Monday, January 05, 2009


JSH: Bizarre mystery, mathematicians non-response

As a researcher now with multiple results, I've been long fascinated by the resistance to the mathematical proofs I've discovered from members of the mathematical community, but now I feel like a big clue as to why they have denied fairly easy algebraic proofs in order to maintain a remarkable error is about "pure math".

There is almost a feel as if modern mathematicians in "pure math" areas no longer even care if it is correct, but are more focused on the style of argument.

Back in 2003, for instance, I was at my alma mater Vanderbilt University, explaining a slightly more complicated form of this result—for a while I was using cubics instead of quadratics—to Professor Ralph McKenzie there, on his blackboard.

And, nothing happened. He went home after I'd explained and later emailed me thanking me for the discussion and he offered some books on number theory I might read.

I was shocked. Overcome with emotion I emailed back a blistering reply. Increasingly angry, I ended up emailing the head of the math department, several other mathematicians in the department and a dean at Vanderbilt, as I could not believe it. Um, of course that didn't really work out. That was years ago.

I had stepped through the proof of this problem with a top mathematician who hadn't disagreed with it, and had agreed on the key points, and he just acted like it didn't really matter.

Understand then, from the major sources I have agreement with this result. It WAS published in a formally peer reviewed journal. To date no established mathematician to my knowledge has shown an error in the argument, and no one has even disagreed with the result outside of math newsgroups.

By all the rules, I shouldn't be elaborating on how bizarrely the mathematical community is acting.

The error should be known, making headlines, as a remarkable find by an amateur of an over one hundred year old error lurking at the heart of number theory.

So how do they do it? How do academics consistently ignore an easy proof of a remarkable problem at the very heart of their field?

Google: SWJPAM

That journal was one of the few cases where mathematicians did the right thing here, albeit briefly, and those editors caved, pulled my paper after publication, and then SHUT THE JOURNAL DOWN in one of the more dramatic instances in this story.

Posters on math newsgroups will rationalize endlessly on how crappy the journal process can be, how crappy the editors must have been, and how it must have just been a mistake that they published a paper from an admitted amateur.

I've kept piling on mathematical results as well with my latest being a general solution to binary quadratic Diophantine equations.

Confronted with it, I've seen posters early on agree with the result, and later now, disagree with it, or simply keep going as if I didn't say anything when I mention it.

With this latest result using the quadratic construction I wrote up a paper, and sent it to the Bulletin of the American Mathematical Society, and the chief editor replied telling me it was a "survey journal" not appropriate for the paper and to please not send them any more papers!

I've sent the paper on to the Annals of Mathematics, a publication of Princeton University with the cooperation of the Institute for Advanced Study. Which I guess is kind of a lark (even if they were going to publish it can take years for them to accept).

It just seemed like the right next place. They've acknowledged receipt.

I wonder if maybe I should just let the process play out? Even if a couple of years go by, is it really all that bad?

Those of you who are theoretical physicists or experimental physicists trying to use number theory tools I've proven are useless, what are your careers worth?

I mean, in the big scheme of things?

So what? A few years go by, and everything you have simply gets tossed as useless, why should any of us at the peak of the intellectual food chain care?

You are all expendable, as, hey, more of you will be born. There will be more eager students to become professors who will have a chance, you will not.

And the world will keep on turning.

YOU are expendable, right?

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