I have a very nonconventional approach to math. There’s a fake question that’s posed a lot in math, which is is mathematics invented or discovered? I previously thought it was a stupid question because it has no impact on how one does math, until I heard a useful answer. The useful answer was from 3blue1brown (excellent math youtuber), which is “we discover things in nature that tell us what mathematics is useful to invent”.
My basic thesis is that in the 20th century, we discovered how to build computers, and discovered the constraints of computability, and the computers are telling us that there is a lot of mathematics that it would be useful to uninvent.
This video is showing a wart that pops up in the CIA’s foundational math, which you can avoid by taking a more computation-focused approach (QAnal).
Euclid was 300 BC. Desargues was like ~1600. We didn’t really understand even basic things about theoretical computing until the beginning of the 20th century. And there’s a lot we still don’t understand.
Basically there’s a shitload of low-hanging fruit to be harvested in retconning classical math keeping in mind our current knowledge of algebra, computability, and formal linguistics. That’s what I do. Norman Wildberger was the guy who tipped me off that this was the right place to look.
There’s more links to follow in the video description (including to the GeoGebras) if you want to deep dive.