Some tasks can be really difficult but really worth doing, even if you're not sure how it will all work out. Have learned to appreciate perspective and just working at things until done.
So yeah back in 2003 I wrote a paper which passed through anonymous peer review and was published, where luckily paper is still available hosted by EMIS as part of its archive. And that paper looks correct. No mistakes under established mathematical rules. But its conclusion contradicts with very well established number theory! So you have to use a separate argument to know the paper must have something wrong.
How is that possible?
Forget that, how can that NOT freak out mathematicians?
Since then I've noted, was demonstrating an esoteric and intriguing flaw with use of the ring of algebraic integers where that flaw is EASY to explain, but let's get back to that paper which has no errors under existing rules which can be shown to contradict with accepted number theory--how can that not just flabbergast mathematicians?
Some may know that there WERE hostiles to my paper, which is SUCH an ironic thing to me, as they attacked it for doing what it was supposed to do. As they pointed out that by a separate argument it had an incorrect conclusion. The paper itself appears flawless--unless you know conclusion must be wrong.
But um how is that possible? Can I ask that enough?
The very ability of a paper to do such a thing challenges so much. And such a paper actually does stand alone. It should not be possible.
The problem gives the potential of writing something that looks like it is correct, and checked against the established rules passes, which is nonetheless WRONG.
To me more than a decade since that paper can find a way to get a bit of dark humor in the situation, which is very serious.
Yes I critiqued the mathematical community--globally.
If YOU could, would you?
Did you pass? Or fail?
Why would I test mathematicians all over the planet in this way? Why wouldn't I?
It was a unique opportunity. Such an opportunity may never exist on this scale again in human history. Test mathematicians all over planet Earth with something THIS simple? Too cool.
Yes, have struggled with the weight of it though, at times. Mathematics is so important for our world. Wondered the fate of our world if I failed. Wondered if I could fail--if reality would let me. Such concerns seem distant now.
The test is perfect. Proper reaction is to understand that until fixed doubt can exist throughout the field of mathematics, though the problem does not exist for arguments that rely on fields. It only exists for number theory relying on the ring of algebraic integers.
And it IS checkable by any mathematician as well as uses elementary methods. So a person doesn't have to be a number theorist, and other mathematicians have no excuse. And yeah I'm NOT a mathematician I note again. Is important, you know? Helps my detachment.
Notice that the test remains until fixed as any math student can simply check the paper, and read through noting--no error with argument under existing rules. And then simply note that conclusion is false under existing number theory.
Until things are fixed of course and is simply a matter of historical record and example is part of the curriculum for future math students.
I have given the fix of course, which lead me to putting forward the object ring.
So yeah the conclusion is wrong in the ring of algebraic integers but IS correct in the object ring.
Oh, so how easy to explain? Imagine someone says they are only using evens and considering factors, so yeah 2, 4 and 8 are ok, and factor easily enough. But they trot out 6, and you say, NO! Because now with those rules 6 and 2 do not share factors because 3 is odd. And yeah evens are NOT a ring. And the ring of integers does NOT have this problem.
But the ring of algebraic integers DOES have an equivalent problem which I've shown multiple ways and even given a full explanation lately. as apparently I just LOVE explaining it. So the problem with the paper is the ring declaration with which it begins.
So why has the global mathematical community failed my simple test on the whole for so long?
I do have theories.
But not everyone really failed. My paper passed two anonymous reviewers and was published. Was chief editor who tried to pull later. And EMIS has kept it up. Am sure there are plenty of people out there who...I don't know. Maybe just figure there should be.
And it could still take awhile. What's good now is EXPLANATION. For those who have wondered you can now finally see the complete picture that took about 13 years to fully get outlined by me. So much work too! But learned so much has been worth it.
Now you can read not only the point of that paper that got published but see a full mathematical system explaining it all out in extreme detail. I think explanation is awesome. At least now people can know why.
Reading through seems so dramatic though. Yup. And we are in the 21st century with new ways.
To me am in a functional process where I see what works, and also it helps me to handle it all.
Figuring it all out is a challenge so worth the effort.
After all, our world's knowledge is what is important. And mathematics is important enough.