Sunday, April 02, 2006


JSH: Consistency check, Riemann Hypothesis

Being a real researcher with wide interests I can talk about my other mathematical research, which should foil posters who like it when I can focus on one thing, like notice at the page that rips on me, that guy only talks about my attempts at proving Fermat's Last Theorem, and lists for supposed refutations of my work, only links talking about older arguments.

That focus on one area is keeping it simple: convince the people with something simple as that's the easy way.

That's part of the consistency check: posters trying to convince you that my work is of no interest need to focus on just one piece, while I have multiple results.

So what does that have to do with the Riemann Hypothesis?

Well, supposedly mathematicians are enthralled by this hypothesis and the question of whether or not it is correct, but I'll give you evidence in this post that actually they aren't that interested in the answer, but instead wish to just hold on to it as being correct.

I can say that because one of my other research results is a find of a special prime counting function, where it's special in that I found a partial difference equation that is SPECIALLY CONSTRAINED so that it counts primes. I put those words in bold because that's very important, and I'll come back to it later.


Ok, so I found a way to count prime numbers with a specially constrained partial difference equation, so, like to count primes up to 100, it finds, on its own—without any sieve—that 2, 3, 5 and 7 are primes, and it spits out the answer 25.

So because it uses a partial difference equation it finds primes as it counts.

Nothing else in known mathematics does that, and that's not a debatable point—it's an ignored point.

But that ability makes the pure math version slow.

The pure math is slow, but you can get algorithms that DO use sieves to speed it up.

And in fact, I did so and made a fast Java program that for its size may the fastest possible, and the fastest currently known—for its size and complexity—in the world, despite being a Java program.

But posters don't talk about that, they compare it against the fastest known period.

That's another consistency check.

So what does this have to do with the Riemann Hypothesis?

Well, remember I emphasized that the partial difference equation is specially constrained, as you have to force it to behave and give a count of prime numbers, but if you don't constrain it, get this, it's slightly off.

It's just slightly different from the prime count.

It has a partial differential equation analog which is close to the partial difference equation, unconstrained.

Any of you getting it yet?

My find indicates the reason for why the prime distribution is close to continuous functions, but also tells why it's not exact: there's this special constraint to the partial difference equation that forces an exact count.

So, it indicates that the Riemann Hyothesis is probably false.

However, standard mainstream mathematical belief is that the Riemann Hypothesis is true.

Now going from the indication that I have that it's false to proof could take who knows what effort, but mathematicians will not make the effort.

In case you hadn't noticed, my results are overturning results.

Every one of my research finds kills a sacred cow of mathematicians.

So far they have been able to hide that fact, go on with what they have, and convince the world that they are serious about mathematics.

The dirty little secret though is that mathematicians don't care about the correct answers, but care about holding on to the answers they believed were right before I came along.

My research takes away ideal theory, standard interpretations of Galois Theory, and in so doing takes away much of a hundred years of mathematical ideas and papers, and that's just one side of it.

My research with prime numbers may take away the Riemann Hypothesis.

So the inner side of the motivation for mathematicians all over the world to avoid my research is that I take away too many cherished beliefs.

The dirty little secret is that acknowledging my research means that most of what many mathematicians have thought was true, goes away, and what is actually the truth is not what they want.

Consistency checks are a good thing.

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