Sometime this month, as don't remember exact day, will be 15 years since found my prime counting function. And thought along with that special event would just list some of my mathematical discoveries. Will not link to anything as everything is on blog somewhere.

So first, yeah found my own prime counting function which fastest for its size in its compact sieve form, but more importantly leads to a difference equation when fully mathematized, which has to be constrained to get it to count primes. But the difference equations leads to a partial differential equation. That is so cool. And celebrate 15 years this month since first found.

Moving on.

Developed my own mathematical discipline using what I call tautological spaces, as rely on complex identities. Entire field call modular symbology, and it realizes the first true modular algebra. And is my best example of my use of abstract reductionism. Oh, before called modular algebra symbology, but like it shorter! So will switch to that now. There is so much related it dominates this blog.

Oh yeah, so in that area found my own way to solve for the modular inverse! That is finally for humanity a third way, with other two there is Euclid's name on one and Euler's name on the other. Is now barely over three months since found that so still absorbing the thrill.

And found an axiom related to primes, decided to call prime residue axiom.

Biggest thing though, is found my own numbers. That one takes SO much explaining will leave it like that, but big part was finding my own ring which call the object ring.

And that I think covers enough of the highlights to satisfy my mood.

James Harris