Our world shifted a lot very rapidly and my story is very much a web story, where computers around the globe endlessly help me, and without them, well you wouldn't be reading these words.
And it's not just about computers and the web allowing me to communicate my mathematical findings, but about them making checking trivial.
So for instance I've decided to focus lately on a better way to reduce binary quadratic Diophantine equations, which doesn't even care about the discriminant.
Well, turns out you can just plug in my way into math software--which I've never done--and it will just check it for you, and for instance solve for a variable I call 's'.
Here's me doing the calculation with a simple example. You can see how it could be difficult with the general case.
If someone plugs my method for reducing into the appropriate math software it gives s, as a function of x and y, which I know because years ago, back in 2008 I think, some people did it.
I've posted about my years on Usenet, where most was on the sci.math newsgroup which some people seem to think is significant from search results I've seen. For me it was a way to get things checked, and I've concluded that math people there thought I looked stupid because of some of the things I was trying. And for them, showing errors in what I was doing was proving my stupidity! So they'd fall all over themselves critiquing my ideas, which often I'd simply brainstorm. So I could generate the ideas meaning credit was always mine alone, while they'd simply critique! Often insultingly, which I don't condone, but it's not like I could control it either. That was their choice. To me it would be easy enough to point out an error without also having to insult a person.
Because it is an example where computers make checking easy, it means there's little effort in some math student verifying. Weirdly enough, if you know the history in this area I can take it up a notch and note that I did in fact improve on Gauss. The computer does ALL the real work. All that student needs to do is know how to use it, and just type in the equations and watch it whirl.
And Gauss is a hero of mine, so that's a big deal to me. And I do not say it lightly.
Actually I'm sure I overrated his importance to the modern math field as for a while I thought that would be it! No way something so huge could be ignored. But mathematicians today are more focused on Riemann I think who came after Gauss.
With such a claim it is a relief for me that any person with a computer and math software who knows how to use it can verify. Computers back me up.
While I wouldn't mind established mathematicians validating my research, this way is more fun. And is less work for me! Besides we're in a fascinating new situation with the arrival of the web, and wouldn't it have been so much more boring without a nice dramatic story like mine?
Why does history seem to require such?
Reality is I'd prefer computers to validate me than mathematicians. Wouldn't you?
Human beings can just be wrong.
And computers have made this story possible.
Puzzling these things out helps me I think and maybe others.
Computers let me reach the world, validate my research, and are tireless in that defense.
I'd rather be validated by computers.