Comment by ndriscoll

And yet coming up with insightful diagrams, even or especially if they are particularly simple, can be a point of fame (c.f. Feynman diagrams). Diagrams often need to "lie" in some sense, so it can actually be quite difficult to find ways to convey the point you want without misleading in some other important way. e.g. I had a geometry professor that would label the x-axis R^n and the y-axis R^m for a bunch of different pictures, which on its face makes no sense, but it conveyed what it needed to.

People tried to prove the parallel postulate redundant for thousands of years because they lacked the right picture to show why it's necessary.