### Thursday, July 15, 2010

## JSH: Some math history

After Gauss died in the mid-1800's, other mathematicians attempted to take up his mantle in various areas of number theory, and a lot of issues I'm currently discussing trace back to that period so it's worth a quick bit of math history, and I like to start with Riemann.

Riemann decided to solve a bit of a mystery that had fascinated mathematicians including Gauss which was the apparent connection between the count of prime number aka the prime distribution and x/ln x, and Li(x) which Gauss contributed. Gauss hadn't figured it out and the so-called prime number theory was not yet considered proven. Though Chebyshev among others had done significant work, with Chebyshev doing some really great work around Euler's zeta function.

(See: http://en.wikipedia.org/wiki/Prime_number_theorem)

Riemann came in trying to figure out the great puzzle and did his own work with the zeta function, and he came up also with his tangential famous hypothesis, but I solved the question much later with my prime counting function by using a P(x,y) function which had a partial difference equation, as I could then casually walk it over to the calculus with a partial differential equation.

Along with the prime distribution itself, questions were raised about the twin primes distribution, and some complicated research emerged, which I've shown was about a false correlation as because the count of primes drops the count of twin primes drops as well, so those mathematicians thought they were intimately connected mathematically, while my prime residue axiom shows that it is incidental connection.

That simplification allows a prime gap equation and the consideration of arbitrary even prime gaps.

My research simplifies huge swaths of number theory. And simplification probably would have been heralded—back in the late 1800's. But today complexity pays the bills for a lot of math people.

So today there is an impasse. Like the mathematical researchers before me I kind of just pile on the results! Which makes it all the more fascinating watching the modern math community ignore them!

But it is enlightening for governments and various institutions.

Oh, the Riemann hypothesis is most likely shot down by my partial differential that follows from the multi-dimensional prime counting function which is a guess that is supported by that attempt to ignore it all by the modern math community as it has a position that it is probably true. If my research supported that position then it seems unlikely that math people would continue to brazenly ignore my P(x,y) prime counting function.

So that's a little historical perspective. It's not clear what will happen to end the impasse but historically these impasses usually end when the old guard dies off. As new students come into mathematics having heard of my ideas—that's why search results are so important—they won't be so invested in the old stuff.

Which is the time line. As kids move into college, they'll probably bring some knowledge of my research. The old guard will probably fight that as hard as they can but historical perspectives say they will eventually fail.

Until then, I get to argue on Usenet and do other things. It's kind of a pass for me, as I'm still too young to be a world figure.

One guess is that the world is taking care of me in this stage. Allowing me to mature, and age. I need to be maybe a decade older to handle this situation gracefully if there is any chance I will.

I may not. I'm just not the old kind of discoverer. I'm 21st century.

So I'm more than a little nutty. A lot more than a little wild. And not really happy with this freaking role anyway, as I try to figure out the best ways to work it.

Maybe it's better when I'm 60? So maybe a couple of decades? By then much of the old guard will have retired out of the math field. And I'll have had lots of fun and could possibly be that old wise geezer the world would probably prefer.

So we're aiming for 2 decades at this point. Or the year 2030.

Riemann decided to solve a bit of a mystery that had fascinated mathematicians including Gauss which was the apparent connection between the count of prime number aka the prime distribution and x/ln x, and Li(x) which Gauss contributed. Gauss hadn't figured it out and the so-called prime number theory was not yet considered proven. Though Chebyshev among others had done significant work, with Chebyshev doing some really great work around Euler's zeta function.

(See: http://en.wikipedia.org/wiki/Prime_number_theorem)

Riemann came in trying to figure out the great puzzle and did his own work with the zeta function, and he came up also with his tangential famous hypothesis, but I solved the question much later with my prime counting function by using a P(x,y) function which had a partial difference equation, as I could then casually walk it over to the calculus with a partial differential equation.

Along with the prime distribution itself, questions were raised about the twin primes distribution, and some complicated research emerged, which I've shown was about a false correlation as because the count of primes drops the count of twin primes drops as well, so those mathematicians thought they were intimately connected mathematically, while my prime residue axiom shows that it is incidental connection.

That simplification allows a prime gap equation and the consideration of arbitrary even prime gaps.

My research simplifies huge swaths of number theory. And simplification probably would have been heralded—back in the late 1800's. But today complexity pays the bills for a lot of math people.

So today there is an impasse. Like the mathematical researchers before me I kind of just pile on the results! Which makes it all the more fascinating watching the modern math community ignore them!

But it is enlightening for governments and various institutions.

Oh, the Riemann hypothesis is most likely shot down by my partial differential that follows from the multi-dimensional prime counting function which is a guess that is supported by that attempt to ignore it all by the modern math community as it has a position that it is probably true. If my research supported that position then it seems unlikely that math people would continue to brazenly ignore my P(x,y) prime counting function.

So that's a little historical perspective. It's not clear what will happen to end the impasse but historically these impasses usually end when the old guard dies off. As new students come into mathematics having heard of my ideas—that's why search results are so important—they won't be so invested in the old stuff.

Which is the time line. As kids move into college, they'll probably bring some knowledge of my research. The old guard will probably fight that as hard as they can but historical perspectives say they will eventually fail.

Until then, I get to argue on Usenet and do other things. It's kind of a pass for me, as I'm still too young to be a world figure.

One guess is that the world is taking care of me in this stage. Allowing me to mature, and age. I need to be maybe a decade older to handle this situation gracefully if there is any chance I will.

I may not. I'm just not the old kind of discoverer. I'm 21st century.

So I'm more than a little nutty. A lot more than a little wild. And not really happy with this freaking role anyway, as I try to figure out the best ways to work it.

Maybe it's better when I'm 60? So maybe a couple of decades? By then much of the old guard will have retired out of the math field. And I'll have had lots of fun and could possibly be that old wise geezer the world would probably prefer.

So we're aiming for 2 decades at this point. Or the year 2030.