Another similar vantage point is that that the math can have no relation to what's actually happening. For example, the author might indicate in one step they i

Another similar vantage point is that that the math can have no relation to what's actually happening. For example, the author might indicate in one step they invert a matrix, but instead use some heavily regularized solver. It might be that only a few eigenmodes are invertible which changes the physics of the problem.