There have been problematic aspects to my discoveries where my ability to easily prove that an accepted mathematical framework allowed one to appear to prove two different and conflicting things should have been picked up and widely discussed by others, leading to changes to address the problem. If that happened I missed it. And since it has been over a decade since my 2003 paper I can assume something went wrong.
My reaction was to figure out exactly what, as I had a functional need which is reminiscent of when I found I needed a definition of mathematical proof which could tell me when something was a proof or not.
There is something weird about finding something wrong on such a scale. It shook me to my core. So I began to search earnestly for a firm foundation again. Needed it badly. There were such strange times when I questioned everything for a bit. My skepticism went total.
Looking at behavior that didn't fit my ideas of a mathematician, I had to figure out what I thought one was. Also I needed to understand how the problem had not impacted science, as well as why I didn't seem to be able to fix it by going to scientists. And then I wondered what relation there was between math and science and whether mathematicians were scientists.
Struggling with accepted definitions I realized I needed a functional definition of science in order to figure it out, and along with it came a definition of scientific theory:
science (noun): the art of prediction using methodologies and tools to expand zones of certainty by discovery of a predictive framework.
scientific theory (noun): predictive framework found by using science.
Those are functional definitions that allow me to determine when science is being done.
For instance I was able to determine that many mathematicians are actually mathematical scholars, and do not behave as scientists. Their emphasis is on gathering knowledge, not advancing predictive frameworks related to numbers.
My analysis also indicated that the people who would help me would need to be mathematical scientists, people who use scientific methods to advance mathematical theory.
That allowed me to finally know the most important audience for this blog, and that audience is mathematical scientists.
Now I can easily explain the behavior of mathematicians, including those I consider to be mathematical scientists and those who are not.
Turns out it's not complicated. Modern mathematics as a discipline for the most part was established in the 1800's. At that time European ideas were dominant and included the now completely out-dated notion of the gentleman scholar, the idea that certain men of distinguished breeding could figure things out because they had superior intellects, and working for a living was a mean activity which they should not face.
Well the error I discovered came into the discipline right around its inception which isn't surprising to me. Some of these hero-worship decisions were fascinating like the decision to hand Euler's zeta function to Riemann. The notion that certain human beings are imbued with extra special superpowers is rampant across fan decisions in the math field of the 20th century. Those ideas were completely discredited in other areas and the cult of celebrity around them was mostly extinguished. But in modern mathematics these heroes of the discipline were deemed infallible, and mathematics was thought to just be a building on the foundations they laid.
But they laid an egg.
Thankfully a lot of important mathematics got done regardless, but most of that was outside of pure mathematics where the gentleman scholars held most sway. Today most of what they did is junk.
One of my favorite oxymorons from this bad phase: "logical paradoxes"
Didn't take me long to handle all of those.
The amount of social structure built around these bad ways of thinking is immense and is resistant to change.
But never fear, it will crumble into dust, eventually.
I can use scientific methods easily. Presumably I might use scientific methods against the social problem of mathematical scholars preferring to continue in error in mathematics. My one concern though was in doing so before I fully understood the problem. Science is the most powerful intellectual tool ever found by humanity.
Just because you can do something doesn't necessarily mean you should.
Science gives certainty, but more importantly, predictive certainty. It's not about just believing something, but about knowing what you can make happen. Like flipping a light switch. For so much of human history such a thing would have been extraordinary, but today it's very predictable. Science has a seductive power.
My analysis is complete and my conclusion is I should rely on natural social processes rather than force anything. That analysis indicates that force would do more harm than good.
Analysis indicates a timeframe for change which is acceptable to me. Humanity will be ok.
In the meantime, mathematical scientists who are the future of mathematics can do their own research regardless.
And have all the real fun.