It makes sense for you to think so: a point in mathematics has no size, and its area is 0. You said there were three points A, B and C on the plane, and others asked: Where are they? Answer: In mathematics, the area of a point is 0, so it cannot be seen. So you can't communicate and write papers! The same is true of lines: mathematically, lines are long and short, but the width is 0. As you said, once you draw a' mathematical point and line', it is no longer defined. But for the convenience of research, you have to draw it, otherwise the parts can't be processed without drawings and the building can't be built!