we do know plenty of cases where a particular system in the brain doesn't share the capabilities other systems do - we might intuitively solve differential equations in order to predict a baseball's flight path, but that doesn't mean we can natively solve abstract equations in our head.

Good point, but I'd go even further: we are not even solving differential equations in predicting a baseball's flight path, but rather, pattern-matching it to typical falling objects. Though I frequently criticize RichardKennaway's points about control systems, he is right that you actually need to know very little about the ball's dynamics in order to catch it. You just need to maintain a few constant angles with the ball, which is how humans actually do it.

To the extent that "you" are solving a differential equation, the solution is represented in the motions of your body, not in any inference by your brain.