Spent a couple of posts recently explaining my supposed independence from the opinion of mathematicians, which I think raises the question of what delusion really drives me if I think I can talk about "some math" without mathematicians?
And I say the primary issue is utility: mathematics DOES something right?
It's like, can you appreciate electricity without physicists?
Mathematicians are the academic specialists in an area of great utility, like physicists are in a HUGE area which includes electricity which I just picked because it's so exciting. I could pick other things, like chemistry, which still requires physics, as well as chemists, but definitely less electric of a topic, and I needed that pun. And most people don't know who any modern mathematicians are anyway, and don't need them to use most of the mathematics they need.
Most people no more need to know any modern mathematicians to do lots of important research and work needing mathematics than they need to know modern physicists to use--electricity.
It's not complicated.
To me the MOST important thing is finding useful mathematics, while for most academic mathematicians usefulness is a strange topic. Many of them focus on something they call pure mathematics.
However, beyond the usefulness where you get that fun thing of helping bring value to the human species, for solutions to problems you can't even imagine, as consider what mathematics helps solve beyond the imaginations of say, Euclid, there is the sheer joy of learning.
So you suppose there will be fans of mathematics.
The issue of math fans is completely different from utility, just like sports fans are a separate category from the sport.
Those are the people who cheer a result.
Which puts it all together! For instance Euclid doesn't need to worry about people's opinions about his work any more. He's been dead for a few thousand years, so he's past worrying anyway. And it's not like he necessarily has a ton of fans with kids forced to learn in school about results he collected. Yet the utility of that mathematics is unaffected. And there ARE fans of Euclid, who are people who get excited about such things, but more importantly there are fans of the results he put in one place--for the good of humanity.
Now does it make sense?
So for instance with any particular result of mine, I'm most interested in its utility, where I get the most positive feedback, which comes from search results. It's the MOST important thing of all, as that is what means your efforts will endure. Nothing else does.
Next I'm curious about fans of the mathematics itself. Where there is a lot less indication to me that there are any. Which is interesting.
Next is the issue of fans of myself, and I tell myself I don't want any. So that one is easy. One wonders of course if that is a lie. Is it just something I want to believe?
Now shift to the modern academic world of mathematics, and I'm sure you could find mathematicians who clearly DO want fans. I'm not a mathematician and I tell myself I don't want fans, which is remarkably easy to achieve. (Not surprisingly, eh?)
But I would like fans of my mathematical research. I'm a fan of it, which is why I cheer about it so much! That's what fans do. You know, like with sports teams.
And I find myself adding more over the question of do I want fans of me, and my feeling is that can bring out the worst in you and is something you don't control. If people consider themselves fans of someone that's their business. No one elses. Almost wish I could have left that subject out entirely but think it's pertinent to the overall picture.
Maybe more important, I think for some people their own need for fans can skew their perception.
For me fans are great. I like fans. But I don't try to make fans. I prefer to be one myself.