Humans as precious "Thinking Machines"

Man has so far been found to be the only "device" that could generate new thoughts and ideas in myriad ways. One might be able to train a computer using all sorts of algorithms and make it do what we expect it to do. But will it ever be able to do a Newton and formulate new formulae by just dropping an apple over it? Or will it ever find out the Buoyancy Principle discovered by Archimedes by putting it in a bathtub filled with water? We might design Robots to do really intelligent things like playing Chess, composing music and what not by just sticking to some basic application principles. But in my opinion, we humans have a sense of intuition, gut feeling or some inexplicable sense of logic that may or may not force us to do what we do. I think it is something that a machine can ever possess because intuition simply cannot be defined in concrete mathematical terms.