Was wondering a bit about why I feel like I don't actually need much if any participation from established mathematicians with regard to my research, as it is math, and pondered: what would happen if I didn't have the web?
Well I'd type things up into some papers and try to figure out some people who understand math, who might appreciate it, who I could mail. Those would most likely be mathematicians.
Probably would maybe lobby a bit as well, as in, visit some college campus, or make friends with people on some college campuses as I worked to get to some level of trust and mutual accord where I could show them some of my research.
But with the web I don't need any of those things. And in fact, they'd just get in the way.
That's HUGE. In essence the scenario without the web involves gatekeepers.
With the web though I can just put my mathematical research online and people who are interested can find it, without needing all that extra.
The web can simply give desired information to the person who wants it, without as many middle-people.
The web can just cut-out the gatekeepers, which it has also done in other areas. So fascinating. So new.
For me it's a major issue which I study quite a bit, and I guess some might be worried about noise gaining traction, where without experts to clarify and critique someone might gain progress with bogus results. However in number theory it's hard to see how that is possible. You'd need people all over the world valuing highly results that don't actually work, and it turns out that's easier to have happen for people with status!
Why would anyone bother with mathematical research from some person without any esteemed social status if it didn't work? It pushes the limits of our understanding of human behavior.
There are areas of course where some people usually members of the public who desperately want something to be true will tend to choose bogus research, but generally there is some wish, which defies scientific reality. It's a need for fantasy. With concrete mathematics like number theory there is very little room for such fantasy.
But if mathematics works very well then it does make sense for it to be valued, regardless of the source, so people would simply need the opportunity to get it.
So the web seeking out and finding math research from a non-established source is I think more evidence in favor of that source than if from an established expert, or other potential gatekeepers, as the motivation is more basic.
People MIGHT seek out research, say, from a famous mathematician, even if they didn't understand it, but from some person without status? Makes sense only if it works and they need it.
Simple. Which means I don't need mathematicians. Worse, if I convinced mathematicians early that my approaches might have merit, I could have a group of people along with me by now--sharing credit.
So the web not only can remove a role for the gatekeepers, it can put you in a situation where using prior ones can feel like a waste of your time.
Will ponder this thing more, but I am sure it's new! My guess is lots of people labor under the belief that if they have some great math idea they should get mathematicians to acknowledge it, rather than seeing them as competitors.
Wonder how that will shift things over time?
Maybe I should give one example of the power of the web: claim from me is that I have the BEST way to reduce binary quadratic Diophantine equations EVER found by humanity?
Search: reduce binary quadratic Diophantine equations
What need I gatekeepers then?
Just did that search for myself on Google and came up only #5, which is lots less dramatic. I'd prefer #1 but I don't control it. Oh well.
Still don't need, or want, gatekeepers.
Of course I could edit to tone done the post, but the reality of web search is that it IS dynamic. Even if I came up #1 in my search that's not necessarily what someone else would see.
Worse, these type posts can actually, yup, drive down such search results! The web tends to react, and not in a good way.
So why do them?
Well I'm not as interested in having top search results as one might think. The competitive side of me loves them but the pragmatic side is less thrilled.
But the real point is: I do have the best way to reduce binary quadratic Diophantine equations ever found by humanity.
So it should be #1.
Which means to me, I just noticed search making what I think is a mistake, as it should return the best not at #5 but at #1. Looks like Google is trying to give some undeserved stature to established sources. And that's of interest.
If someone doubts me it's an objective area where they can compare my method against all others known.
Oh, I know! Maybe I should give one where currently I DO have #1 when I search. So here's another search. I have lots of them actually.
Search: count quadratic residue pairs
That should be more impressive. Again, there is a good reason for me to be at the top of the heap. It is the one that I think best makes sense too!