Harristotelian Logic

The great thing about this latest math result of mine is that it's trivial to prove, involves modular arithmetic, so it's in a critical area to information security, is a simple, general result, so it may be one of those rare things in mathematics that should have been discovered in this case, oh, about 200 years ago.

And now I can test math society without any shadows of doubts.

So far, no surprises. The same mathematicians who ignored me before appear to be ignoring me now. I emailed Granville and Ribet DIRECTLY, though their spam filters may have blocked. I've emailed them off and on over the years (not always nicely).

Oh and I emailed Nicely. Oh and I think I emailed Lenstra. Each may have the spam filter excuse.

So what about those mythical grad students that supposedly are there to protect by seizing on a math result even if professors don't? Hiding I guess. I emailed Lagarias and also emailed two of his grad students. They still though all may claim spam filters blocked.

I have the reply from the Annals of Mathematics noting receipt. But don't know whether or not the Princeton staffer actually forwarded to a mathematician or not, but may have and paper could be in a pile somewhere waiting to be considered.

The result is on my math blog of course, and I'm pushing it in several places, but it's hard to say who is maybe reading it from where.

All in all within the muddle some may wonder if I do have answers, but I do. It is revealed that math society moves like a glacier in this situation. And I have responses on this newsgroup.

With this result it's like bas-relief watching replies as I see the same things I've seen for years, but now there is no doubt.

Contrast in the past when mathematicians have had breaking results which echo around the math community and there is a lot of noise with an expectation that the world will follow along. Silly world.

Here's the result again:

Given an mth residue where m is a natural number, q mod N, to be solved one can find k, where

k^m = q mod N, from

k = (a_1+a_2+...+a_m)^{-1} (f_1 +...+ f_m) mod N

where f_1*...*f_m = T, and T = a_1*...*a_m*q mod N

and the a's are free variables as long as they are non-zero and their sum is coprime to N.

It's trivially proven, and shows that integer factorization and residues are very closely related.

To the mathematics, integer factorization may just be about that result.

Simple results in mathematics that are general results tend to have a huge impact, and so are rare, and supposedly all found at this time.

If that result is really big its greatest impact may be known in the future, as if it leads to a new math of integer factorization, if it had been widely known 200 years ago then much of our recent Internet history could not have happened as it did.

Without RSA encryption the history of the Internet at this point would be entirely different.

So maybe powerful forces guaranteed this reality, eh?

I am the latest major discoverer. I have big shoes to fill. There was no way in this modern age I wouldn't be coming in without some seriously big guns. Quite simply I do have to stand on the shoulders of those who came before me, but I still have to top them.

And given the weight of human history that task gets harder and harder with each major discoverer.

So every single one of us has to be a major bad-ass.