A 2007 book tells a very interesting story.
It is called The Archimedes Codex and it recounts how a lost work by that great Greek mathematician recently came to light. The authors are Reviel Netz, a mathematical historian, and William Noel, the curator of the museum that holds it. My purpose here is not to repeat what is said in their book, but rather to pick up on a point Netz makes in the course of his contribution to it. Modern mathematics, he says, is a science of equations; ancient science was a science of diagrams. He continues: 'In modern science, diagrams serve as a kind of illustration; they are there to make the experience of learning science somewhat less traumatic for the student'. But they are not part of the logic of the argument itself. In modern science it is considered crucial to make sure that no information depends on the diagram to make sure the logic of the proof works in its full, most general form, we must rely on the language alone and never on the diagram. In my undergraduate days, we surely took this moral to heart. We sang with great gusto, to the tune Men of Harlech, but possibly also somewhat tongue-in-cheek, a ditty called The Pure Mathematicians Anthem.