be relied upon for any mathematical research your government needs.

It is your job as governments to determine when these things are true. Good luck.

James Harris

When apparent success is easy

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) = (g1(x) + 1)(g2(x) + 2)

where P(x) is a primitive quadratic with integer coefficients, g1(0) = g2(0) = 0, but g1(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

Sunday, October 15, 2017

Sum two squares and 5

Used my BQD Iterator to highlight the basic result that EVERY power of 10 can be written as sum of two squares, where noticed the squares were even, after the first one where had to use the trivial result that 1 is a square. Well got to wondering--what if divide those powers of 2 off? Here is the result:

42 + 32 = 52

132 + 92 = 2(53)

72 + 242 = 54

792 + 32 = 2(55)

442 + 1172 = 56

3072 + 2492 = 2(57)

Here's the full original list for two squares to powers of 10:

12 + 32 = 10

82 + 62 = 102

262 + 182 = 103

282 + 962 = 104

3162 + 122 = 105

3522 + 9362 = 106

24562 + 19922 = 107