One of those things I learned YEARS ago with my mathematical research is that valid criticism is extremely valuable. Which is because mathematics is a logical discipline, so any valid criticism can only help!
It may not help your ego but the math does not care about your feelings.
But eventually people who would criticize my work realized I was actively seeking out that criticism, so they would at times see errors and refuse to point them out for me. As that got worse and worse it ruined any point in discussing things with them. Why bother?
You see, along with useful critiques they often found it necessary to add gratuitous insults, which is unfortunate.
Incredibly I had people who would go over my math ideas carefully finding mistakes, pointing them out, and all I had to do was not accept as justified insults that came along with those findings.
So I had use of the expertise of some of the top math graduates of some of the top math programs in the world! It was an extraordinary situation.
Seemed like an ok deal to me, while it worked. Later though they wouldn't point out errors and mostly just insulted me, so that was the end of the usefulness.
After reading through this post a couple of times decided I should add more as I do NOT approve of their behavior, though I found I could still get useful information despite it. But I faced a situation where people made it clear they were insulting me to try and make me go away, but it was a public forum where I had as much right to post about math as any of them, though they claimed more rights. So? People can claim more rights but you don't have to give them any. I likened it to a group taking over a public park as supposedly their space and insulting or otherwise threatening other people who tried to use it.
And we've seen it so many other places now so much so that there is a word for it: cyberbullying
So math people weren't out of the ordinary, unfortunately, in exhibiting one of the dark sides of web behavior.
Not all were simply insulting though usually there was some kind of insult in there, where one of the most useful turns out to be a professor at Hamilton College. And I wrote a post, that talked more about him recently:
And I want to add here that he has done to my knowledge the only formal consideration by a mathematician of any part of what I call tautological spaces, for instance:
x+y+vz = 0 (mod x+y+vz)
is an example of the simplest tautological space.
And it so happens that was very important to me in considering them, as it's hard inventing your own thing. It helped my certainty tremendously when I read over Professor Decker's analysis, even if he dismissed the approach at the end. I note I myself no longer care about Fermat's Last Theorem, so that doesn't matter. It was fun thinking about it for a while and then it just wasn't. So it was just easier to drop it. But the validated techniques are a continuing part of my research efforts.
Sometimes chasing down certain paths you can find useful tools, which stay useful even when you move on.
So why would math people be insulting when criticizing the work of someone like me?
Not sure, but that was irrelevant. I didn't care about their opinions of me, but only needed their mathematical knowledge.
Some might wonder, but how do I know they weren't right?
Well, they were right quite a lot of the time, which is the point of this post.
And I valued valid criticism. But insulting someone like saying they're crazy, or calling them a crank or crackpot, or using racial slurs (which some did) are NOT appropriate behaviors and have nothing to do with whether a mathematical result is valid or not.
Critiquing my work was what they could give of value. So that's what I took.
Oh yeah, some people labor under the misconception that people care about their opinions. I don't.