I wrote two years ago about what it means to synthesize concepts, create new rules and systems instead of merely following instructions, and what it means to consider software mathematically (it’s not category theory. and I also wrote why category theory is misunderstood and how to stop doing that).
This is a walkthrough of mathematical thinking via creating a toy graph theory etc, to inspire you to do math.
Also, there’s abductive logic. It’s relevant to AI doomposts.
https://open.substack.com/pub/prapara/p/software-synthetic-math
If you’ve ever had fun tinkering with programming puzzles and games yet dislike math in educational settings, there might be a good reason, and you’re not alone. Despite that, you might’ve been doing mathematics without wielding the full power of its toolkit.