Considering the long haul is better

Knew I probably had a long journey ahead back I guess in 2003. Had been working at trying to prove Fermat's Last Theorem which was exasperating but fun--with TONS of errors. But had my approach to the packing of spheres from 1996, which hadn't made it past an editor, and in my mind seemed too simple like he had said.

Now I realize I'd used a spatial modular approach, and modular is the most powerful...how best to describe? Now of course I have lots more modular but still can be hard to grasp how changes entire field of mathematics.

Oh, so yeah, was chasing Fermat's Last Theorem with lots of frustration, but had also found my own way to count primes with a clever thing. I now know that thing is:

ΔS(x,p_j) = [x/p_j] - 1 - (j-1) - S(x/p_j, p_j-1)

That is the count of composites for a particular prime excluding composites that are products of lesser primes.

Which I copied from this post which I noticed was trending highly. Is so weird how something so short, and simply presented can change so much. That is the key to questions that Gauss, and Euler and so many others had about prime numbers. And we've had the answers now for over 16 years. But yeah I knew I had a long haul ahead, but not because of THAT result.

My heart sunk when I realized what I would call for a bit the coverage problem. When came across a way to present what looked like a perfect mathematical contradiction--within accepted rules. I could declare the ring as algebraic integers, use expressions valid in that ring, and valid ring operations, and nonetheless get to a conclusion not true in THAT ring.

Is kind of funny now. I just felt like the result was too big. Couldn't comprehend why was mine, and back then also hadn't yet resolved fully in my mind that the foundations of mathematics weren't maybe flawed. So I did try, and did my best to write a paper as close as I could to some standard format. And even shopped journals which I hadn't bothered to do with my spherical packing paper.

Even visited my alma mater Vanderbilt University to pitch the paper in person to a math professor who was an editor of some journal.

But it was later found a journal that would publish as have talked so much. And yeah was in conversation by email with editors at that journal for nine months before got word my paper would be published. My first correction to them was to stop them from giving me the title of Dr. Harris in correspondence. Emphasized was not a mathematician and I don't have a doctorate degree.

For me 2004 was not a year when felt well much of that year. Went from that elation and preparation for the world press when knew my paper would be published to the consternation and disappointment as drama played out instead. And then calm resignation as yeah, would be the long haul I feared.

Now appreciate how lucky I was. I DID get a publication. And then was left to myself to pursue mathematical truth. Eventually figuring out all the details which intrigued me so much. Back then I had inklings and intuition. Figured there had to be these other numbers, but how could I be sure?

Without help from the mathematical establishment, realized I needed a functional definition of mathematical proof. So I could know. And built so many others things. Until the activity was my new normal. And later would also accept being a global figure in my own right, where have puzzled there as well.

Now an authority in my own right on my math and I ponder what I owe my world or my species. I think about what I want for mathematics itself globally, and I wonder.

Is better to know. That I firmly believe. Have been so blessed I wonder why. But then again, so much I know now because have been--always with the questions.

And actually got some really cool answers thank God.


James Harris