Fantasy is one thing. Anyone can dream of having major discoveries, but a necessary reality if you actually manage to have major discoveries is pushing trends in mathematics, which is kind of intimidating. But at least it's something you can check! People are weird. They may not acknowledge things publicly, but major math discoveries demand attention. And then it's hard to act against them, or not to follow in the direction they lead.
So trends in mathematics are a reality check.
Necessarily it comes with the discoveries--if you have them. So forget the fantasy with math, just wait for it. If you found something then have no fear, human nature will do the rest, and your results will push trends. To me it is one of the more definitive reality tests from the social arena, and now I consider that years ago "pure math" in esoteric abstract areas relying heavily on Galois Theory with very little demonstration with actual numbers was all the rage.
Now looking at recent Fields Medal winners including finally a woman winner I could find none of it evident. Yeah!!!
Was happily surprised when I read about the research of the 4 winners.
For those who wonder what are current mathematical trends I suggest you look it over.
And I find it hard to believe there weren't women before who should have won. The youth of the modern mathematical field, which is less than two hundred years old, keeps showing. People can get fooled I think by mathematicians from thousands of years ago like Euclid and Archimedes, who didn't just do mathematics! The notion that people could specialize in just mathematics is what's new. And it's still unproven I think as a hypothesis. Match research of any "pure mathematician" against things I now definitively have, for instance if you wish to debate. And I'm not a mathematician. Yeah Hilbert is cool, but really, how cool? And was he just a mathematician? No, he did physics too. I believe the real world anchors a mathematical understanding and challenges it in ways nothing else does.
Scarier thing is if you move trends when you're wrong. I will admit now that one of my concerns over a decade ago was where my story might lead things, and mostly that dropped away as I was in the early web arguing on the dying medium Usenet where things were misleading.
I likened it to hanging out in swamps with some very odd and loud people with opinions that didn't matter, and still don't, but the web can elevate that kind of thing. Even now when I do searches on the web around me and my math I see mostly the loudmouth opinions of nobodies.
One of my favorite little tests years ago was when I asked a poster who just kept saying no to me, some really basic math questions, which he could not answer. And I mean it was some of the most basic math I could try without getting down to simple arithmetic.
But the reality is mathematical discoveries can't help but draw attention: who is the only person to have advanced Gauss in the modern era with a better way to reduce binary quadratic Diophantine equations?
Who is the one person who used old ideas for prime counting to getter a better simple prime counting function which leads to a partial differential equation?
Who is the only person to come up with an entire new mathematical discipline which has advanced modular algebra symbology?
Part of me wants to pull back from the truth here, but why? The answer to those questions is unfortunately definitive. I didn't make this truth. I've had to live it.
And those things and more draw attention from the planet which I noticed years ago. Comes with the territory. But the intimidation of it all takes a long time to ease. After all, who would wish to lead their world wrong? And how do you know that you do not?
People have this thing, where a person being highly successful at very rare so presumably difficult things gets you noticed.
Which means I have the biggest soapbox. My opinions on mathematics and on the academic world, including funding or tenure have already impacted the world and cannot help but impact the world as I get heard. Guaranteed.
I've never been paid for any math research. Real researchers will work whether they are paid or not. I do believe that people should be able to make a living though. However in certain areas I wonder why there is any public funding. That will not impact research that is real as the best people will do it anyway. Money means nothing to them. I should know.
I've had these positions for years.
And there is a purpose to my positions and I also like to explain so people don't think it's about being antagonistic as it's not. But the reality of mathematical discovery does not fit into convenient boxes about who figures things out, or how the results get received. The fight I've had has necessarily impacted how I look at things, and I have a duty to the discipline.
There are necessary changes. The goal is to maximize discovery.
Certain discoveries will get you attention, whether others like it or not, and then your opinions can have an impact. So you end up in a certain position, whether you feel like you should be there or not, and whether others like it or not. These kinds of positions have a steep learning curve, and my fear for a long time was that I might push people in the wrong direction. But now I feel better.