Year ago, but definitely after I was aware there was a coverage problem impacting number theory, was posting on Usenet math groups through Google Groups and on one a person identifying himself as a math grad student at a prestigious university offered to help. He said if I explained to him in detail via email, and he agreed that it would be a plus for me in getting things moving. I verified he was a student at the university.
And I confirmed the offer of help with him, and he emphasized and I agreed, as wasn't that big of a deal for me, and hey, maybe could move things. Back then might have already moved to a quadratic example following same path as my published paper, which the chief editor tried to delete out AFTER publication, before the math journal keeled over and died. So am explaining things carefully to this math grad student and giving him things to work through for himself.
Eventually his email replies took longer and longer, and one had things about wandering around at 4 am think it was staring up at the stars, until he'd finally emailed had stepped through entire argument, which of course is correct. And then was the begging off, where I knew what to expect after the weirdness about wandering around late at night.
That coverage error entered into the math field in the late 1800's and allows people claiming to be mathematicians to make arguments that LOOK correct because of the error. When recognized, it removes the research of top number theorists, where noted yesterday Andrew Wiles as one who loses his claims to fame. For those who need reference as to why error with math can be so potent or a refresher, here is an article on mathematical fallacies. The coverage error should be part of that article by now. The people profiting from it though am sure is why is such a slog. It has been worth hundreds of millions US to a community, which is annual.
Understand why that math grad student, so confident I guess that I was wrong, would crumble when realized I was right? He verified the truth himself. So had nothing to do with math. Had everything to do with humans as social creatures. Hence the social problem.
My research eventually focused also on: x2 - Dy2 = F
A fundamental equation which was known but clearly NOT researched enough, as my discovery of a third fundamental way to calculate the modular inverse flows from THAT equation. Looked back through my posts and looks like first posted a modular solution September 2012, with this post, which means over 5 years ago.
2x = r + Fr-1 mod N and 2my = r - Fr-1 mod N
So yeah, had almost five years of having noticed that modular inverse before figured out a way to solve for it using these equations back in May.
So a math grad student realizes there is a correct argument which undermines the underpinnings of modern number theory, and decides he'd rather stick with the system. By now he could be a full professor, maybe even married with kids, as is over a decade ago.
Did he make the right choice?
Of course, I say, no. Turning to deliberate error could give him social approval, and maybe a career, but is the wrong choice, in my opinion. And to some extent one might argue, his probably social assessment of the odds have not been shown to be wrong, so far.
That is my reference example. Shows you a case where I know of a mathematician who carefully stepped through the argument showing a coverage problem, doing work himself, went through apparent emotional distress, then concluded was better off accepting error than help me fight error in the system.
Note also, he helped then condemn later students to being trained in error, with less opportunity to know was being done to them.
James Harris
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