If you want to peek inside how a model solves a math problem have a look at some data visualizations I made solving basic multiplication.[0]
I wanted to demonstrate capacity (how well it does a thing) instead of capability (which things it does, like drawing a pelican on a bicycle with SVG or solving a Rubik's Cube). To understand how LLMs solve math, look at the simplest case of multiplication. I deconstructed and classified the thinking token output. It is very important that model training yields thinking token output that structurally follows an observe, orient, decide, act (do the multiplication), and observe again loop.