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Monday, November 24, 2014

So what results

My recent post covering an attempt at a research perspective on considering the value of web search results is useful to talk about another more troubling issue which I think is a reasonable concern when you hear some person claiming to have important results that aren't being properly accepted. After all, such a belief can simply be a hallmark of delusion, and I think it of interest to talk about that issue and in my case, how deep that delusion would have to go.

Turns out my first result where I ponder its importance where if it is correct there should be validation from established mathematical institutions is from 1996. I finally wrote about it on this blog May 2008:

somemath.blogspot.com/2008/05/spherical-packing-problem.html

And re-reading what I posted I can see the ambivalence but also I didn't want to talk about my own doubts. While here it is to note that I have a result from my mid-twenties which if correct would have been one of the greatest improbable finds in all of human history. So I naturally doubt it.

One of the biggest things that really bugs me about the concept of the result is that the problem is so old and Sir Isaac Newton tackled it. I find it just so difficult to imagine that he would have missed such a simple thing.

But I had a paper, sent it to a math journal, which rejected it as too simple, and I lost the paper. That is, I had it typed up or something on actual paper, while now everything is online as of course the web revolution happened, so the original paper as far as I'm concerned is lost. And I don't like talking about this thing. It irritates me. I can't find anything wrong with my approach or its logic, and no one else has ever told me anything wrong with it--too simple is not an actual mathematical error--but if that mathematical argument is correct its existence annoys me greatly. It should never have been left for me to solve.

But you know the best and worst thing about having such a result? It's the doubt.

I've had over 18 years now of doubt with that thing. Doubt can be such a treasure. In mathematics, doubt can push you to understand why you think you know something.

Rather than endlessly debate its correctness with myself or others, I gave myself a simple challenge: find something else.

No major discoverer at the highest levels in the area of mathematics to my knowledge has only a single major result.

It's like this tired refrain I'd taunt myself with through the years--find something else--no matter what it was always there until I just let it go.

But it's amazing to realize that 26 year old me, saved my future.

Moving on to something else was the best thing to do in that situation. Don't sit and argue with yourself or others, find something else. And there is always something else to do with your time and attention.

So I went from spherical packing to Fermat's Last Theorem, looking to find something else, where for a long time I've refused to discuss that most infamous, frustrating, and demeaning effort, as it is a lightning-rod for insults. And I think a lot of that pursuit was misguided. Chasing a famous problem can come from the wrong motivations I think. Great thing was I quit caring about that kind of stuff, and started just having fun.

But it's interesting to me that the stigma of that thing is so great. It stalks you, but that's not that big of a deal now.

For others pondering what they may see as indications of delusion, I think there is a natural concern. Especially if you worry about encouraging a person with some kind of mental disability or illness. But I think people naturally tend to focus on what they see as emphasized, with a continuing focus on that thing as somehow proof of something: like, why can't this person just let it go?

For me that's the fun part, I can. My spherical packing approach irritates me. Pursuit of Fermat's Last Theorem was humiliating, and turned into a continuing stain so great I hesitate to even mention the thing. But I stopped working on it over a decade ago. Was done in 2002.

So what about other results then?

It's odd to realize that I can idly throw away what I don't like as what I could consider my first major result. Dismiss my work on the next thing I spent so much time and effort on, and not even touch the areas of current potential controversy.

But I did develop mathematical analysis techniques from tackling Fermat's Last Theorem which I used with my next move on, which lead to my one and only mainstream publication in a formal math journal.

Oh yeah, so I DO have a published result. Turns out that is a lifetime thing which can't be taken away from you, as I checked! I'm listed as a published mathematical author. Where? I forget. It was over a decade ago that I checked. Actually called them up and chatted on the phone. It's funny the things that seem important until they don't. I think it was MathSciNet. Those who care about such things might be able to find it.

So do I hold on to any results?

No. My view is that I chase ideas, and chase certainty. And I pondered mathematical proof maybe because I had the spherical packing thing: How do we know what's true or not?

Correct mathematical results need no defense.

If every person believed just that one thing then you'd remove all of the heated argument out of mathematics.

People might still argue but it'd only be in teasing out the actual logical details and verifying them.

So I don't hold on to results, nor do I defend them. I present them. And thanks to the web that's enough.


James Harris
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