Discovery defines best. Now with over two decades of mathematical discovery upon which to consider will just talk some highlight things here.
Found myself reaching for modular in problem solving and found was underdeveloped which surprised me, as developed use of complex identities I call tautological spaces. And used for many things including finding a better way to generally reduce two variable Diophantine quadratic equations than previously known.
Beyond use of modular have also pioneered in other areas including a dramatic rework with prime counting. There found simple ideas lead to a vastly simplified prime counting function for a sieve form, and a more complex fully mathematized form that can find primes on its own. Which for the first time showed a difference equation is key. That difference equation leads to a partial differential equation, and solves a major math mystery--why any connection between continuous functions and discrete prime count?
Just a couple of highlights in discovery that has helped me to understand numbers better and given our world vastly more advanced mathematical tools. For instance tautological spaces can be used to have the math manipulate expressions for you! Which then is done perfectly and allows you to find things humans apparently otherwise find difficult to find, as have demonstrated.
Have innovated much with mathematics, and social disruption? Am sure! But not so much a concern for me.
Have introduced my own terminology, like modular symbology, which includes modular algebra. Where is beyond previous which from what I've seen was just modular arithmetic. Modular algebra is vastly more powerful.
So many results now, find hard to list them all out, and not really sensible to try? Those with a great enough interest can simply check the blog itself with the posts spanning the bulk of it.
Grew up Southern I like to say in Tift County near a little city called Tifton, GA, USA. Like the small town values, especially the emphasis on hard work and earning your way. I believe merit matters.
And am NOT a mathematician. I do have an undergraduate degree in physics from Vanderbilt University.
Questions drive me.
Answers can be fun, but really what keeps you up at night?
Those things, I think, are usually the questions.
Profile picture where oddly enough whether looks like am smiling slightly or frowning slightly? Is all about YOUR mood.