The world is definitely round. We have know this for 1000's of years. When you see a boat far in the distance it eventually disappears. If the earth was flat you would still see it. If you put two sticks in the ground that are spaced far enough apart, the shadows will be of different lengths. If the earth was flat they would not change.
I suppose it is possible that we may one day discover the earth is not really flat or round, but just a hologram illusion. It is something scientists are actually studying these days.