I'm no math genius. Mr Boxold always said math is about thinking up new ways of looking at things, even old problems. That's all I did. I mean really, how do you expect a 16 year old, junior in high school, on a little island in the middle of the Pacific Ocean, to figure out something this unusual?
It's not like this hasn't been found before. But I can't count how many times I've heard or read: "You can't factor the sum of two squares over the reals." It's repeated all over the internet. There has to be an old time proof or demonstration somewhere. I mean it's not a huge secret.
Being the one to finally publish a proof that $a^2=b^2$ can be factored over the reals is supposedly a huge honor. I mean it's not like I did anything my brother in Pre-Algebra couldn't do, OK never mind that, but you get the idea. It's real simple. I just found that by using your everyday factoring patterns you could factor $a^2=b^2$ with real numbers.