What fields of mathematics rely heavily on pictures, graphs, images, diagrams, and all sorts of visual stuff?
No fields of mathematics “rely” on pictures, diagrams, etc, because it is impossible to be sure you drew the diagram correctly, or that there isn’t a special case that is not covered by your diagram. For example, there is a well-known “proof” (first published in 1892) that every triangle is isosceles, which depends on drawing an incorrect diagram – see http://www.jimloy.com/geometry/every.htm But of course mathematicians do like drawing diagrams, and pictures, even though they don’t rely on them to actually prove things. Apart from geometry, the most “visual” topics are probably topology and graph theory (which is about arbitrary sets of points joined by networks of lines, not the sort of “graphs of functions” that you see school algebra and calculus), but pictures and diagrams are used in almost every part of maths.
