Was surprised myself to find there is another way to figure out a modular inverse previously unknown. Which is the kind of discovery should be cheered! And represents a surprising advance since last known advance was with Euler's totient in 1763. Which I found by web research. Am NOT a mathematician. But am a mathematical discover and over a decade ago found something else surprising.
That find over a decade ago was of a coverage problem with ring of algebraic integers, which underpin modern number theory, as for instance algebraic numbers were defined as a ratio of algebraic integers. And is like if you only consider evens, and 2 and 4 and 8 are ok, but you get to 6 and claim that 2 and 6 do not share factors, you are wrong. They do not in evens but is not a proper ring.
I demonstrated with a paper. The journal which first bravely published the paper, later went through gyrations where chief editor tried to delete out of electronic publication. Then a bit later the journal keeled over and died, suspending publication.
Why might this thing be so huge? Because could bring question on ANY paper that has ring of algebraic integers declared as the ring or is dependent on that ring. And weirdly enough impacts Galois Theory where THAT is WAY hard to explain as out of my zone of expertise.
First off have demonstrated it more easily with quadratic. Where a key equation is:
g1(x) = f1(x)/k
Where that k messes so many things up. If k = 1 or -1, then you have number theory as was known. But if you choose to let be some other integers, then you know something is wrong.
The full factorization is 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.
The other substitution is: g2(x) = f2(x) + k-2
Multiply both sides by k, and substitute for the g's, which gives me the now symmetrical form:
k*P(x) = (f1(x) + k)(f2(x) + k)
The purpose is forcing symmetry. So the f's can be forced to be algebraic integers. But here is what is difficult for the emotions, they STILL can be so forced, when k is say, 2 or 3, and then you are forced that one of the g's cannot be when P(x) is irreducible.
That full post is here.
So yeah is easy to demonstrate the coverage problem. The k does divide off, which you can see with an easy polynomial solution, like let P(x) = x2 + 3x + 2, with k = 1, and g's equal to x.
So easy math but like what major mathematical argument falls?
Well the work of Andrew Wiles goes into the garbage bin for one that is dramatic enough I think.
And people get SO territorial. And the emotion is what's driving what I call the social problem. People think certain things can NOT be considered. As if human need or social status matter to the math. Reality is, this result cleans house across the top of the modern math field, and he's just a good example.
Near as I can tell, if just the simple thing in this post is acknowledged, he may have nothing in his career of note.
Yet now he's a celebrated number theorist. World famous. Encyclopedia articles in his praise. Prize money won.
If you were him, what would you do?
Valid math is the enemy of these people. Which is why suppression has to be so stark, and am noting with my latest discovery. They have to see real discoverers as enemies.
For a bit I called them pseudo-mathematicians. And say they engage in mathematical fiction.
They have I think willfully embraced error since I put the truth out there over a decade ago. That is SUCH a dramatic story too, with the dead math journal. The error though? Is how they made their careers.
They'd probably be unknown to you without it.
Have felt more sympathy for them in the past, but hey, they're teaching NEW people to go down wrong paths, with celebrated approaches! When by now may know very well, do not work!!!
You can stay emotional and support them if you wish, but their math does not actually work. You can learn from them if you wish, but using their techniques your math will not actually work.
And my discoveries are not going anywhere. Eventually the war of suppression will fail.
So dramatic--war of suppression. Primarily seems to just be--silent treatment. Relying on quiet to send the message that a major discovery is not really one. Is very effective too.
Truth does win eventually though. Why? Because it says the same. Same today, same tomorrow.
Their work is wrong today, is wrong tomorrow. And in time the truth just grinds down the techniques that resist it because is relentless. Never lets up.
And the enemies of mathematics who managed to get in charge, will be fully revealed for who and what they are.
So, if you wish to continue with them, then you accept their fate, whatever the world decides.
James Harris
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