I agree the model is predicting language and not actually running the math. That is a point I try to stress too. It is not thinking through a problem, it is predicting what text would look like if someone were working it out.

But the training does not just reinforce plausible continuations, it biases toward text that matches correct answers. So in that sense they are training it not just to predict any likely text, but to predict text that is more likely to contain the right answer to a math or coding problem.

To me that does not look so different from other ML models. They all work by turning a problem into something a computer can handle statistically, and they all face the same trade offs. Prediction errors are inevitable, and you still have to decide whether to tune for recall, which gives hallucinations, or precision, which gives refusals.