To be a realist (and nobody likes a realist), you can't define intelligence, because it is an abstract idea, and every single person's perspective on the true meaning of something that cannot be defined as a physical object is bound to be at least a tiny bit different.
Answering the original question, I believe the Earth is round because I believe that I can provide supple evidence to the theory. I'm not going to quote Einstein, or use gravity, or any of that stuff. I'll simply say that I have seen the horizon. As a matter of fact, I've seen it at least a million times, as have all of you. And I ask you; why does the horizon exist? It exists for the simple reason that we cannot see the entire earth at once, and there exists a line at which you stop seeing land/water and start seeing sky. If the earth was flat, this line would not exist, as we would (assuming we can perceive light at the other "end" of the earth) see the entire earth to either side of us. Rather, we would see everything to a point where the buildings and wildlife impede our vision and prevent us from seeing any further, which we occasionally do, but not always, as anyone who has been in an open field can testify.
If you have any proof which may render this evidence to be invalid, please state it. I will be more than glad to give you a few other reasons.