And GPT4 indeed does just fine with things like 32 * 64 in multiple different ways that humans can also easily memorise the rules for. When I asked it to calculate it step by step, and use easily memorisable shortcuts, it first suggested the "doubling and halving method (though it stupidly started by doubling 32 and halving 64...), and got it right.
I then told it I know the powers of two up to 2^24 by heart, and asked if that changed things.
It then reasonably pointed out this means I know 2^5=32 and 2^6 = 64, and 2^5+2^6=2^(5+6) = 2^11 = 2048 and got the rules right (that was exactly what I intended when I pointed out I remember the powers of two).
So it's not all that awful at these things. It does badly when you effectively try to get it to do maths by blind recall and without nudging it to work step by step, sure.
Where it then falls down tends to be when you ask it to do calculations which involves repetitively applying the same rules many times over, where it will tend to start out well, but occasionally make stupid little mistakes.
If anything the type of mistakes it makes are scarily close to the same kind of lapses in focus humans get when doing the same, where we just get sloppy and fail to add two numbers < 10 correctly for no good reason in the middle of doing it correctly many times, and fail to go back and verify each step.
Where some see LLMs struggling with math, I see LLMs trying to do math in a way that is disturbingly close to how a human school child would, and making the same types of mistakes.
