The mind-body problem has, as you said, been an ancient question. I personally don't know much about it as I am not a fan of Descartes for personal reasons. However, I believe artificial intelligence and computing offers us a whole new perspective on the problem that was not possible before.

I think an important aspect of the problem is what does it mean to be a mind? To be able to think? Okay, but that is still quite general. Think as in come up with ideas, or think as in compute? Think as in rationality, or think as in the ability to learn? I can argue a computer can do all of these things. I believe Searle's Chinese Room demonstrates a lot of these aspects (https://en.wikipedia.org/wiki/Chinese_room#Chinese_room_thought_experiment), but not all of them. Then questions like, does the computer understand what it is doing, or does the computer simply simulate that it understands what it is doing arise.

I think defining the body is a lot easier. I would do so as any container, capsule, or capacity. I cannot output an answer I fully support either, but I think computers offer a lot of food for thought to this question.