Machines are getting interesting today! They are thinking like us... Well, not quite that, I would say, but this is not the kind of machines I'm going to talk about here, they're more abstract like Turing's machine, sometimes more practical like a computer, or even a washing machine. Machines were created to execute dull and boring tasks like calculations with large numbers and matrices, and also, to be as precise as possible. A task that no human brain can sustain for more than half an hour without starting to complain. I'm going to focus on digital electronic machines and mathematical abstract machines.
The reason to study machines is to find their limitations, more than its advantages, because, we're limited too, and we're not machines, neither nature or the universe are machines. Machines follow simple rules to display complex behaviors. Mathematics is a simple way to describe these behaviors, anything more complex than math can describe is a waste of time, and understanding.