Friday, November 28, 2008


JSH: Let's look at the behavior

I am serious in that the question driving things now is, how could professional mathematicians ignore major mathematical proofs for years, and continue doing work in areas where those proofs removed the need for further research or invalidated their current research paths?

The naive or cynical seem to believe that my posting is in order to gain acceptance for my work, but supposedly a more direct route would be fighting for more publication or working to convince individual mathematicians, for instance, at the University of California at Berkeley which is only a few minutes away from me. I have actually visited that campus but when classes were not in session as I was with a woman taking tennis lessons from the Berkeley coach.

I am less interested in talking to individual mathematicians directly than solving this intriguing problem.

I have tried several theories out in various experiments. I want to talk about the results.

In one case a math professor at Morehouse College informed me quite confidently that no prime counting function of that type that I had emailed him existed. I noted that what I sent him clearly DID exist. He did not reply further.

A professor at a northern California university who was asked to look into my prime counting function by a colleague who was himself a sociology professor, said he'd check it, then abruptly went out of the country on a six month sabbatical, and on his return claimed to not remember being asked, but then would not consider it now.

The sabbatical seems to be a consistent theme. The chief editor Ioannis Argyros of the now defunct math journal SWJPAM, left the country after he pulled my paper on non-polynomial factorization after emails from some sci.math posters claimed it was in error.

Less dramatic opting out has been seen from a math grad student from Cornell University who emailed me out of the blue offering help in resolving arguments with my math research which he'd noticed on sci.math, and when I challenged him, what was in it for me, he offered that having a Cornell math grad and possibly that math department in my corner would help, so I sent him the non-polynomial factorization argument, and he proceeded to work through it, translating it into his own words, where he slowed down precipitously as he got closer to the end. After several months of this, he was sending me emails talking about long walks staring up at the sky in the early morning hours. I kid you not. A few more months later he opined that he didn't have the expertise to complete the argument claiming he needed to do further research on algebraic integers.

Consistently what I see when I present my research to mathematicians is this remarkable behavior. So maybe it wouldn't matter anyway if I, say, went to Berkeley and talked to the math people there?

Email allows me to contact mathematicians in every corner of the globe. I've seen this behavior on just about every continent.

I used to liken it to a snapping, as in, I'd say their minds snap. But is that accurate.

Cognitive dissonance is one clear possibility but why does it last so long? Shouldn't any of these people find the results nagging at them until they have to resolve the issue?

Why haven't any of the traditionally available things happened, like grad students anxious to further their careers jumping on results? Or even undergrads at the cutting edge out of curiosity pushing the older establishment to embrace new things that work better?

What is the mechanism for the dysfunction?

And it is global. I am a global player in terms of putting information out there. This month alone my math blog according to Google Analytics shows visits from 66 countries, though only 792 unique visitors.

But assuming that number is correct those were 792 chances in countries around the globe to have a person take up this research as an important cause.

Oh, of course, there are also those who dismiss any statistics and simply state that I am wrong or must be wrong, but my favorite thing to show is the non-rational rejection of Google search rankings.

Posters have proclaimed consistently and with confidence that Google search rankings do not matter, despite my noting that if they did not matter then Google wouldn't be known as a major search engine!!!

Yet they remain adamant and in considering this behavior maybe it's best to end with some enlightening searches where my research should show up in the top 10.

You need to use Google as the search engine for these:

deep variable
define mathematical proof
integer factorization algorithm
spherical packing problem
wrapper theorem
millenium problems
millenium prize mystery
solving quadratic Diophantine equations

I could go on, but those should give some sense of what I mean, if, in your region or country, they show up in the top 10 as they do here in California.

The mystery is a fascinating one: professionals in a major field aren't behaving as expected. Given proofs they "snap", run away, even take sabbaticals rather than face the truth. In the face of what would seemingly be overwhelming evidence to most they maintain denial. And even challenge conventional wisdom with the major search engine Google, maintaining that search rankings are meaningless.

Ok, problem space should be more defined.

Here we have a real world problem. Not some textbook nicety.

Even for the physicists it should be a massively curious problem, as it goes to the question of the value of their own research: is it actually valuable if no one believes it?

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