Discovery defines best. 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 where found a simple idea lead to a vastly simplified prime counting function for a sieve form, and a more complex fully mathematized form, which for the first time showed a partial difference equation was key. That partial difference equation leads to a partial differential equation, and solves a major math mystery--why connection between continuous functions and discrete prime count?
Just a couple of highlights in discovery that has helped me to understand better and given our world vastly more advanced mathematical tools, as 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 then with a process which I call abstract reductionism, where formalize methods for analytical analysis, removing a lot of the guesswork.
Much of that involves what I call modular symbology which includes modular algebra, which allows the mathematics to check an equation an infinite number of ways for me, so I don't need to bother. So many results now, find hard to list them all out, so just kind of highlight a few things.
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.