Monday, July 13, 2015

When math surprises

Years ago I thought it simple enough if you actually found some important math--contact leading mathematicians who specialized in that area, notify them of it, and sit back and watch it get picked up, if it were valid. If it weren't then of course, no.

Not a mathematician myself, when that scenario didn't play out, I was at a loss. Check and re-check, see that it is correct and then got a bit angry, until I wondered to myself if I were antagonistic to math society itself. But of course that's not possible if my results are valid! Why not?

It's kind of weird, but by definition valid mathematics is important to the mathematical community. That is, the global mathematical community is actually focused on valid mathematical results! Obviously it doesn't willingly waste tons of time focused on false results, eh? Of course not.

But there can still be a challenge if you find people who may for whatever reason believe they are members of that community which may not be as simple an assessment as you might think where I have some ideas worth highlighting here and now.

For instance I was published in a troubling story, where recently I noted how much support has been required for that published paper to remain available from an official source despite the attempt to remove it after publication by editors of a math journal which soon after decided to simply roll over and die. I love that story. It's so wild.

Kind of story that just has to give me a chuckle. I readily admit.

For those who may think that math must be wrong, or way too complex, I've spent more time going through the argument, and actually got I think a slightly simpler angle recently, focusing on the factorization:

P(x) = (g1(x) + 1)(g2(x) + 2)

where P(x) is a quadratic with integer coefficients, g1(0) = g2(0) = 0, but g1(x) does not equal 0 for all x.

The conclusions reached from that expression validate my earlier paper, and I can comfortably say there really is no doubt, mathematically. But it's a surprising result! And for some who currently think they are mathematicians, may seem to be a troubling one.

Of course I have other results as well, where am gratified that my work with counting prime numbers seems to have a recent surge in popularity. I not only innovated slightly on ideas that go back to Legendre, I found a way to get a difference equation in a prime counting function that works by calling itself. What was my innovation? I focused on a function that counts composites by each prime excluding counts by smaller primes.

Weird how such a simple thing could have such profound implications! Leading to a far simpler prime counting function which uses a function I decided to call P(x,y), where using my approach I can also get the most succinct, fast prime number counter available. You can get faster with more involved algorithms, but it's a powerful and simple introduction to counting primes, with very simple ideas.

I love that thing.

But it's also surprising mathematics, maybe giving a route to answering some of the great problems in mathematics that some people who the world thinks are mathematicians do not want.

These are not issues that should concern me, however. My joy is in the discovery itself.

You see, I'm a member of the mathematical community--though I don't consider myself to be a mathematician--who greatly prizes valid mathematical results, which I assure you, is the dominant quality of the mathematical community through thousands of years of human history.

More so than any other field I think that mathematics has a problem with people who cannot measure up to its standards for truth.

But thankfully there will always be those like me, who would prefer to stand with the greats in one of the greatest intellectual disciplines of all time. What good is it, if not correct? Through thousands of years it is those who echo the truth who define the discipline. A mere hundred or so with some delusion or other pales in comparison.

Those who prize truth in mathematics are its community.

Our record speaks for itself.

James Harris

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