Benefits of patience though

So yeah, wasn't really affected by lack of proper acknowledgement of my research by math community as reflected in discoveries because discovery was the point. Which is yeah a benefit of NOT depending on other people to do the right thing. Never got too distracted with that social.

Where time my first major discovery now in 1996, where used what I now realize was a modular approach to packing of spheres. Which made the problem SO easy have struggled with accepting solution! Which isn't terrible. Guess first talk that discovery on this blog here. And there am more hesitant I think but at least talk approach. Wow, that was back May 19, 2008. So that post was 12 years after the paper that amazingly was rejected by a math journal as TOO SIMPLE.

Next big thing which was HUGE was when finally got frustrated enough to invent or discover as debate with myself, tautological spaces. Where started with:

x+y+vz = 0 (mod x+y+vz)

Deliberately looking to introduce a new variable, which I put as 'v' for victory. Took a few weeks to figure out that would work, and that happened in December 1999. But was YEARS before had what thought was something, in 2002. (Yeah was still after that Fermat's thing which am NO LONGER considering important.) When promptly tasked myself with finding something else and figured out my prime counting function. My favorite thing to show from it? Is the sieve form:

P(x,n) = [x] - 1 - sum for j=1 to n of {P([x/p_j],j-1) - (j-1)}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

My way to count primes. Have had now for over 15 years and yeah, DID push that HARD, contacting a LOT of people in math community including leading researchers in area. That could have messed me up. Did for a bit. Got very upset. But then I realized there was something bigger.

And has been over 13 years since cleverly published a math paper which correctly gets to a conclusion under established math ideas which can also be shown to be incorrect by them, which is the coverage problem. Knew would have an uphill slog when began to see implications of THAT one, and yeah, when that math journal keeled over and died. Talked why publication matters recently so linking there.

At this point wasn't really any doubt something was wrong. Had THREE major results which had all been rejected in some way by mathematical community, where with last got publication acceptance, then weird. And it gave the full answer as to why with all: was dealing with people who lacked what I had, real achievement.

But I kept going. Eventually got this blog in 2005 and eventually started talking my results primarily here, as they continued to pile up. Until we get to now and my latest major result.

There was another way to do a modular inverse. And I found it. Last way goes back to Euler and 1763 with his totient theorem, found out researching recently.

So the human species has a new third primary way to calculate the modular inverse as of less than six months ago.

Yeah has been worth it. And better for humanity as well that I just kept going. My method for the modular inverse:

 r^-1 = (n-1)(r + 2my₀) - 2md mod N

Where y₀ is chosen as is m, with m not equal to r, and n and d are to be determined. They are found from:

2mdF₀ = [F₀(n-1) - 1](r + 2my₀) mod N

and

F₀ = r(r+2my₀) mod N

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So yeah, have the discoveries. Where in contrast if had let other objectives or emotion rule could STILL be stopped, focusing exclusively and bitter over the prime counting function or even more so over the coverage problem as so dramatically proven, where there is no doubt. Even got publication! Even if things got weird after.

To me shows value with making sure that the point is discovery. Would rather have more of the truth anyway.

Oh yeah, and there were some REALLY cool other things jumped over maybe really should at least mention. Like improved upon Gauss with reducing binary quadratic Diophantine equations. And decided that an idea about prime residues? Was an axiom decided to call prime residue axiom. And could go on.

The discoveries piled up enough have to think for a bit to keep up with them all. Ok yeah, don't actually try to do that any more, as would keep missing things. Is too much work and why do it?

Discovery was the point. And I kept discovering.

Have fun debates with myself at times about whether something is or is not a major discovery. When yeah, it probably is. But have enough can try to use a fine criteria. Is a fun thing for me, will admit.

Benefit of patience with all that other is more truths found, for me, and for humanity.

Who knows when will all be properly acknowledged. But as years go by am definitely more calm about it all. Focused less on math discovery these days. Still curious though, with that urge to discover new truths.


James Harris